# Help with Escape Velocity Problem

• CaptainEvil
In summary, the approximate escape speed needed to completely escape the moon and Earth's gravity is the sum of their individual escape velocities. However, for a more accurate approximation, one would need to consider the masses and radii of both objects. The exact wording of the problem suggests that the escape speed should be regarded as that of a single object, which means the escape velocities can be added.
CaptainEvil
I know that escape velocity is given by v^2 = 2GM/r

My question is what is the approximate escape speed needed to completely escape the moon & Earth's gravity.

Is it the sum of their individual Escape velocities? or is it one equation, with the radius' added and masses added?

Thanks

I would add the escape velocities, the value for the moon is pretty small anyway

Yea I was thinking that something (i.e moons EV) would be negligable since the question asked for the approximate value. But are you sure of that? Wouldn't it make sense astronomically - for something to escape moon's and Earth's gravity - that's on the moon, to have to travel slightly slower than Earth's EV since now we are much farther away?

I read it to mean at a great distance from both what's the escape velocity, ie. of the earth-moon system, in which case the Earth and moon's masses add so you can approx add their escape Vs

The exact wording of my problem is as follows:

"assuming one wished to escape completely from both the moon and Earth's gravity, what would the approximate escape speed be from the moon?"

Thats why I would regard it as a single object - and so for a first approximation add the escape Vs

## 1. What is Escape Velocity?

Escape velocity is the minimum speed required for an object to break free from the gravitational pull of a celestial body, such as a planet or moon.

## 2. How is Escape Velocity Calculated?

The formula for calculating escape velocity is Ve = √(2GM/R), where Ve is the escape velocity, G is the gravitational constant, M is the mass of the celestial body, and R is the distance from the center of the body to the object.

## 3. What Factors Affect Escape Velocity?

The main factors that affect escape velocity are the mass and radius of the celestial body. The higher the mass and larger the radius, the higher the escape velocity will be.

## 4. Why is Escape Velocity Important?

Escape velocity is important because it determines whether an object can escape from the gravitational pull of a celestial body or not. It is also essential for spacecraft to reach and maintain orbit around a planet or moon.

## 5. Can Escape Velocity Be Changed?

Escape velocity is determined by the mass and radius of the celestial body and cannot be changed. However, it can be manipulated by changing the mass or radius of the body, such as through the addition of fuel or altering the orbit of the body.

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