In Jules Verne’s original problem, the projectile launched from the surface of the earth is attracted by both the earth and the moon, so its distance r(t) from the center of the earth satisfies the initial value problem

where M_e and M_m denote the masses of the earth and the moon, respectively; R is the radius of the earth and S = 384,400 km is the distance between the centers of the earth and the moon. To reach the moon, the projectile must only just pass the point between the moon and earth where its net acceleration vanishes. Thereafter it is “under the control” of the moon, and falls from there to the lunar surface. Find the minimal launch velocity v₀ that suffices for the projectile to make it “From the Earth to the Moon.”

Transcribed Image Text:

d²r dt² GMe r.2 + GMm (S-r)2¹ r(0) R. r'(0) = vo