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## Main Question or Discussion Point

I'm trying to make a program which makes use of Newton's law of universal gravitation to model planetary motion.

I've set up a system very similar to the earth-sun system (i.e., masses and distances are similar to the actual earth-sun system). When I run the simulation, the "earth" orbits the "sun" just as it should.

Likewise, I made a earth-moon system, and the moon orbits the Earth just as it should.

However, when I put the two systems together and make the earth orbit the sun while the moon is orbiting the earth, the moon slingshots around the earth and doesn't return.

To determine the initial velocity of the satellite (in both systems), I use the equation for acceleration from uniform circular motion:

[tex]a = \frac{v^2}{r}[/tex]

Substituting this into Newton's law of universal gravitation (using "m a" for "F"), and solving for v yields:

[tex]v = \sqrt{\frac{G \cdot m}{r}}[/tex]

I suspect that the moon needs a different initial velocity since its motion must be a spiral around the sun... but I can't figure it out.

I'd greatly appreciate any help anyone can give... or if someone can point me in the right direction.

Thanks!

I've set up a system very similar to the earth-sun system (i.e., masses and distances are similar to the actual earth-sun system). When I run the simulation, the "earth" orbits the "sun" just as it should.

Likewise, I made a earth-moon system, and the moon orbits the Earth just as it should.

However, when I put the two systems together and make the earth orbit the sun while the moon is orbiting the earth, the moon slingshots around the earth and doesn't return.

To determine the initial velocity of the satellite (in both systems), I use the equation for acceleration from uniform circular motion:

[tex]a = \frac{v^2}{r}[/tex]

Substituting this into Newton's law of universal gravitation (using "m a" for "F"), and solving for v yields:

[tex]v = \sqrt{\frac{G \cdot m}{r}}[/tex]

I suspect that the moon needs a different initial velocity since its motion must be a spiral around the sun... but I can't figure it out.

I'd greatly appreciate any help anyone can give... or if someone can point me in the right direction.

Thanks!

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