(adsbygoogle = window.adsbygoogle || []).push({}); Problem:

One of the asteroids, Ida, looks like an elongated potato. Surprisingly it has a tiny (compared to Ida) spherical moon! This moon called Dactyl has a mass of 4.20x1016kg, and a radius of 1.57x104 meters, according to Wikipedia.

Solve:

- Find the acceleration of gravity on the surface of Dactyl.

- Find the escape speed on Dactyl.

- If you are 10,000 meters above the surface of Dactyl, what must your orbital speed be?

I wanna make sure that I've solved the problem correctly. Can anyone check my work?

What have I done:

- Calculate the acceleration of gravity:

F = (G*M)/R^{2}= (6.67384*10^{-11}* 4.20*10^{16}) / (1.57*10^{4})^{2}= 0.0113717 m/s^{2}=11.3717 * 10^{-3}m/s^{2}

Escape Speed:

I saw on wikipedia that the formula for escape speed is:

v_{e}= sqrt((2*G*M)/r)

That would give = sqrt((2*6.67384*10^{-11}* 4.20*10^{16}) / 1.57*10^{4}) =18.8963 m/s

Orbital Speed:

Formula for orbital speed:

v_{o}= sqrt((G*M)/r)

That would give = sqrt(6.67384*10^{-11}* 4.20*10^{16}) / 1.57*10^{4}+ 10000) =10.4434 m/s

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# Homework Help: Calculating the escape speed and gravity of a planet / moon

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