Consider the gravitational force field F with G = m = M = 1 in 3D with the potential function being F(x, y, z): 1 (√x² + y² + z²)³ -x, -y, z). Show that the work done by the gravitational force as a particle moves from (x1, y₁, 2₁) to (x2, y2, 22) along any path depends only on the radii R₁ = √√√x² + y² + z² and R₂ = √√√x² + y² + z².
Consider the gravitational force field F with G = m = M = 1 in 3D with the potential function being F(x, y, z): 1 (√x² + y² + z²)³ -x, -y, z). Show that the work done by the gravitational force as a particle moves from (x1, y₁, 2₁) to (x2, y2, 22) along any path depends only on the radii R₁ = √√√x² + y² + z² and R₂ = √√√x² + y² + z².
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Transcribed Image Text:3.
Consider the gravitational force field F with G = m = M = 1 in
3D with the potential function being
F(x, y, z) =
1
(√x² + y² + z²)³ 3
(—x, —y, —z).
Show that the work done by the gravitational force as a particle moves
from (x₁, y₁, 2₁) to (x2, Y2, 72) along any path depends only on the radii
R₁ = √√x² + y² + z² and R₂ = x² + y² + z ².
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