posted by Katie .
A satellite moves on a circular earth orbit that has a radius of 6.68E+6 m. A model airplane is flying on a 16.3 m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.
The satellite's centripetal acceleration at orbit radius R can be derived from using
a(sat) = G*Me*R^2,
(where G is the universal gravity constant and Me is the earth's mass), or by using
g(R)*(Re/R)^2 = 9.8*(6370/6680)^2
= 8.9 m/s^2
Set that equal to
where r = 16.3 m, and solve for V of the model plane