Moon earth system escape velocity

[bcjochim07]

Homework Statement

A projectile is fired straight away from the moon from a base on the far side of the moon, away from the earth. What is the projectile's escape speed from the earth-moon system?

Homework Equations

Escape velocity = sqrt[2GM/R]

The Attempt at a Solution

What I'm wondering is, do I just have to use this formula the moon or do I have to take the gravitational potential energy of the Earth and the projectile into account also?

 

[kamerling]

What I'm wondering is, do I just have to use this formula the moon or do I have to take the gravitational potential energy of the Earth and the projectile into account also?

Certainly. you need an equation for the energy needed to escape from the Earth and the moon, and you can add those energies.

 

[Moetasim]

I would approach this problem by first considering the factors that affect the escape velocity of an object from the Earth-moon system. These include the masses of the Earth and moon, the distance between them, and the gravitational constant. The formula provided, sqrt[2GM/R], takes all of these factors into account and provides the escape velocity from the system.

In this scenario, since the projectile is being fired away from the moon, we can assume that the distance between the moon and the projectile is negligible compared to the distance between the moon and Earth. Therefore, we can use the mass and radius of the Earth in the formula to calculate the escape velocity.

It is important to note that this formula assumes a point mass for the Earth and moon, which may not be entirely accurate. However, for the purpose of this problem, it provides a reasonable approximation.

In conclusion, the projectile's escape velocity from the Earth-moon system can be calculated using the formula provided, taking into account the mass and radius of the Earth. Other factors, such as the gravitational potential energy, may affect the trajectory of the projectile but are not necessary to calculate the escape velocity.