Introduction to Classical Mechanics · Problem 1.9

Strategies for solving problems — Morin

Physics — Mechanics · escape_velocity

Problem

Escape velocity * The *escape velocity* on the surface of a planet is given by

v = \sqrt{\frac{2GM}{R}},

where

M

and

R

are the mass and radius of the planet, respectively, and

G

is Newton's gravitational constant. (The escape velocity is the velocity needed to refute the "What goes up must come down" maxim, neglecting air resistance.) (a) Write

v

in terms of the average mass density

\rho

, instead of

M

. (b) Assuming that the average density of the earth is four times that of Jupiter, and that the radius of Jupiter is 11 times that of the earth, what is

v_J/v_E

Related theory

escape_velocity

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