Question

If the orbital speed of moon is increased by $41.4\%$ then moon will

• A. leave its orbit and will escape out.
• B. fall on earth.
• C. attract all bodies on earth towards it.
• D. have time period equal to 27 days.

Answer 1

The correct option is A leave its orbit and will escape out.

Velocity of the planet is $v=\sqrt{\frac{GM}{a}}$

Kinetic Energy is $K=\frac{1}{2}m{v}^2=\frac{GMm}{2a}$

Potential Energy is $U=-\frac{GMm}{a}$

$Totalenergy=K+U=-\frac{GMm}{2a}$

$v=\sqrt{\frac{GM}{a}}$

So if$,v=1+0.414v=1.414v=\sqrt{2}v=\sqrt{\frac{2GM}{a}}$

Escape Velocity is $v_e=\sqrt{\frac{2GM}{a}}$

So the moon will escape.