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315. Problem 29.11 (RHK) “Gauss’ law for gravitation” is
where m is the enclosed mass and G is the universal gravitational constant. We will derive Newton’s law of gravitation from this and explain the significance of the minus sign. |
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Solution: Click For PDF Version Consider a Gaussian sphere, a sphere of radius r centred at the mass
point of mass, m. We assume that the gravitational field
We calculate the gravitational flux under the above assumptions. It will be
The Gauss’ law for gravitation is
We therefore have
And
which is the Newton’s law of gravitation. The significance of minus sign in the Gauss’ law for gravitation is that the gravitational field due to a mass point is radial and is attractive. |
due to the mass point is radial and its magnitude is equal for all points at a
distance r from it but the direction of the gravitational field varies
and is toward the mass point.
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