Moon earth system escape velocity

AI Thread Summary
To determine the escape speed from the Earth-moon system, the escape velocity formula, Escape velocity = sqrt[2GM/R], is relevant but must be applied to both the moon and Earth. The gravitational potential energy of both celestial bodies must be considered, as the projectile must overcome the gravitational pull from both the moon and Earth. Calculating the total energy required involves summing the escape velocities from both bodies. Therefore, the escape speed will be higher than just the moon's escape velocity alone. Understanding the combined gravitational effects is essential for accurate calculations.
bcjochim07
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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?
 
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bcjochim07 said:
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.
 

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