Question

The satellite is orbiting a planet at a certain height in a circular orbit. If the mass of the planet is doubled, the satellite would

• A. fall on the planet
• B. go to orbit of smaller radius
• C. go to orbit of higher radius
• D. escape from the planet

Answer 1

Answer: (D)

escape from the planet

We have,
$v=\sqrt{\frac{GM}{R}}$
$\therefore v\propto \sqrt{M}$
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{M_1}{M_2}}$
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{M_1}{2M_1}}$
$\therefore v_2=\sqrt{2}{v}_1$