Find an expression for the square of the orbital period. Express y

Teddy Dillard

Teddy Dillard

Answered question

2022-01-11

Find an expression for the square of the orbital period.
Express your answer in terms of G, M, R, and π.
The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by
U=−G*Mm/R.
What is the kinetic energy K of the satellite?
Express your answer in terms of the potential energy U.

Answer & Explanation

Vivian Soares

Vivian Soares

Beginner2022-01-12Added 36 answers

(a)The gravitational force must balance the centripetal force acting on the planet.
The velocity of the planet is,
FG=FC
GMmR2=mv2R.(1)
v=2πRT(2)
Substitute equation (2) in equation (1),
Rewrite the above expression for time period.
GMmR2=m(2πRT)2R
GMmR2=4mπ2R2T2R
GMR2=4π2RT2
T2=4π2RGM
Neunassauk8

Neunassauk8

Beginner2022-01-13Added 30 answers

(b)
The potential energy of an object is,
The gravitational force must balance the centripetal force acting on the planet.
U=GMmR(3)
FG=FC
GMmR2=mv2R
v2=GMR
The kinetic energy of the of the object is,
Rewrite the equation (4) by substituting equation (3) to find an expression for kinetic energy of a satellite in terms of potential energy.
K=12mv2
=12m(GMR)
=GmM2R(4)
K=12U

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