BBCode and First Order Equations Involving Gravity

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Let's work with algebra and circles to come up with approximate values, shall we?

Lets set some axioms:

1. Orbiting objects have mass and velocity.
2. Gravity holds these objects in their orbits.

With that said, the force of gravity is what keeps these objects in their, for this discussion, circles (i.e. gravity is the centripetal force.)

[align=center]F[sub]Gravity[/sub] = F[sub]Centripetal[/sub][/align]

The force of gravity is,

[align=center](G*m[sub]1[/sub]*m[sub]2[/sub])/r[sup]2[/sup][/align]

and centripetal force is,

[align=center](m[sub]2[/sub]*v[sup]2[/sup])/r[/align]

Together that is,

[align=center](G*m[sub]1[/sub]*m[sub]2[/sub])/r[sup]2[/sup] = (m[sub]2[/sub]*v[sup]2[/sup])/r[/align]

[align=center](G*m[sub]1[/sub]*[s]m[sub]2[/sub][/s])/r[sup][s]2[/s][/sup] = ([s]m[sub]2[/sub][/s]*v[sup]2[/sup])/[s]r[/s][/align]

[align=center](G*m[sub]1[/sub])/r = v[sup]2[/sup][/align]

Let's call m[sub]1[/sub] = m[sub]Sun[/sub] and the velocity that of Earth.

[align=center](G*m[sub]Sun[/sub])/r = v[sub]Earth[/sub][sup]2[/sup][/align]

For velocity of a planet with low eccentricity:

[align=center]v[sub]Earth[/sub][sup]2[/sup] = (G*m[sub]Sun[/sub])/r[/align]

For the orbit radius of such an object:

[align=center]r = (G*m[sub]Sun[/sub])/v[sub]Earth[/sub][sup]2[/sup][/align]

For the mass of the star that Earth orbits:

[align=center]m[sub]Sun[/sub] = (r*v[sub]Earth[/sub][sup]2[/sup])/G[/align]

For the Gravitational constant (which has been determined already by more feasible means):

[align=center]G = (r*v[sub]Earth[/sub][sup]2[/sup])/m[sub]Sun[/sub][/align]

Now, who would like to try these out?

G = 6.67*10[sup]-11[/sup] (N*m[sup]2[/sup])/kg[sup]2[/sup]

m[sub]Sun[/sub]= 1.99*10[sup]30[/sup] kg

r[sub]Earth[/sub] = 1.49*10[sup]11[/sup] m

r[sub]moon[/sub] = 1.74*10[sup]6[/sup] meters

m[sub]moon[/sub] = 7.35*10[sup]22[/sup] kg

Mass of Earth is derivable from the above, so I'll let that be figured out.