Zero g planet

Classical Mechanics Level 2

If there were a planet with the mass $6\times 10^{24}\text{kg}$ and angular velocity $7\times10^{-5}\text{ rad/s}$ of Earth, what would be the radius required in order for the free-fall acceleration on its surface to be $0 \text{ m/s}^2?$

4.4\times10^{4} \text{m}

4.4\times10^{7} \text{m}

4.4\times10^{10} \text{m}

4.4\times10^{13} \text{m}

1 solution

July Thomas
May 6, 2016

In order for the free-fall acceleration to be equal to 0, all the gravitational acceleration must be used in the form of centripetal acceleration.

$a_\text{g} = a_{\text{centripetal}}$

$\frac{GM}{r^2} = \omega^2r$

$r^3 = \frac{GM}{\omega^2}$

$r = \sqrt[3]{\frac{GM}{\omega^2}} \approx 4.4\times10^7 \text{ m}$

What is the difference between the gravitational acceleration and centripetal acceleration of a planet ?

Aniruddha Bagchi - 4 years, 2 months ago

Why does the problem/solution assume a knowledge of gravitational acceleration?

Amir Parvez - 3 years, 7 months ago

Zero g planet

1 solution

0 pending reports