Calculating the escape speed and gravity of a planet / moon

[mr_miyagi]

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 want to 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)/R² = (6.67384*10^-11 * 4.20*10¹⁶) / (1.57*10⁴)² = 0.0113717 m/s² = 11.3717 * 10^-3 m/s²

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*10¹⁶) / 1.57*10⁴) = 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*10¹⁶) / 1.57*10⁴ + 10000) = 10.4434 m/s

 

[gneill]

Values look okay!

Be sure to use use an appropriate number of significant figures when you report your results.

 

[TSny]

[Removed: Question already answered]

 

[mr_miyagi]

thx for the replies. The teacher didn't specify how many significant figures...

 

[D H]

The teacher doesn't have to say how many significant figures to use. It's right there in the question. How many significant figures are used in the question?