Physics of a geocentric model?

Question

--------------------------------------------------------------------------------

I know that we can model a Geocentric "solar system" mathematically, with the Sun orbiting the earth and the other planets somehow spiralling round the orbiting Sun.

I imagine though that physics tells us that that cannot be the case, that the model is "innacurate" or impossible as things stand. For if the Sun (and planets) were to orbit the Earth daily, the Earth would have to have one hell of a (mass related) gravitational pull to hold such a massive and fast moving body as the Sun in orbit.

What would that (Earthly) mass be if it could hold the Sun in orbit? What calculations would I (or you) have to use to determine that? (Perhaps skip the last question, as I've seen Wikipedia's Analysis of Orbital Motion and given up right away).

How dense would it be, if it's size remained the same, and what would it be compared to, a Black Hole, collapsed dead star or Red Dwarf or something?

Everything on the Earth's surface would collapse, right, underthe G-force?

I even bet that the Geocentric model couldn't possibly be true, even if we could tamper with the masses of the Sun and planets, because with changed relative masses, the current dynamics would break down entirely. Right?

I thank anyone who can help educate me, so that I can educate others

Answer 1

Actually, a geocentric model is still used (mathematically) in many calculations relating to celestial mechanics (e.g., marine navigation). We all know that it is not the true representation, but the math works and it is easier to apply the corrections (because they are based on what we see as "fixed" observers).

We stand on top of the Earth and we are the centre of the universe. The sky rotates once per day with the Sun at 15 degrees per hour and the stars at 15.042 deg. per hour. Panets have a cyclical offset to this rate (equivalent to the epicycles of old).

If the ship moves, then the entire sky is tilting at a rate (and direction) corresponding to the mirror of the ship's course and speed.

---

Up to Galileo's time, the view was in the opposite direction to the one you want to take:

Of the four elements, Earth was the densest, followed by water, air and, the lightest, was fire.

The Sun, being obviously made of the element fire, was very light (unintentional pun) and could not be the centre of the universe. It was clearly Earth, being made of earth and water, which was the densest and was, therefore, the centre.

Predictions made using the geocentric system with all its circles and epicycles were relatively accurate. When Copernicus suggested a mathematical model, placing the Sun at the centre, he claimed that the equations would be easier to use.

They were, but since he kept the perfectly circular orbits, his predictions were not more accurate than the earlier model. Even though we credit him with giving us the heliocentric model, he did not. He, himself, stated that his was simply a mathematical trick to derive simpler equations.

Kepler designed a more precise model by placing the Sun at the centre and using elliptical orbits. Isaac newton confirmed it by explaining how gravity could act at a distance -- the idea of forces acting at a dstance was (and still is) contrary to the common principles of physics.

Galileo did NOT prove Kepler's system by finding moons to Jupiter (if anything, this would have been a demonstration of a Joviocentric system). The idea that not everything orbited the Earth was already accepted since Mercury and Venus were often shown as orbiting the Sun (which was orbiting Earth).

---

In any system, when one body orbits another, they actually orbit their common centre of mass.

The easy way to calculate where the centre of mass is is to place your zero marker at the centre of one mass. Then the moments are:

mass times distance

If we set our zero at the centre of the Sun; we'll use Earth masses and Astronomical units as our units.

Sun: 332946 * 0 = 0
Earth: 1* 1 = 1

Total moment = 0+1 = 1
Total mass = 332947

Distance of centre of mass from 0 =
1/332947 AU = 0.000003 AU = 450 km from the Sun's centre.

So, increase the Earth's mass until the centre of mass is at least closer to Earth than to the Sun.

This would make the Earth at least 332946 times more massive than it is now. If you don't change the radius, then escape velocity from the surface would be 332946 times 11 km/s, obviously more than 300,000 km/s (black hole!).

---

The pre-Galilean option might be better: reduce the mass of the Sun to below 1, then the centre of mass will be closer to Earth.

Answer 2

Well you have answered your own question.
Before Isaac Newton, nobody had any idea what made the planets move the way they do. People like Ptolemy and Copernicus and Kepler just came up with math that could explain where and how fast the planets moved, but nobody had any clue WHY they moved that way. That is one reason the heliocentric models were not more easily accepted. But when Newton's universal law of gravitation explained it all, it just because crystal clear that the heliocentric theory was the only one that could possibly be correct.