Orbits

[bperet]

The Reciprocal System can be though of as "scale invariant," in that the SAME RULES apply, regardless of how big or small a compound or aggregate motion is. In other words, the same rules that keep the atoms of molecules stuck together, also keep planets around the sun stuck together, and moons around the planets.

One can extrapolate the astronomical relations from the latter half of Nothing But Motion, regarding chemical bonds, but here is a simplification to get the general idea. There are three components that come into play:

1. The progression of the natural reference system, the "default" condition of the Universe that wants everything to fly apart at the speed of light (outward, scalar motion), from atoms to galaxies. This is observed astronomically as the "Hubble Expansion."
2. Gravitation, a linear, inward pull in 3D space that originates from the temporal rotating systems of atoms. Gravity wants to do the opposite of progression: pull things together at the speed of light.
3. The Gravitational Limit (unit space boundary of atoms), where the effect of gravity has dropped below one, natural unit and therefore can no longer have an inward effect on the default, outward progression of motion. Note that the RS is "discrete" or quantized... speed is taken as a "floor" function (truncate the fractional parts), so once you hit 0.999, you are at zero. This means that gravitation is not infinite--it has a limited range.

Earth-Moon System

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It is all about balance... if you try to pull the moon out of orbit (as is), the pull of gravity will increase, pulling it back to its old position. If you try to push it closer, the push of progression will increase, pushing it back to its old position. This is exactly the same as molecular bonding.

To aid in understanding, I came up with this simple analogy:

Example of staying in place

RSI-Orbits.png (833.95 KiB) Viewed 36119 times

In this example, the river is flowing downhill from a mountain, so the further up you go, the faster it flows. This is analogous the the progression of the natural reference system and why we see "galaxies" moving closer to the speed of light, the further away they are.

You can only paddle so fast, so the further you go upstream, you will eventually be stopped by the increasing rate of flow of the river and will not be going anywhere. If you start to drift downstream, each stroke of the paddle has more effect (river is flowing slower), pushing you upstream, back to that point where you go nowhere, fast.

It is that simple. (And I'm kidding about the gravitational wave generator... )

[Horace]

So in RST the radius of the orbit is the result of a stable equilibrium and in the LST the radius of orbit is the result of an unstable equilibrium, because it relies only on gravity and inertia/centrifugal force ...and gravity weakens with distance ( it does not act as a stretched spring - it acts as a stretched string of the chewing gum ).

Have you ever tried to twirl a rock on a string of chewing gum ... ?

[bperet]

Have you ever tried to twirl a rock on a string of chewing gum ... ?

Can't say that I have.

But I do remember the old astronomy programs that based orbits on a balance of forces... let them run overnight, and by morning, Pluto was swinging inside the orbit of Mercury because of accumulated errors of precision. That, alone, says a lot... if the balance has to be that perfect, just ONE earthquake should throw the planet out of orbit.

Remember that this concept is scale invariant... you can replace the Earth-Moon system with a molecule, such as NaCl (salt), replace the Moon with sodium and the Earth with chlorine, and all the math comes out the same--just on a different scale.

Also understand that the "law of gravitation" is wrong... F = Gm₁m₂/r². It is actually a logarithmic relation. Gopi has worked out the details for the planets with logs, and the results are quite interesting. Perhaps he can share his findings here.

[Horace]

Also understand that the "law of gravitation" is wrong... F = Gm₁m₂/r². It is actually a logarithmic relation.

Yes and this force still gets weaker with distance, just like a string of used chewing gum gets weaker, the more it is stretched.

[Horace]

I would appreciate if you would help me identify the qualitative differences between gravity and the the force acting on coins/marbles in the "vortex" machine depicted in the video below:
https://youtu.be/bGN1GicCkwk

I have a feeling, that even if there were no friction nor air resistance, that "vortex" would not act on the coins/marbles the same way as gravity does. There is some significant qualitative difference that I don't seem to be able to put my finger on. .
I suspect that without friction and air resistance, the coins/marbles would always form stable equilibriums (orbits) in the "vortex" machine, but with gravity alone - they would not (not even in vacuum).

I need this for a discussion with someone else...

P.S.
For this purpose, let's not discuss the real case where gravity forms a stable equilibrium with the outward progression. The comparison must be made only between the behavior of the "vortex" machine and gravity ALONE.

[bperet]

Yes and this force still gets weaker with distance, just like a string of used chewing gum gets weaker, the more it is stretched.

And, due to the "discrete unit" postulate, it breaks at a certain point and can no longer provide an elastic return.

I suspect that without friction and air resistance, the coins/marbles would always form stable equilibriums (orbits) in the "vortex" machine, but with gravity alone - they would not (not even in vacuum).

If there were no friction/resistance, the coin/marble would not rotate, it would just slide like any flat object. It's speed would not decrease sufficiently to deflect around the corner, and would most likely just fly out.

[duane]

hi Bruce,

if the moon's gravity is enough to cause the oceans and the ground to distort
what does the Earth's gravity do to the lunar surface?
would the liquid in a barometer-type instrument on the moon
rise during the "full earth"
and fall during "new earth"

[bperet]

if the moon's gravity is enough to cause the oceans and the ground to distort what does the Earth's gravity do to the lunar surface?
would the liquid in a barometer-type instrument on the moon rise during the "full earth" and fall during "new earth"

The moon DOES have a "tide," but because it is made of green cheese instead of water, it moves a LOT slower.

Tides are backwards... it isn't the moon's gravity pulling on Earth, but the reduction of the pull of gravity in the dimension that is coincident with the line between the Earth and Moon. Works the same was as thermal motion causing the states of matter. You can think of it as an antigravity beam being shot from the neutral point, through the Earth. Where that beam (a bivector) hits the Earth--and where it comes out the other side--reduces the pull of gravity allowing the progression (outward) to have a stronger effect, which lifts the ocean at that point.

The moon would have tides, if there was something to move--and if you look at a topography map, you will see that some of the highest altitudes are on the line that points right through the center of the visible moon. But the moon is also influenced by a number of other factors, so the effect is not really noticeable.

And note that the lunar tidal force is smaller than Earth, because it is a reduction of gravity from the neutral point, not a bigger Earth pulling on it.