force of gravity = G M m/R^2
if mass is m, what is escape speed from R, M
(1/2) m V^2 speed V at R = work done falling from infinity to R
(1/2) m V^2 = integral oo to R of F dr
(1/2) m V^2 = (G M m/R^2) dr
= (GM)(1/R)
V^2 = 2 G M/R
if R = 1/4 Radius earth
and mass = (1/2) mass earth
Vplanet^2 = 2 G .5 Mearth/(.25)^2 Rearth
so
Vplanet^2 = 8 times Vearth^2
Vplanet = 2.83 * Vearth
mass of planet is half that of earth and radius of planet is one fourth that of earth if we plan to send an artificial satellite from planet the escape velocity will be in km/s
1 answer
1 answer