Throwing a baseball while standing on an Asteroid

[takelgith]

Summary:: Between the orbits of Mars and Jupiter, several thousand small objects called asteroids move in nearly circular orbits around the Sun. Consider an asteroid that is spherically shaped with radius
r and density 2100 kg/m^3.

a.
You find yourself on the surface of this asteroid and throw a baseball at a speed of 28
m/s. If the baseball is to travel around the asteroid in a circular orbit, what is the largest radius asteroid on which you are capable of accomplishing this feat??

- For this I equated GMm/r^2 = mv^2/r and solved for r. I used the density to find M.
I got r = √[(28^2)/(2100π)(6.67^-11)]
it says its wrong!

 

[jbriggs444]

- For this I equated GMm/r^2 = mv^2/r and solved for r. I used the density to find M.
I got r = √[(28^2)/(2100π)(6.67^-11)]
it says its wrong!

Can you elaborate on the part where you used the density to find M?

 

[takelgith]

Can you elaborate on the part where you used the density to find M? You did it wrong.

So I had M = 2100π R^3.

Then I subbed that into the equation, for which the R got canceled and became R^2 and thus my result.

 

[jbriggs444]

So I had M = 2100π R^3

Where does that formula come from?

 

[takelgith]

So I had M = 2100π R^3.

Then I subbed that into the equation, for which the R got canceled and became R^2 and thus my result.

Oh shoot! Its supposed to be 4/3piR^3. So M= 2100 *(4/3 pi r^3) right? that should be right??

 

[jbriggs444]

Oh shoot! Its supposed to be 4/3piR^3. So M= 2100 *(4/3 pi r^3) right? that should be right??

I think so. I did not spot any other errors.