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Gravitational force due to a mass The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = GMm/r, where G is the gravitational constant %3D and r = Vx? + y? + z² is the distance between the masses. a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x, y, z) = –VU(x, y, z). b. Show that the gravitational force points in the radial direction (outward from point mass M) and the radial component is F(r) = GMm/r². c. Show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of U.

Gravitational force due to a mass The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = GMm/r, where G is the gravitational constant %3D and r = Vx? + y? + z² is the distance between the masses. a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x, y, z) = –VU(x, y, z). b. Show that the gravitational force points in the radial direction (outward from point mass M) and the radial component is F(r) = GMm/r². c. Show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of U.

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Gravitational force due to a mass The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = GMm/r, where G is the gravitational constant %3D and r = Vx? + y? + z² is the distance between the masses. a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x, y, z) = –VU(x, y, z). b. Show that the gravitational force points in the radial direction (outward from point mass M) and the radial component is F(r) = GMm/r². c. Show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of U.
Transcribed Image Text:Gravitational force due to a mass The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = GMm/r, where G is the gravitational constant %3D and r = Vx? + y? + z² is the distance between the masses. a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x, y, z) = –VU(x, y, z). b. Show that the gravitational force points in the radial direction (outward from point mass M) and the radial component is F(r) = GMm/r². c. Show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of U.
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