Introduction to Classical Mechanics · Problem 7.17

Angular momentum, Part I (Constant L) — Morin

Physics — Mechanics · gravity-kepler-laws

Problem

Parabola

L

** A mass

m

orbits around a planet of mass

M

in a parabolic orbit of the form

y = x^2/(4\ell)

, which has focal length

\ell

. Find the angular momentum in three different ways: ((a)) Find the speed at closest approach. ((b)) Use Eq. (7.30). ((c)) Consider the point

(x, x^2/4\ell)

, where

x

is very large. Find approximate expressions for the speed and impact parameter at this point.