How to set moon free of its orbit

[yasar1967]

What would happen if we try to set free the moon -theoretically- by applying a force just big enough to overcome its acceleration of a=2.7x10-3 m/s2 (~35km/h2) so that it's off its orbit.
Would she settle on another orbit with smaller value of "a" or else ?

 

[Shooting Star]

To say applying a force to a body does not carry much meaning in the context of Physics – you have to say for how long and in which direction. There is a certain minimum energy required to set the moon completely free, so that it’ll not be bound gravitationally to the Earth any more. If the energy supplied is less, it’ll settle on to a new orbit, the shape and size of which will depend on how the force was applied to it, that is, it’ll depend on not only how much the total energy changed, but also very much on how much change was there in the angular momentum

If you just perturb it a little in a random direction, most likely it’ll settle on to new orbit elliptical in shape, with almost the same energy as before.

 

[wysard]

As Shooting Star pointed out, it all depends. When you say "set her free" the question is "free from what?" Enough acceration would make her free from Earth for instance, but not the Sun. Do it right, at the right time and vector and the same force might cast her free of Earth, only to be recaptured by another object such as Mars. Even if you cast her free of the solar system you still have to contend with the problem of casting her free of the "escape" velocity of the Milky Way or have her recaptured by another solar system (quite possibly an ugly collision BTW no matter what object "captures" her)

 

[CaptainQuasar]

I think we should try to set the moon free by destroying the Earth instead.

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[wysard]

Captain. That would do it. Make her free of Earth I mean, but kinda blows the OP's point of using a force "just big enough". Besides, while it would make her free of Earth, she still wouldn't be "free" of the Sun. Or for that matter if the geometry is just right of anything downhill, like say Venus or Mercury.

 

[CaptainQuasar]

Captain. That would do it. Make her free of Earth I mean, but kinda blows the OP's point of using a force "just big enough".

Oh. I suppose you're right. Well, to get it out of its orbit with the minimal force we could smash it into the Earth then.

Green cheese quesadillas for dinner, anyone?

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[drpizza]

Actually, OP, all you have to do is sit back and wait (grab a six pack of beer or so, because it's going to be a long wait.) This is already occurring! The moon's orbit is increasing by a couple centimeters each century. Although, the moon will eventually find a stable orbit in about 15 billion years, 1.6 times further away than it is now. Here are some of the details that seems to explain it fairly well.
http://curious.astro.cornell.edu/question.php?number=124

 

[Dale]

Oh. I suppose you're right. Well, to get it out of its orbit with the minimal force we could smash it into the Earth then.

Actually, it would still take a lot of force to alter the orbit enough to drop it onto the earth. I am not sure if the delta V to drop the moon onto the Earth would be more or less than the delta V to escape the Earth entirely.

 

[Ulysees]

> you still have to contend with the problem of casting her free of the "escape" velocity of the Milky Way

Any idea with what that velocity equals to?

How fast do we travel along the galaxy at present?

 

[D H]

One silly proposal for getting rid of nuclear waste is to launch it from Earth in such a manner as to make it fall into the Sun. What makes this a silly proposal is that it takes a lot more energy to make something that starts out with the Earth's orbital velocity about the Sun drop into the Sun than it does to make something that starts out with the Earth's orbital velocity exit the solar system completely.

Similarly, it would take a lot more force to make the Moon drop on the Earth than to make it the Moon escape Earth orbit. The Moon is much closer to Earth escape velocity than it is to a null relative velocity.

 

[CaptainQuasar]

Actually, it would still take a lot of force to alter the orbit enough to drop it onto the earth. I am not sure if the delta V to drop the moon onto the Earth would be more or less than the delta V to escape the Earth entirely.

I would think that it would be much less to do it in a given amount of time. Remember, you don't have to push it towards the Earth, gravity will do that for you. All you'd have to do is slow down its rate of orbit or change the shape of its orbit until it impacts.

(Edit) On the other hand, if D H has already worked it out, that's that.

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[Dale]

I would think that it would be much less to do it in a given amount of time. Remember, you don't have to push it towards the Earth, gravity will do that for you. All you'd have to do is slow down its rate of orbit or change the shape of its orbit until it impacts.

(Edit) On the other hand, if D H has already worked it out, that's that.

You are exactly correct, all you have to do is change the shape of the orbit from approximately circular to an ellipse that intersects the earth. The other option is to change the orbit from circular to parabolic (escape). It takes a change in velocity (delta V) to do either one.

If D_H is correct (as I am sure he is) then the delta V to turn it into an earth-intersecting ellipse is larger than the delta V to turn it into an escaping parabola.

 

[CaptainQuasar]

You are exactly correct, all you have to do is change the shape of the orbit from approximately circular to an ellipse that intersects the earth. The other option is to change the orbit from circular to parabolic (escape). It takes a change in velocity (delta V) to do either one.

If D_H is correct (as I am sure he is) then the delta V to turn it into an earth-intersecting ellipse is larger than the delta V to turn it into an escaping parabola.

The thing that confuses me is that it seems like there ought to be a point in trying to get it into an escaping parabola where it doesn't quite make the escape but instead comes back and hits the Earth. Note that it could hit the Earth after multiple passes too.

This is a http://en.wikipedia.org/wiki/Two-body_problem" , right? So figuring out how they could be made to hit each other through any possible unstable orbit is way more complex than just calculating escape velocities. (I think.)

And besides, if we can get the moon out of orbit I'm sure there's some way to sling it around the Sun or Venus or something and smash it back into the Earth. So it's got to at worst be an equal amount of force. Why are you guys trying to prevent me from destroying the Earth?

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[Ulysees]

One silly proposal for getting rid of nuclear waste is to launch it from Earth in such a manner as to make it fall into the Sun. What makes this a silly proposal is that it takes a lot more energy to make something that starts out with the Earth's orbital velocity about the Sun drop into the Sun than it does to make something that starts out with the Earth's orbital velocity exit the solar system completely.

How did you work this out? Earth's speed is about 3 times the escape velocity of objects from Earth according to this:

http://en.wikipedia.org/wiki/Earth

Therefore we just need to accelerate a missile towards the back of the earth, to a speed of 3 times the escape velocity, and the object will fall to the sun.

But to leave the solar system, what is the necessary speed of the missile? It's the escape velocity from the sun, for a starting point at the distance of the Earth from the sun.

What is that escape velocity? It is not obvious whether it is bigger or smaller than 3 times the escape velocity from Earth's surface.

 

[CaptainQuasar]

Therefore we just need to accelerate a missile towards the back of the earth, to a speed of 3 times the escape velocity, and the object will fall to the sun.

Not only that but as I proposed in my destroying-the-Earth example you could sling it around other planets or the Moon.

You're definitely taking a scientist's approach to these problems rather than an engineer's, D H.

But until we have space elevators the resources required to get nuclear waste out of the Earth's gravity well makes it an impractical prospect.

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[glennpagano44]

We have to do absolutely nothing because the moon is slowly moving away from earth. 1.5inches a year and after a certain period of time the Earth gravitational force will have no profound affect on the moon and it will eventually drift off into space. This will cause a big problem with the Earth though. Since the moon is holding the Earth on a 23 degree tilt the climate on certain parts of the Earth are constant. When moon is gone it no longer holds the Earth a 23degree tilt and this will cause the Earth to rotate all different ways. Which will make the climate shift dramatically in parts of the world. For example Arizona and Nevada will be experiencing weather like that of antarctic.

 

[tony873004]

How did you work this out? Earth's speed is about 3 times the escape velocity of objects from Earth according to this:

http://en.wikipedia.org/wiki/Earth

Therefore we just need to accelerate a missile towards the back of the earth, to a speed of 3 times the escape velocity, and the object will fall to the sun.

But to leave the solar system, what is the necessary speed of the missile? It's the escape velocity from the sun, for a starting point at the distance of the Earth from the sun.

What is that escape velocity? It is not obvious whether it is bigger or smaller than 3 times the escape velocity from Earth's surface.

To go from the surface of Earth into the Sun would require:
sqrt((2GM/r)+vinf^2), where vinf is your velocity at infinity, in this case 30,000 m/s. So to launch from Earth into the Sun would require
sqr((2*6.67E-11*5.97E24/6378000)+30000^2) = 32000 m/s or 32 km/s

The difference between circular orbital velocity and escape velocity is a factor of sqrt(2)=1.414. So to escape would require you gain 41.4% more speed, and to fall straight into the parent body would require 100% less speed, (or maybe 98 or 99% will make you hit the edge of the parent body, while 100% is a direct hit to the middle.)

With the Moon, you wouldn't have to accelerate it to escape velocity to make it escape. You can just raise its perigee by a few hundred thousand km, and let the Sun perturb it the rest of the way. And there probably are scenerios where its chaotic trajectory would cause an Earth collision instead.