Calculating the escape speed and gravity of a planet / moon

In summary, the problem involves finding the acceleration of gravity, escape speed, and orbital speed on the surface of the asteroid moon Dactyl, which has a mass of 4.20x1016kg and a radius of 1.57x104 meters. The acceleration of gravity is approximately 0.0113717 m/s2, the escape speed is approximately 18.8963 m/s, and the orbital speed at 10,000 meters above the surface is approximately 10.4434 m/s. The results have an appropriate number of significant figures for the given values.
  • #1
mr_miyagi
4
0
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:
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:
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  • #2
Values look okay!

Be sure to use use an appropriate number of significant figures when you report your results.
 
  • #3
[Removed: Question already answered]
 
  • #4
thx for the replies. The teacher didn't specify how many significant figures...
 
  • #5
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?
 

FAQ: Calculating the escape speed and gravity of a planet / moon

1) What is the escape speed of a planet/moon?

The escape speed of a planet or moon is the minimum speed that an object needs to reach in order to escape its gravitational pull and move away into space. It is calculated using the planet/moon's mass and radius, as well as the universal gravitational constant.

2) How is the escape speed calculated?

The escape speed can be calculated using the formula: v = √(2GM/r), where v is the escape speed, G is the universal gravitational constant, M is the mass of the planet/moon, and r is the distance from the center of the planet/moon to the object's starting point.

3) What factors affect the escape speed of a planet/moon?

The escape speed of a planet/moon is affected by its mass and radius. A planet/moon with a larger mass and radius will have a higher escape speed, while a smaller mass and radius will result in a lower escape speed.

4) Can the escape speed of a planet/moon change?

Yes, the escape speed of a planet/moon can change depending on its mass and radius. For example, if a planet/moon loses mass due to a collision or other factors, its escape speed will decrease. Similarly, if a planet/moon gains mass, its escape speed will increase.

5) How does the escape speed relate to gravity?

The escape speed is directly related to the strength of gravity on a planet/moon. The higher the escape speed, the stronger the gravitational pull of the planet/moon. This is because a higher escape speed is needed to overcome the planet/moon's gravitational force and escape its pull.

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