Consider a satellite in a circular orbit around the Earth. If it were at an altitude equal to twice the radius of the Earth, 2R_E, how would its speed v relate to the Earth's radius R_E, and the magnitude g of the acceleration due to gravity on the Earth's surface? B)v² = 2gR_E

Question

Quizplus · Accepted Answer

For a circular orbit, the gravitational force provides the centripetal force that keeps the satellite in motion. So, Fg = Fcp Therefore, G*MmMe / r^2 = mv^2 / r Here, r = 2R_E So, v = √(G*MmMe / r) Also, g = G*MmMe / r^2 (acceleration due to gravity on the Earth's surface) Therefore, v^2 = G*MmMe / r = g*r Substituting the value of r, we get: v^2 = g*2R_E Taking the square root on both sides, we get: v = √(g*2R_E) Therefore, the correct choice is C.

Consider a Satellite in a Circular Orbit Around the Earth