Why are most planetary orbits nearly circular?

Physics Problem circular orbits?

• This problem concerns the properties of circular orbits for a satellite of mass m orbiting a planet of mass M in an almost circular orbit of radius r. In doing this problem, you are to assume that the planet has an atmosphere that causes a small drag due to air resistance. "Small" means that there is little change during each orbit so that the orbit remains nearly circular, but the radius can change slowly with time. The following questions will ask about the net effects of drag and gravity on the satellite's motion, under the assumption that the satellite's orbit stays nearly circular. Use G if necessary for the universal gravitational constant. A. (i got this one) B. What is the potential energy U of the satellite? (Express you answer in terms of m, M, G, and r

• Answer:

  The potential energy (U) of any object is the product of its mass (m), the acceleration (g) due to gravity, and the height of the object (in the case of a satellite the height is equal to r): U = m(g)(r) However, using two of Newtons equations: F = m(g) and F = {G(M)(m)}/r² we can derive the equation for g by setting the right sides of the above equations equal to each other: m(g) = {G(M)(m)}/r² g = {G(M)}/r² Substitute this into the equation for U: U = m({G(M)}/r²)(r) U = m{G(M)}/r