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 field g 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 field g at some position 7' is g = -(GNm/r²) f.) (a) Compute the flux of the gravitational field through a spherical surface of radius r, and verify that the gravitational analog of Gauss's law is Þ₂ = fg. dà = -47Gymencl- (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational field, 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, ME, and RE.
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 field g 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 field g at some position 7' is g = -(GNm/r²) f.) (a) Compute the flux of the gravitational field through a spherical surface of radius r, and verify that the gravitational analog of Gauss's law is Þ₂ = fg. dà = -47Gymencl- (b) What do you think is the differential form of Gauss's law for gravitation? (c) Determine the gravitational field, 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, ME, and RE.
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Transcribed Image Text: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 g 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 g = - (GNm/r2)î.)
(a) Compute the flux of the gravitational field through a spherical surface of radius
r, and verify that the gravitational analog of Gauss's law is
dÃ= -4nGNMencl-
6.
(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 < Rp, where Rp 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 Rp.
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