The baseball pitcher on an asteroid

[buzz3]

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!

 

[Ratpigeon]

For part (b) you should use the equation PE=mgh (where m is the mass of the object, g is the gravitational force on the object, and h is the height of the object) You know what the initial kinetic energy is, and that at the peak of the throw; the potential energy will be equal to the the initial potential energy.
I'm afraid that I'm not sure about the other two though...

 

[SHISHKABOB]

B uses pretty much the same method as the other two, you just need to find the PE of the baseball at 50 km