What is the largest diameter of an asteroid with a density of 2 gm/cm^3 and an...

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taybaxter

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...escape velocity of 40 m/s?

I need to know what the diameter is of the largest asteroid (with density of 2 gm/cm^3) from which one could launch a ball into space.

The escape velocity of said asteroid would be 40 m/s.

I figure that I need to plug it into this equation for velocity:

Ve=sqrt(2GM/r)

WHERE:

40 = sqrt (2 GM/r)

If I calculate radius I will know the diameter but I need a mass of the asteroid to do that. I need to know how to use the density to find the mass. D=M/V however I can't calculate the mass without the radius....

So I have the escape velocity and the density but I do not have a mass.
 
You started correct:
(1) Ve=sqrt(2GM/r) = 40 m/s

with r=radius of asteroid
and M=mass of asteroid

M=volume * density
M=4/3*Pi*r^3 * density

Now replace M in (1) and solve the equation to r
 
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