Question 412: Gravitation

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 R
1
to another of radius R
2
(R
2
> R
1
) is

Accepted Answer

Total energy of the orbiting satellite of mass m having orbital radius r is
$$E =  - {{GMm} \over {2r}}$$
where M is the mass of the planet.
Additional kinetic energy required to transfer the satellite from a circular orbit of radius R
1
to another radius R
2
is E
2
Ã¢ÂÂE
1
$$ =  - {{GMm} \over {2{R_E}}} - \left( { - {{GMm} \over {2{R_1}}}} \right) =  - {{GMm} \over {2{R_2}}} + {{GMm} \over {2{R_1}}}$$
$$ = {{GMm} \over 2}\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$

Answer

GmM $$\left( {{1 \over {R_1^2}} - {1 \over {R_2^2}}} \right)$$

Answer

GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$

Answer

2GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$

Answer

$${1 \over 2}$$GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$

Gravitation

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

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