# Show that moon would depart forever if its speed were increased by 42%

Expression for orbital velocity:
${v}_{0}=\sqrt{\frac{GM}{R}}$

Expression for Escape velocity:
${v}_{e}=\sqrt{\frac{2GM}{r}}$

From, the above expressions, it is clear that ${v}_{e}=\sqrt{2}{v}_{o}$

Escape velocity: It is the velocity required by moon to escape or depart forever.

Percentage increase of velocity required to reach terminal velocity.

(100)

Hence, it is proved that  moon would depart forever if its speed were raised by 42%.

• 45
What are you looking for?