Planet X-39 has a mass equal to 1/3 that of Earth and a radius equal to 1/3 that of Earth.If V is the escape speed for Earth,what is the escape speed for X-39?
A)V
B)3V
C)6V
D)V/9
E)9V

Question

Quizplus · Accepted Answer

The escape speed $v$ from a planet is given by the formula $v = \sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $r$ is the radius of the planet. For planet X-39, $M = \frac{1}{3}M_{\text{Earth}}$ and $r = \frac{1}{3}r_{\text{Earth}}$. Substituting these into the escape speed formula gives $v_{X-39} = \sqrt{\frac{2G(\frac{1}{3}M_{\text{Earth}})}{\frac{1}{3}r_{\text{Earth}}}} = \sqrt{\frac{2GM_{\text{Earth}}}{r_{\text{Earth}}}} = v_{\text{Earth}}$. Therefore, the escape speed for X-39 is the same as that for Earth, which is $V$.

Planet X-39 Has a Mass Equal to 1/3 That of Earth