Total energy of satellite at height $h$ from the earth surface,

$E=PE+KE$

$ =  – \frac{{GMm}}{{\left( {R + h} \right)}} + \frac{1}{2}m{v^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,…\left( i \right)$

Also, $\frac{{m{v^2}}}{{\left( {R + h} \right)}} = \frac{{GMm}}{{\left( {R + {h^2}} \right)}}$

or, ${v^2} = \frac{{GM}}{{R + h}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,…\left( {ii} \right)$

From eqns, $(i)$ and $(ii)$,

$E =  – \frac{{GMm}}{{\left( {R + h} \right)}} + \frac{1}{2}\frac{{GMm}}{{\left( {R + h} \right)}} =  – \frac{1}{2}\frac{{GMm}}{{\left( {R + h} \right)}}$

$ =  – \frac{1}{2}\frac{{GM}}{{{R^2}}} \times \frac{{m{R^2}}}{{\left( {R + h} \right)}}$

$ =  – \frac{{m{g_0}{R^2}}}{{2\left( {R + h} \right)}}\,\,\,\,\,\,\,\,\,\,\,\,\left( {{g_0} = \frac{{GM}}{{{R^2}}}} \right)$