Question

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.

Answer 1

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
a(plane)= V^2/r
where r = 16.3 m, and solve for V of the model plane

Answer 2

thank you