Suppose mass of planet is M and mass of object is m. Object is r meters away from planet which is R+H where R is radius of planet and H is height. At any instance, object is x meters away from centre of mass of planet. According to Sir Issac Newton Gravitational force on object = ma = - GMm/x 2 a = - GM/x 2 dv/dt = - GM/x 2 dv/dt dx/dx = - GM/x 2 dx/dt dv = - GM/x 2 dx v dv = - GM/x 2 dx Integrating both sides v 2 /2 = GM/x + C At x = r, v = u u 2 /2 = GM/r + C C = u 2 /2 - GM/r = (ru 2 - 2GM)/2r Now, v 2 = 2(GM/x + C) v = - sqrt(2) sqrt((GM + xC)/x) dx/dt = - sqrt(2) sqrt((GM + xC)/x) dt = - 1/sqrt(2) sqrt(x/(GM + xC)) dx Let xC = GM tan 2 c x = GM/C tan 2 c dx = GM/C 2 tan(c) sec 2 c dc = 2GM/C tan(c) sec 2 c dc tan 2 c = xC/GM tan(c) = sqrt(xC/GM) sec 2 c = xc/GM + 1 sec(c) = sqrt((xC + GM)/GM) Putting in equation dt = - sqrt(GM/2C) sqrt(tan 2 c/(GM + GM tan 2 c)) 2GM/C tan(c) sec 2 c dc ...