(a) Suppose a projectile is launched vertically from the surface r = R of the earth with initial velocity v₀ = √2GM/R, so v²₀ = k²/R where k² = 2GM. Solve the differential equation dr/dt = k/√r (from Eq. (23) in this section) explicitly to deduce that r(t) → ∞ as t → ∞.

(b) If the projectile is launched vertically with initial velocity v₀ > √2GM/R, deduce that

Why does it again follow that r(t)  → ∞ as  t → ∞?

dr R dt k2 ta> k F