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

1. Jul 20, 2012

### 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 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)/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:
ve = 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:
vo = sqrt((G*M)/r)
That would give = sqrt(6.67384*10-11 * 4.20*1016) / 1.57*104 + 10000) = 10.4434 m/s

Last edited: Jul 20, 2012
2. Jul 20, 2012

### Staff: Mentor

Values look okay!

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

3. Jul 20, 2012

### TSny

4. Jul 20, 2012

### mr_miyagi

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

5. Jul 20, 2012

### D H

Staff Emeritus
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?