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## Homework Statement

A baseball pitcher can throw a fastball at a speed of 150 km/hr. What is the largest size spherical asteroid of density rho=3 g/cm^3 from which he can throw the ball fast enough that it:

(a) escapes from the asteroid into heliocentric orbit?

(b) rises to a height of 50 km?

(c) goes into a stable orbit about the asteroid?

## Homework Equations

i think...

KE = 1/2mv^2 (kinetic energy)

PE = GmM/r (potential energy, gravitational)

Fc = mv^2/r (centrifugal force)

Fg = GmM/r^2 (gravitational force)

## The Attempt at a Solution

v = 150 km/hr ~ 42 m/s

rho = 3 g/cm^3 = 3000 kg/m^3

M = rho*V

V = 4/3*pi*r^3

(a) make KE = PE and solve for r, which i get r = v*sqrt(3/8*pi*rho*G) = 32439 m

(b) not sure...

(c) make Fc = Fg and solve for r, which i get r = v*sqrt(23/4*pi*rho*G) = 45876 m

Did I do (a) and (c) correctly, and how should I approach (b)? Many thanks!