Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law dependence on distance, a formula analogous to the formula for Gauss's law can be found for gravity. The gravitational ficld ĝ at a location is the force per unit mass on a test mass mo placed at that location. (Then, for a point mass m at the origin, the gravitational ficld g at some position 7' is j = – (Gym/r²) î.) (a) Compute the flux of the gravitational ficld through a sphcrical surface of radius r, and verify that the gravitational analog of Gauss's law is dÃ= -4TGNMencl· (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational ficld, g, a distance r from the center of the Earth (where r < RE, where RE is the radius of the Earth), assuming that the Earth's density is uniform. Express your answer in terms of GN, the mass of the Earth, МЕ, and Rg.

Because the formulas for Coulomb's law and Newton's law of gravity have the same inverse-square law dependence on distance, a formula analogous to the formula for Gauss's law can be found for gravity. The gravitational ficld ĝ at a location is the force per unit mass on a test mass mo placed at that location. (Then, for a point mass m at the origin, the gravitational ficld g at some position 7' is j = – (Gym/r²) î.) (a) Compute the flux of the gravitational ficld through a sphcrical surface of radius r, and verify that the gravitational analog of Gauss's law is dÃ= -4TGNMencl· (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational ficld, g, a distance r from the center of the Earth (where r < RE, where RE is the radius of the Earth), assuming that the Earth's density is uniform. Express your answer in terms of GN, the mass of the Earth, МЕ, and Rg.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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