A satellite moving around earth at a height $R$ (radius of earth) from the surface of earth needs to be put into another circular orbit of radius $8 R$ . How much more energy needs to be provided to take the satellite to the new orbit? ( $M_{e}$ is mass of the earth and $m$ is mass of satellite).

\frac{3 G M_{e} m}{16 R}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{G M_{e} m}{10 R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3 G M_{e} m}{20 R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 G M_{e} m}{R}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{3 G M_{e} m}{16 R}$
Total energy at satellite at a height $R$ from the surface of the earth

$E_{i} = - \frac{G M_{e} m}{2 (R + R)} = - \frac{G M_{e} m}{4 R}$

Total energy of satellite at an orbit of radius $8 R$

$E_{f} = \frac{- G M_{e} m}{2 (8 R)} = - \frac{G M_{e} m}{16 R}$

Energy to be provided = $E_{f} - E_{i} = - \frac{G M_{e} m}{16 R} - (- \frac{G M_{e} m}{4 R}) = \frac{3 G M_{e} m}{16 R}$

Hence, option $(a)$ is correct.

Suggest Corrections

Similar questions

M_{E}

R_{E}

R

m

h

R

g

^{'} m^{'}

10 R

R

= M_{e}

Join BYJU'S Learning Program