Lloyd wrote:Bode's Law Thoughts
If Venus, Mars, Earth and the Moon used to be part of the Saturn system in that order, can you calculate how far each of them should have been apart, either at the heliopause or approaching Saturn's present orbit slowly from outside?
That would require a lot of knowledge that we don't have. One of the biggest factors would be the shape of the comas. We have a rough idea of the density of the interstellar medium. If we knew what kind of atmospheres the planets had, and how fast they were traveling, we could start guessing at the length of the comas, the robustness of which would determine the strength of the attractive force between the planets. In other words, if the planets are negatively charged, and the atmospheres are positively charged, and if the atmospheres are swept into comas by friction with the interstellar medium, you've got rubber bands connecting the planets, made of the attraction of negatively charged planets to the shared positive charge between them in the comas. How strong are the rubber bands? And what is the equilibrium point, where if the planets got too close together, their repulsion from each other would be stronger than their attraction to the opposite charge between them? I dunno.
Lloyd wrote:In the solar system, would the sizes of the planets have much to do with the charge on them and thus on the spacing between adjacent planets?
I guess that there could be a lot of factors. Venus is smaller than the Earth, but it appears to have more surface charge, with its highly electrified atmosphere. But I agree that charge would determine the spacing.
Lloyd wrote:Do you think the asteroids would collectively have enough charge to repel Mars and Jupiter over long periods of time? I imagine they'd have little effect on Jupiter.
No, but maybe Ceres did, before Theia hit it.
Lloyd wrote:Bode's Law of electric repulsion would apply to each planet's moons too, I suppose. Agree? And to the Kuiper belt objects?
Yes.
Lloyd wrote:Wouldn't such electric repulsion between orbiting objects help to circularize the orbits of Venus, Mars, Earth and the Moon within a thousand years, if they broke away from Saturn at Saturn's present orbit?
I "think" that it
would help circularize the orbits, but not in a thousand years. Halley's Comet was first observed in 240 BC, and has been observed a total of 30 times in just over two thousand years, and it has a highly elliptical orbit. My guess is that the circularizing would take at least 3.79 RLT, where RLT = "Really Long Time".
In other words, I don't have a clue, but my guess would be that it isn't in range for human memory.
Lloyd wrote:Have you thought about a better formula for Bode's Law that would take orbiting bodies' electric charges into account?
I could run my Debye cell code if it was just a static distribution. Of course, it isn't -- the planets are in orbit, and the forces between them are complex. Just roughly speaking, the ratio of the size of the planets to the distances separating them is in the same range as the size of the dust grains in space plasmas versus the size of the Debye cells.
earth diameter (km) = 1.27 × 10
4
distance between earth and venus (km) = 4.14 × 10
7
planetary diameter over distance = 3.08 × 10
−4
dust grain diameter (m) = 1.00 × 10
−4
distance between dust grains (m) = 10.00
dust grain diameter over distance = 1.00 × 10
−5
So that's within an order of magnitude. To get better numbers, I'd have to know the electrostatic profiles of all of the planets and their atmospheres. I guess I could just calculate it with all of them in line, and see if there is a net attraction or repulsion. Of course, we'd guess that they're in equilibrium, but it would be interesting to see the calcs (someday).