22/09/2022
Derivation of equation of escape velocity:
For a body( rocket) to leave the Earth's surface ( astronomical body) , work in form of kinetic energy must be done on d body.
Recall that F= Gmem/r² and distance =r
Work done = kinetic energy
Work = force x distance
W = Gmem/r² x r = 1/2mv²
Gmem/r =½mv²
Dividing throughout by m
Gmem/r/m = ½mv²/m
Gme/r = ½v²
But me ( mass of the earth) = gr²/G
G(gr²/G)/r = ½v²
gr =½v²
2gr = v²
Let v =Ve and r =R
2gR = Ve²
Taking the square roots of both sides
√2gR =Ve
Ve = √2gR
