Question

g the total mechanical energy of the satellite-Earth system when the satellite is in its current orbit is E. In order for the satellite to orbit Earth in a new stable circular orbit at an altitude of 12RE, the energy of the satellite-Earth system must be

Answer 1

Answer:

The correct answer is "$\frac{4E}{3}$".

Explanation:

According to the question,

Energy of satellite,

⇒ $E_s=-\frac{GM_sM_E}{2r}$

For the very 1st case:

$r = R_E+R_E$

  $=2R_E$

or,

⇒ $E=-\frac{GM_sM_E}{4R_E}$...(1)

For the new case:

$r = R_E+\frac{R_E}{2}$

  $=\frac{3R_E}{2}$

then,

⇒ $E'=-\frac{GM_sM_E}{2 \frac{3R_E}{2} }$

        $=-\frac{GM_sM_E}{3R_E}$...(2)

From equation (1) and (2), we get

⇒ $E'=\frac{1}{3}(4E)$

        $=\frac{4E}{3}$