(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

above equation

3. The attempt at a solution

i cant get the answer right for this .. heres 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Gauss' Law for Gravitation

**Physics Forums | Science Articles, Homework Help, Discussion**