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Gravitational force due to a mass The gravitational force
Chapter 14, Problem 46E(choose chapter or problem)
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 \(U(r)=\frac{G M m}{r}\), where G is the gravitational constant and \(r=\sqrt{x^{2}+y^{2}+z^{2}}\) is the distance between the masses.
a. Find the components of the gravitational force in the x-, y-, and z- directions, where \(\mathbf{F}(x, y, z)=-\nabla U(x, y, z)\).
b. Show that the gravitational force points in the radial direction (outward from point mass M) and the radial component is \(F(r)=\frac{G M m}{r^{2}}\).
c. Show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of U.
Questions & Answers
QUESTION:
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 \(U(r)=\frac{G M m}{r}\), where G is the gravitational constant and \(r=\sqrt{x^{2}+y^{2}+z^{2}}\) is the distance between the masses.
a. Find the components of the gravitational force in the x-, y-, and z- directions, where \(\mathbf{F}(x, y, z)=-\nabla U(x, y, z)\).
b. Show that the gravitational force points in the radial direction (outward from point mass M) and the radial component is \(F(r)=\frac{G M m}{r^{2}}\).
c. Show that the vector field is orthogonal to the equipotential surfaces at all points in the domain of U.
ANSWER:Solution 46EStep 1