The gravitational field g due to a point mass M may be obtained byanalogy with t

Question

The gravitational field g due to a point mass M may be obtained byanalogy with the electric field by writing an expression for thegravitational force on a test mass, and dividing by the magnitudeof the test mass, m. Show that Gauss' law for the gravitationalfield reads:
=
(integral)

g ·dA = 4GM Use this result to calculate the gravitational acceleration g at adistance of R/2 from the center of a planet of radius R = 5.0× 106m and M = 9.0 ×1024kg.

**WORK

I am using the formula g(r)=-GM/R^2 and plugging in:

-(6.67x10^-11)(9.0x10^24)/((5.0x10^6)/2)^2

this is not coming out to be the correct answer though.. help! =
(integral)

g ·dA = 4GM

Explanation / Answer

the problem is with your mass because you are 1/2 the distance from the outer edge, not allthe mass is contributing to your gravitational acceleration. =mV=(m)*(4/3r^3) For your new mass: =m'V=m'[4/3(1/2r)^3] density is equal so set them equal to eachother solve for m' Your new mass: m'=1/8m plus this back into your equation you showed above: g=-G(1/8M)/(1/2R)^2 This will give you the right answer. I just used it for ahomework problem and got the right answer

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