Calculate the ratio of the escape velocities from the moon and Earth.

Question

Calculate the ratio of the escape velocities from the moon and Earth

In order to escape the gravitaional pull exerted by a central body on an orbiting object, it must must achieve a minimum inertial velocity relative to the central body. This velocity is called the escape velocity. You can determine the minimal escape velocity required to escape from any planet yourself. Escape velocity from a planet is given by Ve = sqrt[2µ/r] where Ve = escape velocity in feet per second, µ = the planet's gravitational constant, ft.^3/sec.^2 (equal to GM where G = the Universal Gravitational Constant and M = the mass of the planet), and r = the radial distance from the center of the planet in feet. For the earth, µ = 1.407974x10^16 and r = 3963 miles = 20,924,640 ft. so the general escape velocity, direct from the surface, would be Ve = sqrt[2(1.407974x10^16)]/20,924,640 = ~36,685 ft./sec. = ~25,007 mph.

The same calculation can be made for the moon using µ = 1.731837x10^14.

Divide the two and you will have your ratio.