## mercredi 31 octobre 2012

### F = GMm / R^2

 series: Sir George Darwin corrected Galileo on Tides F = GMm / R2 The Plot Thickens ... "'The high tide,' King Alfred said... ... 'The High Tide and the Turn.' " Correction to Previous For Math Freaks: I take it the gravitational constant is below zero ...Some Experimental Challenges

Before agreeing or disagreeing with conclusion of this video, I will resume the Mathematic aspect of this:
• F=GMm / R2 where according to Newton
• F=concrete item of gravitational pull
• G=gravitational constant
• M=mass of one object
• m=mass of other object, like earth
• R=radius=distance, but it is really R2 that matters.
• F for moon on earth = F for sun on earth (approx.), known from tides, if Sir George Darwin's theory is correct
• GMsm / Rs2 = GMmnm / Rmn2
• Rs = x*Rmn (both distances are known from trigonometric observation)
• Ms = y*Mmn
• y is some kind of function of x
• Either M is some kind of function of m=mass of earth and of G=gravitational constant
• m (mass of earth) and G (gravitational constant) are not distinguishable from each other.
• Since the Sun is so much further away than the Moon, the Sun must for exercising same gravitational pull on earth have a much greater mass than the Moon.

The place which Newton gives the above equation is noteworthy: he is using it as if orbits of "planets including earth around the sun" depended solely on initial speed and gravitational pull. As if you could get the masses from the laws of Kepler (who was also a Geocentric), because masses are there considered the essential causation of planetary orbits.

If that were true and known to be true:
• Ms in the other equation for Sun and Earth would of course equal Ms in corresponding equation for Sun and Mercury, Sun and Venus, Sun and Mars, Sun and Jupiter, Sun and Saturn and so on since a mass is identic to itself and does not vary according to what other mass is involved
• And you would be able to make a ratio between Msol and mtellus
• And from mass of sun to other masses in solar system
• Which is what Laplace offered

But as Christians we do not know that causation to be the true one, sice we cannot exclude angels. Just as a Shintoist cannot exclude Kamis. Just as a Pagan of Greek school cannot exclude the Pantheon. (Abstracting now from the fact that Shintoists and Greek Pagans are wrong about the moral nature of such spirits and that we Christians know all spirits above earth atmosphere to be unfallen angels devoted to worshipping their and our Creator who is also our Redeemer).

If F=GMm / R2 were the only relevant cause of movements of a football, with M=mass of earth (this time) and m=mass of socker ball and distance=0 or approximately so, then we would predict that on a flat field (the field must be flat: otherwise we could not call distance 0, since another part of slope would be closer to earth even if both are on earth) the ball would not move.

Ask Zlatan and Maradona if socker ball movements are determined only by F=GMm / R2 or if personal wills are involved as well!

Not only we who believe there are spirits cannot use the Newtonian interpretation of Kepler's laws as indicative of the masses, since we cannot exclude spirits involved in moving heavenly bodies, but we do not even know if left to itself - without any guiding spirit - such a mechanism would work. The orbits are supposed to be a balance between two forces, inertia and gravitation. We know something about balancing forces in bikes: and if the guiding purpose of a bike is either absent or absent minded or just not sufficiently muscular or quick or whatever, the bike won't continue to go forward and keep its balance.

Even if orbits are mostly determined by the two forces supposed by Newton-Laplace, it does not follow that there is no God powerful enough to keep earth still or stars and the whole solar system spinning around it daily.

We do know that any spirit even powerful enough to guide a planet in an orbit must be far more powerful than man. It does not follow that man is supposed to worship it. St Thomas Aquinas said in a sermon about the Creed that those who worship heavenly bodies are similar to a pauper who goes to pay the King a visit, but mistakes the first valet for the King, because he has very fine clothes.

Hans-Georg Lundahl
Paris: Audoux
All Hallows Eve
31-X-2012

#### 4 commentaires:

1. When going over the formula after writing, I concluded that:

GMsm / R(s)^2 = GMmnm / R(mn)^2

reduces to:

M(s)= M(mn)R(s)^2 / R(mn)^2

always supposing of course the current gravitational explanation of tides being the right one.

One should also for the "=" read the curvy variant (approximately equal to).

2. It would then seem that the Sun is
497 point 8 times as far away
as the Moon in a mean, and that the Sun's mass would be square that number as many masses of the Moon,
i e 247 thousand 804 point 84 times as massive.

I calculated from a mean distance of 149,098,261 km of Sun to Earth and from a mean distance of 384,990 km of Earth to Moon.

In the video it is said that sun may have less mass than earth, but if moon is 1/81 of earth's mass that would not be so.

My solution for Geocentrism, without excluding Sungenis' is that masses are not all there is to it, see above, his is that the Sun and Earth would indeed behave Heliocentrically if alone in the Universe, but as they are not ... his solution is basically that the Universe circulates around a hollow without any significant mass, but that by Divine choice earth is upheld in that hollow and would immediately be pressed back to its place if trying to move.

3. I worked out mass relations between Sun and Moon according to French wiki, and it makes the Sun
2 million 700 sth thousand times as massive.

Either one calculation is wrong or there is a discrepancy between tides and the other ways of calculating their relative masses.

Or the not quite equality in gravitational pull gives that great a discrepancy? Is that Mathematically possible?

4. Actually no. The difference of masses between Sun as given and Moon as given and the number of Moon masses per Sun mass I calculated is more than 10:1. That should mean a difference of 10:1 in gravitational pull also.