A spherical asteroid with radius of 9.40 km has uniform density 3500 km/m^3. Find the gravitational acceleration at the asteroid's surface.

I have found the mass of the asteroid by multiplying the found volume and given density. This gives me a result of 1.22*10^6 which I then adds to the equation g=GM/r^2. I get a result of 9.2 * 10^-3, which the site says is wrong. Anybody has any clue as to what I am doing wrong? I have converted the radius to meters for both the volume and g part.

Question

A spherical asteroid with radius of 9.40 km has uniform density 3500 km/m^3. Find the gravitational acceleration at the asteroid's surface.

I have found the mass of the asteroid by multiplying the found volume and given density. This gives me a result of 1.22*10^6 which I then adds to the equation g=GM/r^2. I get a result of 9.2 * 10^-3, which the site says is wrong. Anybody has any clue as to what I am doing wrong? I have converted the radius to meters for both the volume and g part.

anonymous · Answer

Units of uniform density doesn't make sense. Is it kg/m^3?
Mass of the asteroid is Volume x Density, don't forget to change the units.

mos1635 · Answer

mass 1.22  10^ not 6
try again

shayaan_mustafa · Answer

I am supposing that your given data is
$$r=9.40km=9400m$$$$\rho=3500\frac{kg}{m ^{3}}$$now use formula$$g=\frac{GM}{r ^{2}}-----(1)$$use density formula$$M=\rho*V$$$$M=\rho*\frac{4}{3} \pi r ^{3}$$your equation 1 will be then.$$g=\frac{G*\rho*4 \pi r }{3}$$substitute values and your answer will be $$g=9.19*10^{-3}m/s ^{2}$$



But remember this answer is using assumptions. because your density unit is wrong as Ishaan94 said.

shayaan_mustafa · Answer

so check your units because my and your answers are same.

anonymous · Answer

Thank you for your help.