# Closest stable orbit of a body around earth

1. Apr 5, 2015

### AndrewC

1. The problem statement, all variables and given/known data
This is a problem I picked for my calculus one class that I would like to solve, then model the solution using the sandbox video game universe sandbox. I would like to calculate the closest stable orbit of the moon, if possible allowing for some eccentricity in the orbit making it an ellipse. If this is the wrong forum to post this in I apologize.
mass of moon = 7.348x10^22kg
Mass of earth = 5.97x0^24kg
Gravitational constant = 6.674x10^-11m^3kg^-1s^-2
Gravitational parameter of moon = G(m1+m2) = u = 4.03x10^14

2. Relevant equations
V=sqrt(u ((2/r)-(1/a)))
r = current distance from parent body
a = semi major axis of orbiting body
u = Gravitational parameter = GM if orbiting body's mass is small compared to parent body.
u = G (m1+m2) if orbiting body's mass is comparable to parent body.

3. The attempt at a solution
I'm not sure calculating velocitiy of tge moon or acceleration due to gravity is the best way to find the closest stable orbit? Looking for any input.

Last edited: Apr 5, 2015
2. Apr 5, 2015

### rcgldr

By stable orbit, it this considering low earth orbits are affected by the outer fringes of the atmosphere, so they are slowed down and the orbit is not "stable"?

3. Apr 5, 2015

### AndrewC

Sorry I needed to update all of the info. I'm specifically thinking of the moon. So this is not a very real world problem. It's so e thing I picked for fun for a math project.