Escape velocity from the surface of earth depends upon mass of the earth and radius of the earth. Find the realtion between these quantities dimensionely.

Answer 1

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.