Escape Velocity Altered by Other Masses?

[Curtis15]

Earth's Escape velocity is approximately 11.2 km/s, which is derived from the equation v = (2GM/R)^1/2. I know that this equation is derived from energy conservation, K + U = 1/2mv^2 + (-GMm/r). My question is regarding the addition of other masses to this equation based on location.

Basically the question came up whether the moon's location could alter the escape velocity. Assuming a position where the a rocket is being launched from the surface of the earth, and the moon is placed so the rocket is between the Earth and moon, I would suspect that the moons gravity would cause the rocket to accelerate, however small this acceleration to be, causing the net acceleration on the rocket to decrease, meaning the rocket would require less initial velocity to leave Earth's orbit.

Conversely, if the moon is placed so that the Earth is in the middle, then there would be an additional acceleration on the rocket causing the initial velocity to be higher than normal.

I know the equation doesn't allow for this, but if the equation is derived from an expression involving potential gravitational energy, then if the moon is taken into consideration, then it would also provide its own potential energy, changing the escape velocity.

Thanks for the assistance everybody. And also, if possible, any links to sources that can be found that would help me understand this better would be appreciated.

 

[JaredJames]

The moon certainly has an effect. However, you have to realize that the rocket is so small this effect is negligible to the point of being useless.

Everything the moon has can give the tides - but it requires that immense mass of water to have an effect on things.

 

[revnaknuma]

moon's effect is small but air resistance forces a greater escape velocity.

 

[sophiecentaur]

The velocity to 'escape' from Earth would be significantly less is you aim to get into orbit around the Moon (which would imply that you had escaped). So the answer must be Yes. Also you could imagine using the Moon for slingshot, which would also involve using less fuel.

 

[JaredJames]

The velocity to 'escape' from Earth would be significantly less is you aim to get into orbit around the Moon (which would imply that you had escaped). So the answer must be Yes. Also you could imagine using the Moon for slingshot, which would also involve using less fuel.

Huh?

Isn't the question about lining a rocket launch up with the moon (so the moon is overhead if you like) so that you get the benefit of it's gravity to aid the launch?

 

[skeptic2]

There is a current, nearly parallel discussion here https://www.physicsforums.com/showthread.php?t=487600 and a different conclusion was reached.

 

[sophiecentaur]

Huh?

Isn't the question about lining a rocket launch up with the moon (so the moon is overhead if you like) so that you get the benefit of it's gravity to aid the launch?

No. Not at all. I can't be sure of what the questioner meant but I have given 'a' correct answer. The actual gravitational force due to the Moon is very small (undetectable, I reckon) when on the ground. It would make damn all difference. If you want to benefit from the Moon then you are better off using just enough fuel to get you near enough to the Moon so that you would then 'fall down' onto it - or go into orbit. This means you have 'escaped' from the Earth.That means less fuel needed at takeoff from Earth than if you wanted to really escape - which means having enough energy to get 'to infinity'. A slingshot orbit would also benefit you for the same reason.

 

[JaredJames]

No. Not at all.

Basically the question came up whether the moon's location could alter the escape velocity. Assuming a position where the a rocket is being launched from the surface of the earth, and the moon is placed so the rocket is between the Earth and moon, I would suspect that the moons gravity would cause the rocket to accelerate, however small this acceleration to be, causing the net acceleration on the rocket to decrease, meaning the rocket would require less initial velocity to leave Earth's orbit.

Conversely, if the moon is placed so that the Earth is in the middle, then there would be an additional acceleration on the rocket causing the initial velocity to be higher than normal.

Pretty clear from where I'm sitting.

In one case the moon would 'help' (provide some acceleration) but it would be insignificant, in the second it would 'work against' (add to Earth's gravity) but again would be insignificant. (In the former you could reduce the acceleration by fuel by the amount the moon adds and reduce it subsequently in the latter.)

Of course, what you said was correct (re 'getting close enough to fall down') but would that change the required escape velocity from ground to the point for that to occur?

I say no, the moons effect is too small to reduce/increase the escape velocity by a useful/detrimental amount.

 

[Curtis15]

Thanks for the replies, and yes I was referring to a direct shot away/toward the moon, not the slingshot method.

And I realize that the general consensus is that the effect would be negligible, but from a conceptual standpoint, is it correct that the location of the moon would have some effect?

For instance, if the mass of the moon was multiplied by a factor of 10 and its distance from the Earth was decreased, the effect would be more observable, correct?

 

[JaredJames]

Thanks for the replies, and yes I was referring to a direct shot away/toward the moon, not the slingshot method.

And I realize that the general consensus is that the effect would be negligible, but from a conceptual standpoint, is it correct that the location of the moon would have some effect?

For instance, if the mass of the moon was multiplied by a factor of 10 and its distance from the Earth was decreased, the effect would be more observable, correct?

Correct.

 

[sophiecentaur]

My point is that 'escape velocity' has a specific meaning. It doesn't refer to getting into orbit - (that isn't escape) or just 'taking off'. You have to get to infinity for it to be 'escape'. The difference introduced by the position of the Moon in the sky is, as you say, there in principle but too small to measure. (Of course, altering the mass and separation would have an effect but the inverse square law is very 'powerfull'!
However, if you want to really escape, the Moon can help you.

There is also an important point that you don't point at the Moon if you want to get to it. You have to aim to rendezvous with it.

 

[sophiecentaur]

And . . . . . I just realized that to 'escape' fully from the Earth and Moon, you would need more energy than to escape just from the Moon - unless you use some of the Earth-Moon rotational energy.