Question

3. We've primarily looked at closed orbits of planets, but a lot of what we've done can be used to treat projectiles and particle collisions under central forces. For example, a projectile of mass m is launched from a very large distance away with energy E toward a spherical planet of mass M >> m and radius R. Show that the maximum value of the angular momentum for the projectile to hit the planet is Imax = 2yR(1 + ER/Y), where E is the energy, y=GMm, and u is the reduced mass.

Answer 1

The angulan momentuun is maxiuum whon thuveloelte uet befane the cmpenet amol the raoliys ane penpenolieulan to eaoh omn Am mlo Cape mulan momentum,is Imax Imax The neng Just befane the Ampaat R Since 9t ts brojected wtm eneng E, Rom Campenvattan ennweet R (Imax R (Tm 2 2HR2 Iman E+ 2HR2 R 2R2E2URT Imax TmaR( RE Y

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