A satellite is orbiting the earth in a circular orbit of radius `r`. Its

Options

A. kinetic energy veries as `r`
B. angular momentum varies as `r^(-1)`
C. linear momentum varies as `r^(2)`
D. frequency of revolution varies as `r^(-3//2)`

Answer

D

Explanation

Orbital velocity of the satellite is
`v=sqrt((GM_(E))/r)` where `M_(E)` is the mass of the earth
Kinetic energy, `K=1/2mv^(2)=(GM_(E)m)/(2r)`
Where `m` is the mass of the satellite.
`K prop 1/r`
Hence, option (b) is incorrect.
Linear momentum, `p=mv=msqrt((Gm_(E))/r)`
`p prop 1/(sqrt(r))`
Hence, (c) is incorrect.
Frequency of revolution, `v=1/T=1/(2pi)sqrt((GM_(E))/(r^(3)))`
`v prop1/(r^(3//2))`
Hence, option (d) is correct.