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arl146
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Homework Statement
The gravitational field g due to a point mass M may be obtained by analogy with the electric field by writing an expression for the gravitational force on a test mass, and dividing by the magnitude of the test mass, m. Show that Gauss' law for the gravitational field reads:
[itex]\Phi[/itex] = [itex]\oint g\bullet dA[/itex] = -4*pi*G*M
Use this result to calculate the gravitational acceleration g at a distance of R/2 from the center of a planet of radius R = 8.05 × 10^6 m and M = 8.45 × 10^24 kg.
Homework Equations
above equation
The Attempt at a Solution
i can't get the answer right for this .. here's what i did
[itex]\Phi[/itex] = [itex]\oint g\bullet dA[/itex] = -4*pi*G*M
g[itex]\oint dA[/itex] = -4*pi*GM
g[4*pi*r^2] = -4*pi*GM
g[4*pi*(R/2)^2] = -4*pi*GM
g*pi*R^2 = -4*pi*GM
g = (-4GM)/R^2
and since r=R/2 the mass is halved also. therefore g = (-2*G*M)/R^2
i plugged in the values for G, M, and R .. and got -17.40267737 m/s^2 but its not right