Question

6. (10 points Extra Credit) Electrodynamics is not the only subject that utilizes Gauss' Law. We can also use it to study Newtonian gravity. The acceleration due to gravity (9can be written as, where G is Newton's gravitational constant and ρ is the m ass density. This leads us to the usual formulation of Newton's universal law of gravity,或刃--GM(f/r, as expected (if we assume V xğ-0). This "irrotational" condition allows us write (in analogy to the electric field), --Vo and Gauss' Law becomes Poisson's equation, Let the origin of Cartesian coordinates be at the center of the Earth and let the moon be on the z-axis, a fixed distance R away (center-to-center). The tidal force (also known as the Roche force) exerted by the moon on a particle of mass m at a point on the surface of the Earth (point r,y, z) is given by F:+2GMm R3 R3 Find the potential (1) that yields this tidal force. Can you write this in terms of the Legendre polynomials (you will need to draw a diagram)?

Answer 1

Solution Giuen Thod max ueeauution: oround Chaase So ds Gpuus naente (o Slade Thod divergence of eleto 2Jet vo Change densty povadifferent

Pandaycu of indushon 19 dt d L Anphere lau Skal-e That- Sum of The lengTh elern tHme