A test particle is moving in a circular orbit in the gravitational field produced by a mass density rho(r) =
K/r² . Identify the correct relation between the radius R of the particle’s orbit and its period T:
(A) T/R²
is a constant (B) TR is constant
(C) T²/R³ is a constant (D) T/R is a constant
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Explanation:
ANSWER
m=∫0Rρ4πr2dr
m=4πkR
v∝4πk
RT=4πk2π
s0 RT is a constant.
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