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

$GmM space open parentheses fraction numerator 1 over denominator straight R subscript 1 superscript 2 end fraction minus fraction numerator 1 over denominator straight R subscript 2 superscript 2 end fraction close parentheses$
$GmM space open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses$
$2 GmM space open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses$
$1 half GmM space open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses$

Solution

1 half GmM space open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses

The kinetic energy changing the orbit of satellite
$KE space equals space open parentheses fraction numerator GMm over denominator 2 straight R subscript 1 end fraction close parentheses space minus open parentheses negative fraction numerator GMm over denominator 2 straight R subscript 1 end fraction close parentheses KE space equals space GMm over 2 open square brackets 1 over straight R subscript 1 minus 1 over straight R subscript 2 close square brackets$