The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M , to transfer it from a circular orbit of radius R1 to another of radius R2(R2 R1) is :

Question

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M , to transfer it from a circular orbit of radius R1 to another of radius R2(R2 > R1) is : (A) GmM((1/R12) - (1/R22)) (B) GmM((1/R1) - (1/R2)) (C) 2GmM((1/R1) - (1/R2)) (D) (1/2)GmM((1/R1) - (1/R2))

Tardigrade Admin · Accepted Answer

KE=(- (GMm/2 R2))-(- (GMm/2 R1)) KE=(GMm/2)[(1/R1) - (1/R2)]

Q. The additional kinetic energy to be provided to a satellite of mass m revolving around a planet
of mass $M$ , to transfer it from a circular orbit of radius $R_{1}$ to another of radius $R_{2} (R_{2} > R_{1})$ is :

$G m M (\frac{1}{R _{1}^{2}} - \frac{1}{R _{2}^{2}})$

$G m M (\frac{1}{R _{1}} - \frac{1}{R _{2}})$

$2 G m M (\frac{1}{R _{1}} - \frac{1}{R _{2}})$

$\frac{1}{2} G m M (\frac{1}{R _{1}} - \frac{1}{R _{2}})$

$K E = (- \frac{GM m}{2 R _{2}}) - (- \frac{GM m}{2 R _{1}})$
$K E = \frac{GM m}{2} [\frac{1}{R _{1}} - \frac{1}{R _{2}}]$

Q. The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M , to transfer it from a circular orbit of radius R1​ to another of radius R2​(R2​>R1​) is :

GmM(R12​1​−R22​1​)

GmM(R1​1​−R2​1​)

2GmM(R1​1​−R2​1​)

21​GmM(R1​1​−R2​1​)