## Friday, 20 January 2017

### Newtonianly speaking, Can Earth Still Orbit Sun After 4.5 Billion Years?

George F.R. Ellis was on FB quoted as saying or writing some time in the past (I'll try to contact him to see if the quote is genuine):

I can construct you a spherically symmetrical universe with Earth at its center*, and you cannot disprove it based on observations. You can only exclude it on philosophical grounds...we are using philosophical criteria in choosing our models. A lot of csmology tries to hide that.

On a more humdrum level ... I was discussing whether the scientists who are constructing an Earth orbitting around the Sun by the interplay of two forces, gravitation as centripetal one and tangential inertia as centrifugal one can have missed factors which would make this possible.

It was on theologyweb, and when I tried to just browse the previous discussion this morning, I saw this:

500 - Internal Server Error

So, I'll have to discuss this a bit on my own, before my readers ...

Mean orbital velocity (km/s) 29.78 **
Max. orbital velocity (km/s) 30.29
Min. orbital velocity (km/s) 29.29

Mass (1024 kg) 5.9723**

I had in that debate been told that the "dust" which hits Earth on a "daily basis" is 200 tons***.

I was asking - before this blackout 500 error - whether meteors dissolving in the atmosphere or hitting ground during the annual meteor showers was a myth, or if not included or excluded from the 200 tons of dust.

The other guy had been counting on my backing down very quickly on seeing the results he had allowed me to calculate on his terms, and was perhaps not ready for my challenging the terms with things that imply one should take a few more things into account too.

I didn't do quite what he had counted on. Your guess, if that has anything to do with the 500 error or not.

Also, the 200 tons, I am here presuming that is what is hitting Earth. In the orbit of Earth around Sun (or supposed such) it is also a question of how much is hitting the Moon. Since Moon too is involved in Earth's orbit around Earth.

Earth has a Volumetric mean radius of (km) 6371.008.

Moon° has a Volumetric mean radius of (km) 1737.4

The volumetric mean radii are given as compared:

Volumetric mean radius (km) (Moon) 1737.4 (Earth) 6371.0 (Moon/Earth ratio) 0.2727

I'll now take the Moon/Earth ratio, square it, since Earth and Moon are both hovering by space (supposedly) and hitting space from an angle describing a circle which has a surface proportional to the tens that hit it.

0.2727*0.2727 = 0.07436529.

So, Moon has an added 0,07436529 of the surface. 1 + 0.07436529 = 1.07436529

This means the tons are more like 214 873.058 than like 200 000 kg.

On the other hand, they should be added to a larger mass, Earth and Moon = Mass° (1024 kg) 0.07346+5.9724=6.04586 (1024 kg).

I am not here sure whether the 200 tons include or exclude what confronts the ring of the 8.5 km atmospheric height around the 6371.008 km around midpoint, and due to gravitation, a meteor or even dustparticle which comes outside the 8.5 km limit will perhaps also be sucked in. On the other hand, sometimes Moon is before or after Earth in orbit, and so is getting or leaving no extra, but only one gets the dust? If so, this might even out.

Should this be added to the 200 tons per day, or should it be considered as already included in them? I'll go with the latter one. If it is the former, you ask someone else, and add this to the problem.

Also, I think someone else might have to ask whether the 200 tons dust per day are also including or more probably excluding the Perseid and Aquariid meteor showers in August.

I'll just calculate for the dust.

Now, I made a mistake in relation to translating the 1024 kg to correct number of zeros.

1024
=
1,
000 000 (another six = 12 zeros)
000 000 (18 zeros)
000 000 (24 zeros)

=

1 000 000 000 000 000 000 000 000

Let's get going.

6.045 86 *
1 000 000 000 000 000 000 000 000

= 6 045 860,000,000,000,000,000,000 kg present mass

214 873.058 * 365.2425 * 4 500 000 000 (years in which Earth has supposedly been in orbit, projected into future):

353 163 477 989 542 500 kg added mass.

Added to what? To 6 045 860 000 000 000 000 000 000 kg of Earth and Moon.

= 6 045 860 353 163 477 989 542 500 kg new mass

Ratio : 1.000,000,058,414,101,2

This well also be the ratio of changing gravitation from Sun, since gravitation is directly proportional on mass.

Now, the kgm/s of Earth+Moon is for present Mass:

6 045 860 000 000 000 000 000 000 kg * 29 785 m/s = 180 075 940 100 000 000 000 000 000 000 kgm/s

Each day what is deducted is same speed times the 214 873.058 kg.

214 873.058*29785 = 6 399 994 032.53
6 399 994 032.53 * 365,2425 * 4 500 000 000 = 10 518 974 191 918 523 362 500 kgm/s

180 075 940 100 000 000 000 000 000 000 - 10 518 974 191 918 523 362 500 kgm/s = 180 075 929 581 025 808 081 476 637 500 kgm/s

Ratio present to new : 0.9999999415858988

So, in 4.5 billion years, kgm/s lowers to 0.999,999,941,585,898,8 of original, and gravitational pull from Sun rises to 1.000,000,058,414,101,2 of original.

Shall we just try to consider them as at present "in balance" 1:1 and check the imbalance?

1:1 - > 1.0000001168282092244:1 = for the gravitational pull against tangential momentum of Earth and Moon.

Or 10 000 001 168 282 092 244:10 000 000 000 000 000 000.

Or 10 000 001:10 000 000.

I am now presuming speed as such is irrelevant, it is just momentum vs gravitation.

But what if speed does count?

New momentum : 180 075 929 581 025 808 081 476 637 500 kgm/s
New mass : 6 045 860 353 163 477 989 542 500 kg
Momentum/mass = m/s (kgm/kgs=kgm/kgs=m/s)

New speed : 29 784.996,520,272,193,712 m/s.

The average velocity change is therefore about 3 mm/s lower on near 30 km/s.

But let's suppose that the velocity and the gravitation from Sun are a 1:1 balance, and see where the balance goes, if it is speed instead of momentum which needs to balance gravitation?

29 784.996,520,272,193,712 m/s / 29785 m/s = 0.999,999,883,171,804,389

So balance gravitation:speed shifts from 1:1 to
1.000,000,058,414,101,2:0.999,999,883,171,804,389 = 1.000,000,175,242,317,284,244:1

Or 1 000 000 175 242 317 284 244:1 000 000 000 000 000 000 000

Or 10 000 002:10 000 000.

So, the shifting balance, probably discounting all meteor showers, would be 1:1 to 10 000 001:10 000 000 in gravitation:momentum or, in gravitation:speed, it would shift to 10 000 002:10 000 000.

Now, while this is certainly insignificant, I don't know enough physics to determine whether a balance of 10 000 001:10 000 000 in gravitation:momentum or a balance of 10 000 002:10 000 000 in gravitation:speed can work.

I don't know how many orbits such an imbalance can take before toppling over. Ten million, perhaps? Or perhaps a bit more than five million, if we take second imbalance?

Remember, I have now only calculated from present rates forward, 4.5 billion years into the future. We are supposed to have already 4.5 billion years behind us. With an initial imbalance that size, we would not have lasted 4.5 billion years. With an initial balance, we would already have an imbalance about that size.

So, we could perhaps predict that Earth has perhaps only ten million years to go?

But ten million years ago, was 4.49 billion years from start. With nearly same imbalance. So, we should be gone any moment. 15 million years ago was 4.485 billion years from start. With nearly same imbalance. So we should already be gone.

Or, the Newtonian and Evolutionistic (large sense) view of Earth's rotation around the Sun might NOT be correct, Earth might be in centre of Universe, and Sun be ceasing to rotate anytime God wants, but not one nanosecond before that. That is what I think makes sense.

But hey guys, why take my word for it? One debater (not on that forum, but on youtube) told me I should remove my possibilities of procreation, and another I should take my meds, but was lobotomised by a rusty saw instead of proper equipment. So, do the math yourself. And, if in a sane moment I see your comment as correcting mine, I'll be happy to let it stay there.

Or I might try to see any faults there could be with your maths too ...

Or, more importantly, the suppositions behind them.

Hans Georg Lundahl
Nanterre UL
Abbot St Euthymius°°
20.I.2017

Credits for all actual calculations (multiplications, divisions, additions, subtractions) to http://web2.0calc.fr/

Credits to oxmixmudd on theologyweb for giving me a setup of initial calculations, somewhat differing from these. Obviously, I "suffer from" severe Dunning Kruger for thinking the parameters I took into account as being finally more relevant than his, but nevertheless, he gave me the model I am imagining to have corrected for relevance to the supposed physical reality of Heliocentrism.

* No doubt American spelling for centre.

** http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html

*** I presume he meant metric ones, 1000 kg each?

° http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

°° Last saint of today : In Palaestina natalis sancti Euthymii Abbatis, qui zelo catholicae disciplinae et virtute miraculorum, tempore Marciani Imperatoris, in Ecclesia floruit.

Update:

 www.theologyweb.com Website is offline No cached version of this page is available. Error 521 Ray ID: 3243a2b887f33608 • 2017-01-20 15:42:19 UTC Web server is down You Browser Working London CloudFlare Working www.theologyweb.com Host Error What happened? The web server is not returning a connection. As a result, the web page is not displaying. What can I do? If you are a visitor of this website: Please try again in a few minutes. If you are the owner of this website: Contact your hosting provider letting them know your web server is not responding. Additional troubleshooting information.

Otherwise I was going to try to bring this home to oxmixmudd, well, must wait ...

Update on theologyweb :

 vBulletin Message Sorry, the board is unavailable at the moment. We were doing a needed OS upgrade and were up for a bit, but we've gone down again. Too many things were having issues with upgrading to php7 (which was needed as Ubuntu 16.04 LTS doesn't play with php5). I am just downloading a db backup (10GB) and and then will be restoring to the previous version and then restoring the database. We'll leave the OS update to happen when we update vBulletin (on the roadmap for later this year) We will be back soon... In Christ Raphael

1. I thought I had spotted a problem in the maths, since momentum was presented as "present to new", as if present/new.

Fortunately 0.9999999415858988 was actually new/present.

And "present to new" was thought as "from present to new momentum is like 1 to" 0.9999999415858988.

2. Now that the site is up, the thread seems to involve some "deletions" since my last answer.

3. I can't see how the argument is only on philisophical grounds, being that you can't prove one (heliocentric) over the other (geocentric).
The reason I can't see it, is because a massive planetary body covered with water and gas, not showing any difference or variation of surface or internal environment, whether is is motionless, or whirling and spinning, is hard to understand.

1. I am most certainly not pretending to have proven heliocentric.

On the contrary, as you know I am geocentric.

I am on the other hand taken out the consequences of Heliocentric+Newtonian only mechanism in what I hope to be a reductio in absurdum for it, especially if coupled with the clearly anti-Christian 4.5 billion years.

4. Two things.

Let's start with the idea that we can't disprove a geocentric universe. There are degrees of proof and disproof, but let's start with the idea that we have to take some philosophical arguments. It is true that we need to take at least one assumption to draw any observation-based conclusions about the universe at all. This is that the fundamental laws of the universe, whatever they are, are consistent through all of space and time. We assume this because without it, nothing can be derived from observation at all.

That's the only non-empirical (so, essentially, philosophical) premise we need. Everything else about the "heliocentric"* model can in fact be derived from observation. For example, we can easily observe the effects of acceleration on objects that have mass. In order to fully explain the apparent paths of the outer planets of our solar system in a geocentric model, they'd have to be undergoing huge and massively-variable accelerations, the effects of which would be easy to observe. So we have a hypothesis (the Earth is the centre of the solar system and possibly the universe) which is testable (we look for the accelerations which would necessarily follow in the outer planets). We don't see these acceleration-effects, ergo they cannot be accelerating in this way, ergo the Earth is not the centre of the solar system. QED.

(* the current understanding is not actually that the universe is heliocentric. It's believed to be acentric. The solar system, however, is heliocentric in the current scientific model. The difference is significant: this model doesn't have the stars circling the sun. Rather, in it the sun circles the centre of the galaxy, and the galaxy is itself moving with respect to other galaxies, and so on and so forth. No single centre for the entire universe is believed to exist, but smaller-scale ones are.)

1. "Heliocentric" was used for commodity.

I am well aware that the universe is, if supposed to be infinite, acentric and if supposed to be finite, agnostocentric.

"the fundamental laws of the universe, whatever they are, are consistent through all of space and time. We assume this because without it, nothing can be derived from observation at all."

Before you go on to acentric or for solar system heliocentric, by way of the rest of your proofs, you also need to state as a premiss that the physical laws are the most fundamental ones, like no spiritual ones being more fundamental.

Which obviously I do not grant.

God ruling everything in the universe is a more basic law throughout the universe than anything else.

Mind ruling matter in diverse degrees is the second most fundamental one.

So, if we have minds which can move bodies the sizes of sun or perhaps even larger, the bodies are not required to have all details of their movements explained by accelerations or gravities.

Your model is as predictive as predicting a football match by ignoring the players : obviously without players, the ball is staying on the ground due to the masses of ball and Earth multiplied by each other and gravitational constant and divided by the ball's distance from centre of Earth, that distance squared.

Now, I admit that Geocentrism will not function without angelic movers.

BUT, the thing is, I was discussing in above essay whether your current understanding of Heliocentrism will so work.

And concluded that the balance between gravitation and momentum which is supposed to hold the Earth in orbit would be slightly off in 4.5 billion years.

And a balance which is slightly off,

10 000 001:10 000 000
or
10 000 002:10 000 000

instead of 1:1, sooner or later will get the orbit out of balance.

That is the issue here, and I would like an aswer on it, if you have one.

If you are not a specialist in physics, your good intention is noted, but Father Fewel already did some with less ignorance of theology and Thomistic metaphysics than you show.

2. I don't grant that we require a premise that physical laws are more fundamental than spiritual ones. If spiritual laws are more fundamental, as long as they are *consistent*, we will be able to observe their effects just as well as those of physical laws.
I've run the numbers myself, just to confirm, and I get slightly different ones, as we shall see:

Above, th'art assuming that the only change in the Earth's mass is from the dust. In actuality, it's losing mass in other ways (mostly in the form of hydrogen escaping from the atmosphere). This is apparently something like 92,000 tonnes per year, for a net *loss* of 50kt/y.

All of this being said, if we assume a change of 40-50,000,000kg per year in *magnitude*, without regard to whether it's a gain or a loss, and multiply this by the 4,500,000,000 years that current understanding suggests the Earth has been around, we get 225,000,000,000,000,000 kilograms in total. That's 2.25*10^17kg, which certainly sounds like a lot - but the Earth, as thou notest, masses a little less than 6*10^24kg, which means we're talking about a difference in mass of roughly 37 parts per *billion*. And since both gravitational force and momentum are directly proportional to mass, that's the change we're talking about over the *entire currently-understood life of the Earth so far*. That's 3.7 *millionths* of 1%. The Earth's orbit *is* unstable in this model, but consider that the same model has the Sun expanding and effectively swallowing the Earth in about 5,500,000,000 years - by which time that discrepancy in the Earth's mass will have just about doubled. So we're still talking about seven parts per hundred million. The point here is that this is not sufficient to have destabilised the orbit.

Yes, we could look at the ratio of speed to gravitation, too, but all we'll really see there is a doubling of the ratio (because the speed is altered in one direction while gravitation is altered by the same proportion in the other; either speed decreases while gravity increases or vice-versa, depending whether mass was gained or lost): still not even close to enough to be significant over the Earth's entire lifespan.

3. As an addendum, I ran the numbers assuming that the change would compound multiplicatively rather than additively, because the reduction in orbital speed also reduces the semi-major axis of the orbit, which increases effective gravitational force, and this is what I got:

50kt(=50,000,000kg)/6,000,000,000,000,000,000,000,000kg = 5/600,000,000,000,000,000,000. Add 1 to get the ratio, and that's 1.0000000000375. Raising that to the 4,500,000th power (one-thousandth of the way there) gets us 1.000000000037500000000703124843758789056640708265406630437... - which illustrates quite neatly that even if we raise *that* to the thousandth power, equivalent to raising our starting number to the 4.5 billionth power ((x^y)^z == x^(y*z)) we're not going to get a statistically significant difference.

5. "If spiritual laws are more fundamental, as long as they are *consistent*, we will be able to observe their effects just as well as those of physical laws."

If we trust geocentrism, we do that very well in Tychonian orbits.

"Above, th'art assuming that the only change in the Earth's mass is from the dust. In actuality, it's losing mass in other ways (mostly in the form of hydrogen escaping from the atmosphere). This is apparently something like 92,000 tonnes per year, for a net *loss* of 50kt/y."

That hydrogen would be lost is comprehensible, but where do yo get it from so much is there to be lost? Shouldn't Earth have lost all significant hydrogen long ago?

"but the Earth, as thou notest, masses a little less than 6*10^24kg, which means we're talking about a difference in mass of roughly 37 parts per *billion*."

I did note that the difference in mass per se is not very great.

I did not give any numbers suggesting otherwise.

"And since both gravitational force and momentum are directly proportional to mass,"

I sense a selight of hand.

With a given speed, momentum is proportional to mass. BUT, here we are talking of added mass which takes away part of momentum, and therefore even more of speed.

Now, the problem is that when we get very small changes upward in one and downward in the other, they are combining to an imbalance. Setting, arbitrarily, the stable ratio of gravitation : momentum or grvitation : speed as g:mom=1:1 and g:v=1:1 for stable, we get over 4.5 billion years a combined instability of

10 000 001:10 000 000 (g:mom)
or slightly less than
10 000 002:10 000 000 (g:v).

This means there will be only 5 to 10 millions of something before the instability takes over.

And I am not sure whether this unit is orbits or even seconds. This being one of the units in the included mathematically studied factors.

1. This comment has been removed by the author.

2. Part the first, owing to comment-size limits. Please read both if either, but feel free to respond independently if at all.

"We do that very well in Tychonian orbits"

No. We don't. The Tychonian model is a lot closer to what we observe than the Ptolemaic, it's true - the latter requires truly vast numbers of epicycles to provide a good approximation of what we observe - but it still doesn't adequately explain the imperfectly-elliptical observed orbits of most celestial bodies. And that's if we're talking about the variant in which the Earth rotates, but does not orbit - the fully-static-Earth model can be disproved immediately by looking at the apparent motion of any celestial body in the solar system besides the Earth, Sun, and Moon. It also does absolutely nothing to explain stellar parallax and aberration, which are both incredibly well-documented. I suppose one could claim that the furthest stars move around Sol rather than Terra, too, but even that doesn't hold up: we have records of stars with apparent motion relative to each other that would require them both to be orbiting yet another point. Eventually the number of epicycles involved reaches a point where the only reason to hold that the Earth alone is static is a pre-decided insistence that it is special. At this point we have the phenomenon known as "belief-in-belief", but we'll talk about that another time, maybe.

"Shouldn't Earth have lost all significant hydrogen long ago?"

Believe it or not, the answer's "no". We actually have lost most of the elemental hydrogen from Earth's atmosphere, but methane and other such compounds decompose in the upper atmosphere. Hydrogen and methane together comprise about 0.000235% of the atmosphere today. Factor that methane is roughly three-quarters carbon by mass, and we're looking at 0.0001% hydrogen in total, which sounds tiny, but the current mass of the atmosphere is 5*10^15 tonnes, meaning that between these components the atmosphere currently contains around 5,000,000,000 tonnes of hydrogen. That's only 50,000 times what we lose annually (it'd be a hundred thousand, but remember that we lose almost 100,000 tonnes per year, but gain back more than 40,000 in other materials, so while the net loss is closer to 50,000 we're looking at a hydrogen loss of more than that), it's true, but there are two extra things to consider here: We have geological evidence that there actually was a lot more hydrogen in the early atmosphere of the Earth, and there are various processes (many, but far from all, having nothing to do with humans, by the way) that add methane to the atmosphere. Current numbers suggest that methane enters the atmosphere at a rate of around 450-600Tg (=450-600,000,000kg = 450-600,000 tonnes) per year, though there are enough natural sinks to reduce the gain to around 50-60,000 tonnes annually. All of that's ignoring another huge source of atmospheric hydrogen, which is thermal decomposition of water.

The point is, the "reserves" involved are far larger than th'art imagining, and being replenished by the release of hydrogen from various sources in parts of the Earth that aren't the atmosphere, mostly the crust.

3. Part the second, on the actual numbers and physics. I suggest reading the other part, above, first, but...

"With a given speed, momentum is proportional to mass. BUT, here we are talking of added mass which takes away part of momentum, and therefore even more of speed."

And here we come to thy fundamental error. Adding mass does not, in any scientific model since and including the Newtonian, reduce momentum. It reduces speed precisely because it does not reduce momentum. The momentum is conserved, so the increase in mass requires a decrease in speed.

I shouldn't have even mentioned momentum in the first place, though. Yeah, I slipped for a moment, and suggested the momentum of the Earth is variant, when it mostly isn't (tidal forces from the moon and the other planets, as well as radiation pressure from the Sun, actually do affect the Earth's momentum, but let's not complicate the situation any further, eh? The tidal forces largely cancel out in terms of linear momentum, though they contribute to slowing the spin, and the radiation pressure is so small as to be negligible, anyway). Let's talk about gravity and speed: this is exactly what my "follow-up" comment was about. Even if we assume that the change in mass counts twice, once in direct-proportion reduction of orbital speed and again in direct-proportion increase of gravitational force (or vice-versa, if we're losing mass, which we are; the maths is fundamentally the same), and that it compounds multiplicatively, we get a figure that is in the millionths of one per cent. Even if it's closer to one part per ten million, as thy figures have it, those numbers were based on the change in mass over 4,500,000,000 years (I just went back and checked; the ). That's per-age-of-the-Earth-so-far, not per-second or per-year. Bearing in mind that the projected lifespan of the Sun is about another 5,500,000,000 years, I don't think we need concern ourselves with an instability that will take 5-10,000,000 times 4,500,000,000 years, or on the order of 25-50,000,000,000,000,000 years.

But I think (and please correct me if I'm wrong) th'art rather claiming that the reason those ratios are a problem is not that they're the amount by which the Earth's orbital parameters change, but that if gravitation and speed aren't "perfectly balanced" the Earth's orbit must decay, and that they represent such an imbalance. This represents a fundamental misunderstanding of orbital mechanics: Any object moving fast enough to orbit and at a speed lower than the escape velocity of the thing it's orbiting will remain in a stable orbit. Slow the Earth down, keeping its distance from the Sun and its mass (I know, I know, but we'll come back to that) unchanged, and the opposite side of the orbit will fall. That changes the semi-major axis, which can be thought of as the average distance from the primary, though it's a tiny bit more complex than that. The resulting orbit is stable. The Earth is closer to the Sun, but it moves faster during the altered parts of its orbit than it otherwise would have, and so it has increased linear momentum during those parts of the orbit, which we can prove mathematically will mean it comes back to where it was on the previous orbit. Increase the mass, and the same thing happens. Increasing the mass and reducing the instantaneous speed will compound the effect, but the resulting orbit is still stable; the only times it wouldn't be are if the periapsis was inside the Sun's atmosphere (yes, the Sun has an atmosphere, though not a breathable or otherwise survivable one), at which point drag becomes a factor; and if the speed were increased (and mass decreased to the point where the Earth exceeded Solar escape velocity, at which point it would leave the Sun behind - but this would require an alteration of multiple orders of magnitude, not fractions of 1%.

6. This comment has been removed by the author.

7. "The Tychonian model is a lot closer to what we observe than the Ptolemaic, it's true - the latter requires truly vast numbers of epicycles to provide a good approximation of what we observe - but it still doesn't adequately explain the imperfectly-elliptical observed orbits of most celestial bodies."

With angelic movers, no problem.

Art.

"And that's if we're talking about the variant in which the Earth rotates, but does not orbit - the fully-static-Earth model can be disproved immediately by looking at the apparent motion of any celestial body in the solar system besides the Earth, Sun, and Moon."

Namely?

" It also does absolutely nothing to explain stellar parallax and aberration, which are both incredibly well-documented."

One other movement on the count of angelic movers : not one for just each planet, but one for each star.

Note I said "one", not "two". Aberration is the commonality of it, parallax the individual smaller variations in it.

Note very well also that it is mechanistic as opposed to angelic explanations which forces modern scientists to analyse these as two different "apparent movements".

If "aberration" had individual variants, it would not be "aberration".

This also inflates the distances, taking the 20 arc seconds as aberration and the smaller variants as the real parallax. If a heliocentric had taken 20 arc seconds as the actual parallax, he would have landed with a sphere of fixed stars much closer than accounted for - and the fixed stars would all be much smaller. On my view, they are closer and smaller still.

Also, one catalogue of parallaxes (Hipparcos or Tycho) has negative parallaxes. In a modern Heliocentric view, accounting for parallaxes as mechanically caused by the one single actual movement of earth around the sun, a negative parallax has to be an error of measurement.

Correspondence of Hans Georg Lundahl : With Erik Høg on Parallax in New Catalogues
http://correspondentia-ioannis-georgii.blogspot.fr/2015/09/with-erik-hg-on-parallax-in-new.html

With angelic movers causing parallax and aberration (or the complex phenomenon analysed in these two terms), negative parallax is simply some angels doing a variation in size the other way from the common medium movement.

1. Fully-static Earth: The relative motions of the planets to each other, to the Sun, and to the Earth, are incompatible with each planet being on an elliptical (including circular!) orbit around the Sun, which is moving around the Earth with a period of 24 hours, while the accelerations (and, more relevantly, the jerks - that's the change in acceleration over time, or third derivative of position, not an insult) that they experience are kept to low enough levels that we wouldn't observe their effects. Based simply upon the masses involved and the strength of various kinds of rock (all of which we can verify experimentally, rather than theoretically, including that enough to matter of several planets is made of those kinds of rock), along with the effects of acceleration and jerk on things relative to their tensile and compressive strength, we can know that in the Tychonic model, there wouldn't be any planets any more, just vast asteroid clouds. This isn't some forcing of an elegant theory to fit: I want to reiterate that all of these things can be modelled and tested experimentally, and that while we can't swing planets around at enormous velocities we can swing things of varying sizes enough to form a reliable model, which thanks to the Cosmological Principle we absolutely can scale up to planets.

2. "The relative motions of the planets to each other, to the Sun, and to the Earth, are incompatible with each planet being on an elliptical (including circular!) orbit around the Sun, which is moving around the Earth with a period of 24 hours, while the accelerations (and, more relevantly, the jerks - that's the change in acceleration over time, or third derivative of position, not an insult) that they experience are kept to low enough levels that we wouldn't observe their effects."

What if vectors, gravitation, accelerations only make sense in relation to aether, which is moving westward each day WITH Sun and Moon "lagging behind" (or moving back, rather)?

This one is also relevant for geostationary orbits.

3. "Based simply upon the masses involved and the strength of various kinds of rock (all of which we can verify experimentally, rather than theoretically, including that enough to matter of several planets is made of those kinds of rock), along with the effects of acceleration and jerk on things relative to their tensile and compressive strength, we can know that in the Tychonic model, there wouldn't be any planets any more, just vast asteroid clouds. This isn't some forcing of an elegant theory to fit: I want to reiterate that all of these things can be modelled and tested experimentally, and that while we can't swing planets around at enormous velocities we can swing things of varying sizes enough to form a reliable model, which thanks to the Cosmological Principle we absolutely can scale up to planets."

Retry the modelling with aether moving westward each day.

It would be equal to the modelling in an aetherless universe of earth rotating.

And there is an elegant theory involved in this, namely your aversion to admitting the aether.

What if vectors, gravitation, accelerations only make sense in relation to aether, which is moving westward each day WITH Sun and Moon "lagging behind" (or moving back, rather)?

4. Aether theories make solid, falsifiable predictions - which have, indeed, long since been falsified. The most famous example of this is the Michelson-Morley experiment.

5. "The most famous example of this is the Michelson-Morley experiment."

It does not falsify aether per se.

It falsifies (aether + annual movement of earth) combined.

So, to a Geocentric, Michelson-Morley does NOT falsify aether.

6. That's simply not true. Michelson-Morley tested for relative motion of the aether to the Earth, which is present in thy model too. Whether the Earth is moving through the aether, or the aether moving around the Earth, matters not: either theory predicts a difference in the speed of light in perpendicular directions, which is exactly what the Michelson-Morley experiment disproved. Likewise, whether the relative motion of aether and Earth is linear or angular (which is to say, whether the one streams past the other as if in an orbit around something larger or moving in a straight line, or is in a rotational movement) doesn't change that fundamental prediction.

More recent experiments have confirmed this to an incredibly precise level (18 significant figures; far more than enough to prove that if there was an aether wind, it wasn't even close to enough to explain what thou claimest it does). Even if we instead suppose an aether that is entirely static relative to the Earth, this is disproved by the Kennedy-Thorndike variant on the experiment.

These are merely the best-known instances; other methodologies have also demonstrated that an aether theory is insufficient to change the results.

Quite apart from which, there is no reason for a luminiferous aether to alter the effects of acceleration upon objects in the way thy comments of 06:21 and 06:24 server-time yesterday imply in the first place. Consider the possibilities: In the model th'art proposing, acceleration "only make[s] sense in relation to aether" (thy words), in which case the acceleration of objects with which we can experiment would be subject to the same effects, in which case we can meaningfully extrapolate the effects of acceleration and jerk upon large masses of rock. In the Newtonian model, acceleration doesn't require an aether to make sense, but we can still extrapolate the effects of it and of jerk upon large masses of rock from smaller ones on which we can experiment.

Thus the aether is irrelevant to the point: Under the accelerations necessary for a fully-static-Earth-with-Sun-orbiting-once-per-day Tychonic model to work, those planets would be ripped apart, and we can use experimental data at multiple combinations of sizes and accelerations to verify this.

8. " I suppose one could claim that the furthest stars move around Sol rather than Terra, too, but even that doesn't hold up: we have records of stars with apparent motion relative to each other that would require them both to be orbiting yet another point."

I am not saying that ANY "stars" (modern terminology) or "fix stars" (older one) are orbitting Sun. The movement is a dance movement in rhythm with the annual movement of Sun around ecliptic, but not keeping full pace with it.

Any number of epicylces are possible with angelic movers, as they can be trusted to be good artists, and obey a common choreographer who is also so : God.

" Eventually the number of epicycles involved reaches a point where the only reason to hold that the Earth alone is static is a pre-decided insistence that it is special."

The number of epicycles per se cannot add up to that.

With a mechanistic view, even one epicycle without a physical body as centre (epicycle of Moon around Earth around Sun in your view, for instance) is an insurmountable problem.

With an angelic view of causation, any number of epicycles are possible as long as they are good art.

" At this point we have the phenomenon known as "belief-in-belief", but we'll talk about that another time, maybe."

If you will kindly define it, I will see if there is not such on your terms too.

1. 'I am not saying that ANY "stars" (modern terminology) or "fix stars" (older one) are orbitting Sun.'

I didn't say thou wert so saying. I had jumped ahead, to a potential response to my point that our observations don't match what would be expected if they (again, regardless of what they are: vast fusion reactors a long way off, small "torches" much closer, fixed points on a celestial sphere) were centred on the Earth. I didn't know (or think I knew) that thou wert going to claim that, as indeed thou didstn't, but I wanted to address it just in case thou wert. That is all. Now, if th'art claiming they're on yet more epicycles, well, that's a deviation from the Tychonic model, which doesn't itself invalidate the position, but does mean that the particular fragment to which thou here objectest is irrelevant.

"The number of epicycles per se cannot add up to that."

Let me rephrase. The only reason to choose the explanation where the Earth alone is static over all others (including the one where, for example, these claimed angelic movers move the Earth too; it's not only "mechanistic" models that th'art rejecting here) is such an insistence.

2. I'm going to deviate from pure evidence-based reasoning for a moment, to engage with the comments about "art" on their own terms. I maintain that the only philosophical premise needed to support physics is the Cosmological Principle (which is the name of the one I mentioned when I first entered this conversation: that the laws, whatever they are, are consistent and universal, so that observations can be used to draw conclusions), but if th'art going to use philosophical arguments then those I can only engage with on a philosophical level.

Surely a creation that maintains itself, without requiring vast numbers of sentient creations to keep it moving, is better art than one which requires constant maintenance?

3. OK. Belief-in-belief.

The phenomenon I'm addressing is one wherein someone takes a hypothesis - like, to steal an example from Carl Sagan, that there's a dragon in their garage - and constructs it in such a way as to make it untestable. For example, one might ask to see it, at which point they say it's invisible. They claim that it's also intangible, so it won't leave footprints and can't be covered with paint. They claim it doesn't breathe, so there's no way to hear it.

It is conceivable that such a dragon really exists. However, the much more plausible explanation, given that the only evidence available is this person's word for it, is that they are either making it up or under a delusion. That they are able to counter everything that could be used to test it, in such a situation, requires that they have a very solid mental model of what a world with no dragon in the garage looks like, and consciously or unconsciously they are constructing the claimed dragon in such a way that it appears exactly like no dragon at all. They may or may not believe that they believe, but to have a model that good they must, on some level, believe there is no dragon.

So it is with a static Earth. To explain it, in light of every observation that fits consistent models wherein it moves, keeps requiring the addition of extra complexity just to preserve this one ideal. Sometimes, as with the Tychonic model displacing the Ptolemaic, it requires effectively scrapping the old model and starting again. That, too, is not a problem - after all, the Copernican model, too, required that the Ptolemaic one be thrown out. However, the Tychonic began with a more complex question. The Copernican model (which, by the way, I'm not advocating; we've moved past that one, too, but it's a useful stepping-stone of understanding) began with the question "what could explain what we observe?", while the Tychonic began with "what could explain what we observe and keep the Earth unmoving?" - it inserted an additional premise. That hidden, additional premise is unsubstantiated, and while there can be any number of things invented to justify it, they are developed with it in mind, rather than it being derived from them. This is closely related to the logical fallacy of begging the question.

4. Yes, I think there is belief in belief in your position too.

To St Thomas, stars were not alive. They were moved by angels, but not alive themselves. Reason : they didn't change. Tycho Brahe saw a nova. "Just an explosion". Well, though he was not a believer in angelic movers himself (those who were did not take up living stars again just because of that), at least he had not given any argument against angelic movers.

Bradley saw a variation in position 20 arc seconds back and fourth per year. "Just aberration". Now, if it had been just aberration, it would have been equal around the game. Friedrich Bessel saw slight variations around the 20 arc seconds, like By 1911, further observations had improved on Bessel's parallax measurement of 313.6 mas to 310.0 mas per year for 61 Cygni. "Oh, just parallax". Then the stars dance together in a slow reel and they say "oh, Earth is wobbling".

Recently a telescope detected a smiley. If it was fake news, a French science paper for teens and pre-teens was not taking it so. "Oh, it is a fortuitous result of gravitational lensing" ...

If on judgement day you will find yourself criticised by angels who were in fact conducting stars (or by stars who were in fact alive), they will probably tell you "tried to tell you so!"

"So it is with a static Earth. To explain it, in light of every observation that fits consistent models wherein it moves, keeps requiring the addition of extra complexity just to preserve this one ideal."

It is not just an ideal, but a direct observation. And its more and more extra movements are only geometrical complexions if you take into account that there is artistry involved.

"The Copernican model (which, by the way, I'm not advocating; we've moved past that one, too, but it's a useful stepping-stone of understanding) began with the question 'what could explain what we observe?', while the Tychonic began with 'what could explain what we observe and keep the Earth unmoving?' - it inserted an additional premise."

But the Earth unmoving is one of the things we do observe, every day!

Your solution requires the throwing out of our common sense about common realities, like Earth and Sky, Sun and Moon, Day and Night.

Your solution requires the scrapping of one datum because the rest of the data just have to fit a real added premiss "only Newtonian mechanistic causes allowed".

I bet the letters on your keyboard were not struck by only Newtonian mechanistic factors, but by your choice of communicating a message!

5. "Let me rephrase. The only reason to choose the explanation where the Earth alone is static over all others (including the one where, for example, these claimed angelic movers move the Earth too; it's not only "mechanistic" models that th'art rejecting here) is such an insistence."

No, there is a reason behind the insistance it is non-moving, and it is not it is special, even if in fact it is.

It is we see it as unmoving each day.

It is a trust our Creator put us in the right position to discover the universe the right way.

There are added instance, like parallax landing us with a cosmic distance ladder which either pust Empyrean heaven VERY far away, or makes heaven non-physical.

With epicycles for stars, we can have stars' sphere (no longer fix stars's sphere) at 1 lightday above us, and Empyrean heaven just above, where Christ is seated at the right hand of the Father.

6. "we see it as unmoving each day."

When we stand in a moving train, the world as seen through the windows appears to be moving backwards, while we stand still. In many modern trains, we can feel the bumps brought about by imperfections in the track, but not on all, so just assume for a moment that I'm talking about a maglev or something. Yet it is not generally considered reasonable to assume that the train is perfectly stationary, while the entire universe moves around it.

Why, then, should it be considered reasonable to assume that the entire Earth is perfectly stationary, while the universe moves around it?

"a trust our Creator put us in the right position to discover the universe the right way"

I know a couple of Christian physicists who would use the exact same line of reasoning to say that we shouldn't reject the evidence that the Earth moves.

"There are added instance, like parallax landing us with a cosmic distance ladder which either pust Empyrean heaven VERY far away, or makes heaven non-physical"

Firstly, there are other explanations even if we insist on a physical heaven, such as a small offset in a fourth or fifth physical dimension - I don't hold this view, but its validity is at least equal to that of a stellar sphere a light-day away, and it preserves the physicality of a heaven without requiring the vast additional complexity of an angelic mover for every celestial body.

But perhaps more importantly, why should we accept the physical existence of an Empyrean heaven as a premise? It's adding an additional, philosophical (or, OK, theological, but theology is ultimately a subset of philosophy) assumption to the entire system - something thou wert keen to suggest I should avoid.

7. I would note that I do not at any point argue that there cannot be angelic movers. Here are the fundamental things I am arguing:

1: Thy claims that the Earth cannot, under Newtonian mechanics, still be orbiting the Sun after 4,500,000,000 years are false, probably owing to at least one misunderstanding of the physics involved. Note that this position doesn't involve the actual accuracy of Newtonian mechanics, which are known to be imperfect, having been supplanted by relativistic mechanics.

2: That angelic movers operating a Tychonic system, while possible with enough tweaking or supplementary claims, do not provide a better-fitting explanation for what is observed than the Newtonian model

Ultimately, that's all. I don't claim there can't be angelic movers, I don't claim a Tychonic system when heavily augmented with unfalsifiable* hypotheses is ultimately impossible, and I don't claim there is no Empyrean heaven. I merely claim that these beliefs are not a good fit for available evidence.

*A note on falsifiability: if something is falsifiable, it doesn't mean it's false. Falsifiability means a claim has some piece of evidence which if that evidence were found to exist would disprove - or falsify - the claim. The Cosmological Principle is falsifiable - we could find a region of the universe where the physical laws were demonstrably different - but has yet to be falsified. Something that's unfalsifiable cannot have evidence supporting it because to support a hypothesis, evidence must make it less likely that the thing that falsifies it can be shown to be true. Thus the weight of evidence directly for or against an unfalsifiable hypothesis is always zero.

Tycho didn't believe in angelic movers, and neither did he use religious texts as his primary source. Nevertheless, his arguments were consistently based in what he thought was a philosophically better universe. His question was still "how can we explain these observations while keeping the Earth still".

I do not only require Newtonian mechanics. Indeed, I am entirely willing to throw them out when another model better fits the available data, such as the behaviour of objects around black holes, which is far better explained by relativistic mechanics. I merely require, before I will use (which is not the same as believing) a model, that it makes useful predictions that have not been falsified, and that it does not contradict available observations in any way that will affect the use I plan to make of it. It is for this reason that I'm entirely willing to use Newtonian models of the Solar system for most purposes even though they are known not to be a perfect fit: because they are good enough to send a spacecraft through the solar system on a multi-year trajectory, and have it arrive within less than 20 seconds of the time planned. Angelic movers may be more theologically satisfying in the minds of some, but unless they move things in such a way as to simulate nearly-Newtonian mechanics (in which case they are for practical purposes redundant) they cannot be used to make predictions of that kind of utility, so I'm not going to bother with them in the models I use.

8. On the subject of the smiley: I think it's a fascinating phenomenon, and I think that pareidolia combined with the absolute vastness of space is sufficient explanation. I also think that these things provide plenty of wonder, and we need not postulate the huge complexity of an intelligence to have brought the phenomenon about. That said, I can't rule such an intelligence out completely; I just don't think it's enough, especially given that humans are entirely capable of seeing faces in things not designed to contain them - not because they weren't designed at all, which I'm sure would be a claim that would lead to a theological rabbit-hole, but because they were designed by other people without that intent. If a "face" can appear where it was not part of the design intent, it can surely appear where there was no design intent at all.

9. "When we stand in a moving train, the world as seen through the windows appears to be moving backwards, while we stand still."

Yes, and very solid experiences both of trains and of trees tell us which of these which is moving. Therefore the next question is where exactly you have a parallel argument for our view being parallactic.

"Yet it is not generally considered reasonable to assume that the train is perfectly stationary, while the entire universe moves around it."

Based on observations of trains from the outside, based on observations of trees from the view of walkers.

"Why, then, should it be considered reasonable to assume that the entire Earth is perfectly stationary, while the universe moves around it?"

Because we do not have parallel evidence against stillness of earth.

"I know a couple of Christian physicists who would use the exact same line of reasoning to say that we shouldn't reject the evidence that the Earth moves."

They are then making God and His truthfulness more indebted to a small and recently originating minority of physicists than to the great mass of mankind all through history.

"Firstly, there are other explanations even if we insist on a physical heaven,"

Which we must. Christ is seated on a throne there.

"such as a small offset in a fourth or fifth physical dimension"

God created space with three dimensions, as an image of Holy Trinity.

"- I don't hold this view, but its validity is at least equal to that of"

Surprise, surprise, another view you don't hold.

"a stellar sphere a light-day away,"

Five dimensional space is a counterintuitive thing.

Stellar sphere a light day away is a presumed disproven thing, but disproven only by acceptance of heliocentrism as "proven" which it is not.

10. "and it preserves the physicality of a heaven without requiring the vast additional complexity of an angelic mover for every celestial body."

It is "an additional complexity" only in so far as it saves other "additional complexities" - like stars 13.8 billion light years away, either contradicting Biblical chronology or involving "local time conventions" differing over the universe.

I can't see how it would be a vast complexity either way. It is a very unitary one. Either God on day Four gave each celestial body an angelic mover, or He didn't. If He did, that is not sth to be decided separately and on different grounds for Son, Moon, Jupiter, alpha Centauri and so on. It is exactly one statement, even if it is one about millions of celestial bodies and millions of angels.

"But perhaps more importantly, why should we accept the physical existence of an Empyrean heaven as a premise? It's adding an additional, philosophical (or, OK, theological, but theology is ultimately a subset of philosophy) assumption to the entire system - something thou wert keen to suggest I should avoid."

It is not a premise, but an explanation. An explanation of Heaven as physical.

"Tycho didn't believe in angelic movers, and neither did he use religious texts as his primary source."

Riccioli did, for theological reasons. And he valorised Tychonian orbits, which is why he named his work Almagestum Novum, as indicating Ptolemy needed an update. The Tychonian one.

"2: That angelic movers operating a Tychonic system, while possible with enough tweaking or supplementary claims, do not provide a better-fitting explanation for what is observed than the Newtonian model"

Exactly how many supplemental claims (on top of assertion of aether, God moving it westward each day, angelic movers for individual bodies, these being artists) do you suppose it involves?

11. " I merely require, before I will use (which is not the same as believing) a model, that it makes useful predictions that have not been falsified, and that it does not contradict available observations in any way that will affect the use I plan to make of it."

Exactly what use are you planning to do with astronomy? Make predictions about what can be seen from Earth? Angelic movers will allow you as precise predictions as any mechanics, insofar as the real predictors are the past observations of the movements.

"It is for this reason that I'm entirely willing to use Newtonian models of the Solar system for most purposes even though they are known not to be a perfect fit: because they are good enough to send a spacecraft through the solar system on a multi-year trajectory, and have it arrive within less than 20 seconds of the time planned."

OK, compass needles didn't do their work, before Maxwell explained electro-magnetism?

They did. An explanation can be factually wrong, and still do its work. Because the things do.

"On the subject of the smiley: I think it's a fascinating phenomenon, and I think that pareidolia combined with the absolute vastness of space is sufficient explanation."

Belief within belief.

" I also think that these things provide plenty of wonder, and we need not postulate the huge complexity of an intelligence to have brought the phenomenon about."

Why would an intelligence bringing it about be a "huge complexity"? In art produced on earth, as long as it isn't modern, an intelligence bringing it about is usually seen as the least hugely complex explanation.

" That said, I can't rule such an intelligence out completely; I just don't think it's enough, especially given that humans are entirely capable of seeing faces in things not designed to contain them - not because they weren't designed at all, which I'm sure would be a claim that would lead to a theological rabbit-hole, but because they were designed by other people without that intent. If a "face" can appear where it was not part of the design intent, it can surely appear where there was no design intent at all."

In such cases, a human designer can either have been the unwitting tool of a higher design or simply be lying about his intentions.

12. Oh, no. Oh, no. What have I done? I apologise in advance for the incoming wall of text.

"Because we do not have parallel evidence against stillness of earth."

Given that thou'st already used a video recorded on the ISS to back up an argument (and by the way, it might have been based on a misunderstanding about how drag scales with size, but I should note my respect for the attempt) I'm going to assume th'art willing to acknowledge that it exists. We do in fact have observations from that very same space station that back up the motion of the Earth. There's also the question of space-launch mechanics: the spin of the Earth makes it, both theoretically and empirically, more efficient to launch things into a West-to-East orbit than an East-to-West one. By this I mean that it takes less fuel (because it takes less acceleration) to achieve an orbit of the same dimensions, and that we have records of space-launches and how much fuel they needed to back this up. Notice that this is precisely the opposite way around to what we would expect from drag induced by an aether moving westward relative to the surface, as thou proposest elsewhere.

Furthermore: It would not be reasonable even for someone who spent their entire life on the train to assume that it was perfectly stationary, while the entire Earth moved around it. Why, then, is it reasonable simply because we have spent our entire lives on the Earth for us to assume that it does not move?

"They are then making God and His truthfulness more indebted to a small and recently originating minority of physicists than to the great mass of mankind all through history"

Alternatively, they are allowing for God to have provided us with a universe such that every time we learn to look deeper, we can come closer to the truth of it. What wonderful generosity.

After all, th'art making God and His truthfulness more indebted to a marginally-less-small and recently-originating minority of theologians than to the great mass of humankind through history before them, who believed that everything moved around the Earth (or even that nothing beyond the Earth was physically real in the same way that the Earth is). Why is adopting the Tychonic model over the Ptolemaic, when the latter failed to fully account for observations, better than doing the same thing with the Newtonian over the Tychonic, or the relativistic over the Newtonian, or (hopefully, one day) the quantum-gravitational over the relativistic?

[...even if we insist on a physical heaven]

"Which we must. Christ is seated on a throne there"

How do we know? Even if we accept the authority of the Bible and whichever set of texts thy particular denomination includes in it rather than considering apocrypha, what reason is there to accept it as literally true? The literal truth of the Bible is an unsubstantiated premise. Indeed, I challenge thee to derive even its authority, let alone its literal truth from a source that does not depend circularly on said authority.

"God created space with three dimensions, as an image of Holy Trinity"

How dost know that? I could say "God created space with seven dimensions, symbolising completion and perfection, and allowed us to see three of them to remind us of the Trinity", and that would be just as well-supported by both the available physical evidence and the text of the Bible.

13. "Surprise, surprise, another view you don't hold."

So what? The point was to illustrate a possibility that is equally consistent, to show the flaw in thy false dichotomy (that if we accept parallax we must accept either that Heaven is a very long way away or that it's non-physical). It's true that I don't believe Heaven is necessarily physical, but the point I was making was that even if I assume for a moment that it is, thy claim does not automatically follow. It's simple logic: A implies not-B doesn't actually mean that not-A implies B. Not-A doesn't imply not-B, either: we cannot decide the truth of B based on the falsity of A alone. A false dichotomy, such as the one thou presentedst, boils down to the fallacy of the inverse: denying the antecedent.

"Five dimensional space is a counterintuitive thing."

Intuition is not a reliable guide to the world. A fixed sphere of stars that happen to be moved across its surface in such a way as to simulate a much larger universe is also pretty counterintuitive, but thou dostn't seem to have any issue with that idea. Likewise, time being variant in such a way that the speed of light is constant, regardless of reference frame, is pretty counterintuitive, but we have experiments that strongly suggest it to be the case.

'Stellar sphere a light day away is a presumed disproven thing, but disproven only by acceptance of heliocentrism as "proven" which it is not.'

On the contrary. There is evidence aplenty that does not depend on a heliocentric solar system that there is not a sphere of fixed stars a light-day away. For example, we have images from Voyager 1, which is a little under 19 light-hours away. No heliocentric model is necessary to illustrate that, by the way: speed-of-light delay in communications with it is entirely sufficient. Also the speed at which it departed Earth, on which basis whether it simply slowed due to gravity or was carried by an "angelic mover" through the aether, that distance can be calculated, though this latter method requires that we can accurately convert between fractions of c and metres per second (which we can, but for all I know thou dostn't accept that). We'd be able to see the effects of drawing close to that sphere on the apparent position of the stars. The trigonometry is very simple. We do not see such effects, ergo there is no such sphere.

'It is "an additional complexity" only in so far as it saves other "additional complexities" - like stars 13.8 billion light years away, either contradicting Biblical chronology or involving "local time conventions" differing over the universe.'

Thy multiplication is off. The same quantities of apparent stars are necessary in thy model to explain such things as the Hubble deep-field images, yes? Thus we are choosing between these things moving according to consistent physical laws, on the one hand, and being directed by an intelligence each, on the other. The latter is an infinitely greater fundamental complexity. The apparent motions are the same, but the means by which they are produced is more complex: an intelligence is fundamentally more complex than a physical law, and th'art positing an infinity of them as being fundamental to the universe (as opposed to arising out of it). I stand by my statement.

[Tycho's didn't start from his religion or believe in angelic movers]

14. [Tycho's didn't start from his religion or believe in angelic movers]
"Riccioli did"

Just to be clear, that particular bit wasn't an attempt to argue against thee. It was meant to be in agreement with thine own earlier (correct) claim that Tycho didn't mention angelic movers. What I was trying to get at is that even though he didn't posit angelic movers as his explanation, he still began with the unsubstantiated premise that the Earth ought to be static. He threw out the old model because it didn't work, and quite rightly so, but he hung on to a bit of it for no reason other than that he preferred that it be the case. It is this that I am saying is a problem, and the fact that Riccioli chose "because I think that's what God would do" over "I like it better that way" as a justification for a static Earth does not make it a compelling line of reasoning. Quite apart from anything else, they're effectively much the same claim.

"Exactly how many supplemental claims (on top of assertion of aether, God moving it westward each day, angelic movers for individual bodies, these being artists) do you suppose it involves?"

Four is already quite a lot, when one of them has been falsified and the other three are untestable. But if thou insistest: I already see a number of implicit claims about the capabilities of angelic movers (to make this work they have to be able to change the speed of large masses without the usual effects of acceleration and jerk on the same, to take just one example). There is also an implicit claim - one I asked thee about earlier, though I never got a response - that a universe that needs an infinity of "helpers" to keep it from falling apart is more reasonable to describe as "good art" than one that maintains itself.

"Exactly what use are you planning to do with astronomy? Make predictions about what can be seen from Earth?"

That's a good start, yes. Why not? Also calculations about the paths of the various asteroids in the Solar system, so as to know whether they could possibly hit the Earth. Or how about working out how to get a space probe where I want it to go, so I can see what Mars is like? Capturing asteroids, for access to the mineral resources that we know - because we've already sent probes to some of them! - they contain. So, so many things.

"Angelic movers will allow you as precise predictions as any mechanics, insofar as the real predictors are the past observations of the movements."

In an abstract sense, this is entirely true. However, given what the actual past and current observations of the movements are, it's not at all so: Angelic movers working a Tychonic model simply do not produce the outcomes we observe. Angelic movers simulating a Newtonian model wouldn't quite do so either, but they would at least come usefully close. Of course, in such a case the angelic movers are redundant to the model, so there's no reason to include them. I don't really want to get into that here, though, because angels-simulating-a-Newtonian-universe is explicitly not what th'art arguing for, unless I am very much mistaken.

15. "An explanation can be factually wrong, and still do its work."

Yes, indeed. And the predictions it makes can be less than perfectly correct, as with the Newtonian model, and still be close enough to be useful, too. But, leaving aside whether or not it's implemented by angelic movers or some other mechanism, a Tychonic model does not come close enough to the facts to be useful.

Just to be clear, a model comes in two parts: The rules, and the mechanisms behind those rules. Compass needles don't need us to understand the mechanisms (that is, exactly what it is that makes magnetism work) to be useful, but they do need us to understand at least one of the rules: The needle aligns itself to the (magnetic) poles. As we get closer to the poles, it turns out that we need to understand another rule: The place to which the compass needle points is not necessarily the same as the pole as measured by the apparent motion of the stars. Then we get close to certain rocks, and we learn that the needle can be disrupted by the presence of certain metals. All these understandings came before Maxwell. They were incomplete models, but they were testable models, and when something didn't fit (like the needle not pointing towards the pole star if one was far enough North or South) we were able to notice that the old model didn't fit, and modify it. In the case of this example, we actually had to throw out an old idea (that we knew exactly where the needle was pointing, and it was the North Pole) and introduce a replacement, even though we didn't understand the mechanism. Regardless of the theological, philosophical, and/or physical reality of a system of angelic movers, we can likewise disprove the specific Tychonic model th'art advocating simply because it does not fit the facts.

We disproved the Newtonian model decades ago, and the vast majority of advanced physicists no longer believe it is true. And that is okay.

16. [on pareidolia and the vastness of space being sufficient to explain a smiley]
"Belief within belief"

Two things, here. First, and not relevant to the claim but just the linguistics, it's belief-in-belief - it's not about belief inside belief, but the case where belief is the object of belief. It's by analogy with belief in justice or belief in god. Just to be clear.

More importantly, the second thing. I don't know whether I didn't explain what belief-in-belief entails well enough, or what, but I'll explain why I don't think this qualifies.

Pareidolia - the tendency of (many-to-most) humans to see faces everywhere, even when there is no actual face, has been well-documented since decades before the smiley was discovered. I'm not inventing an additional constraint or a new phenomenon; pareidolia is part of the same phenomenon, apophenia, which allows us to "see" images in clouds and constellations. Take a set of points on a page, representing numbers that are mathematically completely random, and a human will generally still find an image. Again, this is documented and has been so since long before the "smiley" came up.

Likewise, the vastness of space. The Hubble telescope (which took the most famous smiley-face-in-the-stars photograph (and indeed the only one I know of, but that's beside the point), the photo being noticed in 2012 and making the news in early 2015) is not the most powerful ever built, but it has a pointing accuracy of 0.01 arcseconds, or 1/(100*60*60) = 1/360000 of a degree. There are (and thou canst look this up) around 41,253 square degrees in a sphere. There are 1.296 x10^7 square arcseconds to a square degree, so by the small angle theorem there are approximately 1.3 x10^11 square hundredths of an arcsecond in a degree. That means that, only considering maximum magnification, Hubble can produce on the order of 5 x10^15 distinct images. Throw in stuff that's too "large" for a single image, and can only be effectively captured at lower magnification, and that number gets larger still. I am entirely willing to bet that, given the density of stars in the high-resolution Hubble images, the probability is a couple of orders of magnitude higher than one in five trilliard (that's one in five quadrillion, if thou preferest the short scale) that at least one such image contains something that looks a bit like a smiley face. This one was actually about 25 square arcseconds in size - and there are still 2.139x10^10 non-overlapping possible Hubble images of this size. Factor the things that cross multiple such images without being recognisable in the individual parts, and... yeah. That's a lot of possibilities. Thanks to the Law of Large Numbers (again, it's been part of statistics since long before we had space telescopes), we absolutely should expect that somewhere in that lot will be a smiley face.

I don't need to alter the parameters of the hypothesis, which is what characterises belief-in-belief. I simply point out that we already have evidence for things that suffice to explain this, and thus while we cannot automatically rule out all other possibilities it certainly doesn't provide noticeable evidence for anything else.

17. "In art produced on earth, as long as it isn't modern, an intelligence bringing it about is usually seen as the least hugely complex explanation"

In the specific case of faces, it's actually not. The most common explanation is "they look a bit like their parents", but the actual appearance there is not derived from the volition of said parents. But including human faces, as I just did, is more than a little facetious in this context, so we'll move beyond that, shall we? Even excluding actual human faces, which is fair enough, we see all kinds of things that look a bit like faces all the time, without assuming that a human artist put them there. To take just one of many examples, this kind of thing is one of the reasons cloud-gazing can be popular! I don't see the man in the moon, as is English-speaking tradition, or the rabbit, as is Chinese and Japanese tradition, but I know that other people do. Human pattern-matching is one of the most powerful forces on our perception of the world.

We see entire shifting ecosystems, most of which have no evidence that they were created by the particular volition of an intelligent agent. We see beautiful rock formations, carved by wind and rain - and we don't generally assume that wind and rain are intelligent.

It is true that in art we tend to assume an intelligent agent produced it, because regardless of complexity and wonder we don't usually call things that weren't obviously created by such an agent art. Thou dostn't get to claim that the universe must have been made (or must be operated) by a sentient agent "because it's art" when one of the primary criteria for what constitutes art is something made by such an entity. This is the fallacy of begging the question.

[on the topic of unintentional faces]
"In such cases, a human designer can either have been the unwitting tool of a higher design or simply be lying about his intentions"

Both of these things are possible. There is no reason to suppose that between them the fill the entirety of explanation-possibility-space. These two things are not the only options; there is no reason to suppose that the appearance of a face is always the result of an intelligence's will. Unless, of course, we presuppose that an intelligence that governs absolutely everything exists - but in such a case, it is fallacious to argue the existence of such an intelligence from its governance of anything, because it is only thought to govern things because it's already assumed to exist. Once again, we have come back to petitio principii.

We seem to have moved beyond thy claim that the Newtonian model is drastically inconsistent, though, which is what I came to engage.

18. "We seem to have moved beyond thy claim that the Newtonian model is drastically inconsistent, though, which is what I came to engage."

On the scale of eternity, Newtonian model is certainly inconsistent.

I'd like to know, how much closer to the sun and how much faster would our on your view presumed orbit be:

1) 4.5 billion years from now (which is what we have been calculating) than now;
2) now than 4.5 billion years ago.

This may have other implications excluding atheism. Of the modern kind.

At least, Newtonian model is inconsistent on an eternal level, as required by Epicurean atheism.

Now, you might however admit that:

1) for an orbit to switch between gravitation giving a vector in and back to it giving a vector in and on exactly opposite where it is switching between gravitation giving a vector in and a vector on to a vector in and a vector back across exactly diametrically/axially opposed aphelia and perihelia with one moment just a vector in, we would need som fine tuning;
2) and angelic movers would at least be useful in providing it ...

or is this too much to ask?

19. "These two things are not the only options; there is no reason to suppose that the appearance of a face is always the result of an intelligence's will. Unless, of course, we presuppose that an intelligence that governs absolutely everything exists - but in such a case, it is fallacious to argue the existence of such an intelligence from its governance of anything, because it is only thought to govern things because it's already assumed to exist. Once again, we have come back to petitio principii."

Not really.

We can argue from faces appearing we have the alternative between governance and pareidolia.

We can argue that with certain things, like the Hubble smiley, pareidolia is really more farfetched than governance.

20. "We see entire shifting ecosystems, most of which have no evidence that they were created by the particular volition of an intelligent agent."

If evidence here means evidence of human agriculture, you are making it too narrow. Irreducible complexity in non-humanly controlled ecosystems or sub-systems of these (like fig trees and certain mosquitos) make a purely by chance development of the ecosystem very implausible, or rather impossible unless some credible scenario could be provided.

"We see beautiful rock formations, carved by wind and rain - and we don't generally assume that wind and rain are intelligent."

We can assume - and most of humanity does assume - there is intelligence behind wind and rain.

With very many rocks, Flood of Noah makes at least as good or better geological sense as wind and rain.

Obviously, a global Flood with one surviving packboat which as non-navigating doesn't break the waves and isn't broken by them and a land rise into mountain chains beforeto unknown so as to quickly drain the ground after the Flood is NOT what blind natural forces can achieve.

9. [Shouldn't Earth have lost all significant hydrogen long ago?]

"Believe it or not, the answer's 'no'."

Here is where I have two options : believing an expert, or asking for how this is measured or otherwise calculated.

"The point is, the "reserves" involved are far larger than th'art imagining, and being replenished by the release of hydrogen from various sources in parts of the Earth that aren't the atmosphere, mostly the crust."

I have nothing against Shakspearean English, are you usually using "th'art"? If you like to use Shakspearean, how about "th'imaginest" instead of "th'art imagining"? So many circumlocutions with -ing, known as progressive forms and the circumlocutions with "do" with negatives and questions have entered English (at least the latter ones) after Shakespear.

If you are not doing so regularly, but for me, know thou then that the rumour I am doing so for Swedish is simply false.

My Swedish is (though this won't be apparent to certain Swedes) more like insisting on English rather than American spelling. Or, for plural verbs, like using passé simple rather than passé composé in writing only. It is far more recent than Shakespear.

That said, should I stumble on a pre-Johnson spelling (as I did with epithete rather than epithet), I'll defend it as such.

1. I wasn't aware of the Swedish thing at all. I use thou and family all the time, because the singular-plural distinction is really useful. Although some people don't accept that, at which point I fall back on the "excuse" that I'm a Quaker and we basically never stopped.

In this case, by the way, I'd have used "than you're imagining" if I was you-ing rather than thou-ing; the choice of that over "than thou imaginest" doesn't arise from the use of "thou", just from my own speech patterns.

2. Oh, you are a Quaker!

Good for you, as far as linguistics are concerned!

Sorry for mistake!

3. No apology necessary. The thing for which I perceive thee to be apologising was much better than one of the more common responses, which is to claim that I'm just doing it to be a pretentious git. And while I am something of a pretentious git sometimes, that's nothing to do with why I use thou and family :-þ.

10. "Adding mass does not, in any scientific model since and including the Newtonian, reduce momentum. It reduces speed precisely because it does not reduce momentum. The momentum is conserved, so the increase in mass requires a decrease in speed."

Please reread all of my article. It should include some notion that momentum is reduced when the added mass comes in dust not sharing at first the velocity of Earth. Like friction.

So, the dust does two things with Earth and Moon : reduces momentum (because it has a momentum related to earth when arriving) and adding mass (because it is caught in atmosphere or lower, as for what is caught by moon, lower).

So, first there is a reduction of momentum, then there is an added mass, these are TWO factors, not just one, which reduce the speed.

A nice tip for you : if ever you think I misunderstood the actual physics (or what you were saying, as Damien Mackey of AMAIC did today!), reread what I wrote before saying I misunderstood anything.

" Even if we assume that the change in mass counts twice, once in direct-proportion reduction of orbital speed and again in direct-proportion increase of gravitational force (or vice-versa, if we're losing mass, which we are; the maths is fundamentally the same), and that it compounds multiplicatively, we get a figure that is in the millionths of one per cent."

With my calculations involving both reduced momentum by friction for Earth/Moon and added mass by the dust causing friction getting caught by gravitation of these bodies, we get a millionth of ten percent for balance gravitation to momentum, and a millionth of seventeen point five percent for the balance gravitation to speed.

I am not sure if you are familiar with Poincaré and his work on tides.

Why is the Lunar tide stronger than the Solar tide? With angelic or demonic or elvish or elementary spirits movers of the waves, we don't need to answer. But YOUR side needs an answer.

It is not that gravitation of Sun is weaker on Earth than graviation of Moon. It is that the tidal force of Moon is tronger than the tidal force of Sun, because the tidal force is the difference between two gravitation forces, the one at centre of earth, affecting all of earth as far as solids reach, and the gravitation on water either side of Earth being so much closer or further from pulling celestial body than the bulk of earth.

Now, this means that the tidal force per se is the difference between two gravitations, which is approximated by an inverse cubed law : G*M*m/d^3.

When the distances count one factor more, the lunar one is less diluting of pull than the solar one.

The reason tides go so high is therefore that this imbalance is acting time after time, moment after moment, on the waters.

1. Remember also that the dust, too, is in orbit. It's not static, because if it were it would fall into the Sun and not impact the Earth. As a consequence, it hits the Earth from all sides, so the net momentum imparted is very, very close to zero. Likewise, the mass lost from the upper atmosphere carries momentum away with it, too - but in all directions, so that the net change in momentum of the Earth is once again close to zero. Momentum as discussed here is a vector quantity, not a scalar - that is, we need to consider momentum using velocity, not just speed - so the direction is important.

2. " As a consequence, it hits the Earth from all sides, so the net momentum imparted is very, very close to zero."

It would be its weight multiplied by equal velocity as that of Earth.

Remember how you calculate friction!

The dust in the ground is not moving 60 mph anywhere, but it impacts the locked wheels with the 60 mph opposite direction of how car moves.

This means that an average per se zero velocity in friction calculus counts as an average velocity exactly equal and opposed to the one of the moving object.

" Momentum as discussed here is a vector quantity, not a scalar - that is, we need to consider momentum using velocity, not just speed - so the direction is important."

Implications?

3. Firstly, this isn't friction. It's not even quite comparable to atmospheric drag, which is also mostly not friction (common misconception), but I'll get to that in a moment.

Th'art quite correct. I miscalculated for a moment. The mean momentum imparted is equal to that of the mass of dust multiplied by the Earth's average velocity, because the differences cancel. However, all that means is that this dust doesn't change the net velocity at all! This is a very simple algebraic rearrangement: m[d]*v[d]+m[e]*v[e] == m[d]*v[e]+m[e]*v[e] == (m[d]+m[e])*v[e]. Thus no net effect on orbital speed. Gravitational force goes up, because mass does, but so does momentum, for the same reason and by the same ratio. Thus I don't even need, as I thought I did, to illustrate that eccentric orbits remain stable (though I'm still willing to do so if th'art unconvinced of this fact); the orbital parameters are in effect being multiplied by (m[d]/m[d]) == 1.

The only implications that are relevant of momentum being a scalar are those that lead us to conclude that the net velocity of all the dust relative to the Earth is zero at the time of impact, meaning that relative to the sun its net velocity is equal to that of the Earth, and hence the above.

11. Now, the imbalance of
< 10 000 001 : 10 000 000
for gravitation : momentum or of
> 10 000 002 : 10 000 000
for gravitation : speed would be acting, moment after moment on the orbit of Earth.

It would be active in each fluctuation of the orbit.

And since the orbit is not a straight line, but an ellipse, there are rather many of these. Each time there was an acceleration, i e each time Earth went either slower or faster but especially in a direction bending around the Sun, which is all the time, this imbalance of
< 10 000 001 : 10 000 000
or of
> 10 000 002 : 10 000 000
would be "felt" by the equilibrium of the system.

And you are saying this would NOT affect the stability of the orbit, just because the disequilibrium is very small? Look at tides, and how Poincaré explained these!

" Even if it's closer to one part per ten million, as thy figures have it, those numbers were based on the change in mass over 4,500,000,000 years (I just went back and checked; the ). That's per-age-of-the-Earth-so-far, not per-second or per-year. Bearing in mind that the projected lifespan of the Sun is about another 5,500,000,000 years, I don't think we need concern ourselves with an instability that will take 5-10,000,000 times 4,500,000,000 years, or on the order of 25-50,000,000,000,000,000 years."

That is presuming the instability will not affect the orbit until it becomes an instability of 2:1 or 3:2 or 11:10 or sth.

I am presuming the instability would be affecting the orbit at each act of acceleration, positive or negative or sideways, and that the very small disequilibrium, affecting these accelerations time after time, would end up pushing Earth into the Sun.

If Newtonian factors were all there were to it.

"But I think (and please correct me if I'm wrong) th'art rather claiming that the reason those ratios are a problem is not that they're the amount by which the Earth's orbital parameters change, but that if gravitation and speed aren't "perfectly balanced" the Earth's orbit must decay, and that they represent such an imbalance. This represents a fundamental misunderstanding of orbital mechanics: Any object moving fast enough to orbit and at a speed lower than the escape velocity of the thing it's orbiting will remain in a stable orbit. Slow the Earth down, keeping its distance from the Sun and its mass (I know, I know, but we'll come back to that) unchanged, and the opposite side of the orbit will fall. That changes the semi-major axis, which can be thought of as the average distance from the primary, though it's a tiny bit more complex than that. The resulting orbit is stable. The Earth is closer to the Sun, but it moves faster during the altered parts of its orbit than it otherwise would have, and so it has increased linear momentum during those parts of the orbit, which we can prove mathematically will mean it comes back to where it was on the previous orbit. Increase the mass, and the same thing happens. Increasing the mass and reducing the instantaneous speed will compound the effect, but the resulting orbit is still stable; the only times it wouldn't be are if the periapsis was inside the Sun's atmosphere (yes, the Sun has an atmosphere, though not a breathable or otherwise survivable one), at which point drag becomes a factor; and if the speed were increased (and mass decreased to the point where the Earth exceeded Solar escape velocity, at which point it would leave the Sun behind - but this would require an alteration of multiple orders of magnitude, not fractions of 1%."

The orbit is on such a view closer to the Sun, but how does this not involve gravitation getting even more of an upper hand?

12. "The orbit is on such a view closer to the Sun, but how does this not involve gravitation getting even more of an upper hand?"

Simple mechanics. As the planet moves closer to the Sun, it accelerates. Not just in the sense that its direction of motion changes, though this is certainly the case, but also in the sense that its speed (or, to put it another way, the magnitude of its velocity) increases. This is because in an elliptical orbit, the tangent is not perpendicular to the radius (except at apoapsis and periapsis), so the gravitational force can be understood as two perpendicular components: one acting normally-to-the-orbit (which causes the change in direction), and one acting tangentially (which causes the change in speed). As a consequence, the planet speeds up, and gains both linear and instantaneous angular momentum. This is lost again in the other half of the orbit, with a net result that when the planet returns to its "starting" position it has the same vector-momentum (in the reference frame of the primary) as the last time it was there.

That's in a two-body system. N-body gravitation will modify this slightly, which is fine - we observe approximately (I'll address this in a moment) the expected orbital aberrations in the the various bodies of the solar system that we'd predict on this basis. I say approximately because N-body gravitation, even under Newtonian rather than relativistic models of gravitation, requires iterative numerical solutions which converge, so we can produce extremely precise approximations but ultimately they technically are approximations. That being said, we've managed to calculate those for the solar system to greater precision than our actual limits of measurement for the bodies in question, and the data still fits. Indeed, this is how the existence of Neptune was discovered: Analysis of the aberrations in the orbit of Uranus predicted its precise location, and it was found exactly there.

The point is that the increased gravitational pull alters the planet's momentum in such a way as to prevent it from spiralling. The maths is a little dense, so thou canst either look it up and run it thyself or take my word for it; the outcome will be the same. I invite thee to do the former, by the way; were I biased enough to lie about any of this it would be the only way to catch me out.

(irrelevant side-note: why does Blogspot prohibit correctly marking up quotations with <q> tags?)

1. This is why it is only the cumulative ratio so far that matters, or equivalently why that 10,000,001:10,000,000 applies only once, not iteratively.

2. "The point is that the increased gravitational pull alters the planet's momentum in such a way as to prevent it from spiralling."

And the explanation for this video is of course that the change in momentum (but none in electric attraction) is much greter than our

10 000 001 : 10 000 000?

This video here:

[ISS] Don Petit, Science Off The Sphere - Water Droplets Orbiting Charged Knitting Needle
Space Videos

Just before 0:58 one drop had touched the needle.

3. I did explicitly state (in a previous comment) that the orbit is stable only outside of an atmosphere. Even before I've watched the video (additional comment to follow once I have) I can answer that while that experiment took place in microgravity (due to being on the ISS) it did not take place in vacuum or the near-vacuum of space. Combine this with the fact that atmospheric drag has much more effect on small bodies (it increases with the square of volume, but mass, and therefore the reciprocal of acceleration, increases with the cube and thus quickly outstrips it) and we have an easy explanation.

4. Update: Yup, that's exactly what I would have expected.

5. I was comparing atmosphere to dust and also to meteorites which come in each year.

6. You see, Newton was probably counting, like Galileo, on complete vacuum, no dust, not much meteorites, perhaps just the gravitational disruption of comets.

7. Yes, I got the comparison between the dust and the atmosphere, and I tried to explain why it doesn't scale: because force is mass multiplied by acceleration, and thus acceleration is force divided by mass, and drag forces increase with the square of linear size (that is, with surface area), while mass increases with the cube of the same (that is, with volume). The limit as x tends to infinity of x²/x³ is zero: a divisor of x³ will very quickly dominate a multiplier of x², so while drag can dominate at the scale of water droplets, at the scale of planets it is reduced to negligibility. Just to prove it, let's go with numbers: suppose the atmosphere slows the water droplet by n metres per second per second, and suppose just for the sake of argument that the Earth encounters as much drag per unit surface area as the water droplet does (it doesn't, because space dust is far less dense than air-on-the-ISS, but I'll alter the model in thy favour). Now, a water droplet masses on the order of a gram, and the earth on the order of 6*10^24kg, or 6*10^27g. To make the numbers easier, I'd round that to 1*10^28, but let's go in thy favour again and call it 1*10^27. Actually, I'm glad I did it that way, because I'll be taking a cube root momentarily. So our mass ratio is very approximately 1:10^27. Now, to get our drag ratio, we take the cube root (to get a linear-size ratio) and then we square it. The cube root of 10^27 is 10^9, and the square of that is 10^18. So now we're looking at 1:10^18 (for an area ratio which is directly proportional to drag ratio). Now we look at the equation of motion, which says that acceleration is force divided by mass, and we plug in our force and mass ratios: (1/1):((10^18)/(10^27))==1:(1/(10^9))==1:(10^-9). So the Earth would be experiencing - in a model deliberately adjusted to better support thy claims an acceleration of one billionth of that of the droplet (in the reference frame of the primary for each). Now factor the relative starting velocities (in the same reference frames) and this becomes even more negligible.

8. You recall how many months this was ago?

Well, I came up with another point.

The Sun is presumably losing mass all the time, at least when emitting alpha particles.

This means, the gravitation of the Sun is also changing.

Does this affect things?

And if so, how?

13. "(irrelevant side-note: why does Blogspot prohibit correctly marking up quotations with <q> tags?)"

Only tags allowed in comments : a, i, b.

1. It does also allow <em> and probably <strong> (let's find out!), but these are effectively synonyms for <i< and <b< respectively, so...

I still think blocking <q> was pointless.