Why doesn't the moon eventually drift into space?

[pheadden]

How does conservation of energy relate to Gravity? The moon seems to rotate around the Earth for eternity (so it seems). But intuitively I would think that the energy of Gravity would eventually deplete and the moon would drift off into space. This apparently isn't the case. I know that F_g=Gm₁m₂/r², but I can't get my pea brained head around the idea that this goes on for eternity; and the energy of gravity doesn't run out as long as their is two bodies of mass.

 

[Vanadium 50]

I don't know what to tell you. You say you understand why, but are uncomfortable with the explanation. What would make you more comfortable?

 

[OmCheeto]

...the energy of Gravity would eventually deplete...

...F_g=Gm₁m₂/r²...

Where in your equation does it show energy being depleted? Everything on the right hand side of the equation appear to be constants.

But this brings up another question. With the recent meteor event over Russia, we've learned that 10's of thousands of tons of meteors fall on the Earth every year. And we would assume it's also happening to the moon as well. So m₁ and m₂ are both increasing, which means F_g is going up! Which means, intuitively to me, that we are going to collide! And yet, everything I've read says that the distance between the Earth and Moon is increasing.

An interesting discussion of that: why is the moon drifting into space

Oh wait. That's very similar to the title of this thread. I need to pay attention once in awhile.

I guess the answer to your thread title question is: It is.

 

[pheadden]

Boy what a great question. I agree, the force of gravity would be going up with the increased mass. Something else is "impacting" the equation.

 

[Judgeking]

The moon is slowing drifting away, about 1inch per year. It will eventually float away, but may take millions of years.http://www.bbc.co.uk/news/science-environment-12311119

 

[Naty1]

The equation is approximate. A few that come to mind...The Earth is not a fixed point, nor is it in a circular orbit around the sun,there are other gravitational influences like the sun, and some energy is radiated away via gravitational waves.

If either mass goes up, the force to hold everything in place must also go up.

 

[McLaren Rulez]

The moon is slowing drifting away, about 1inch per year. It will eventually float away, but may take millions of years.http://www.bbc.co.uk/news/science-environment-12311119

No, it will not float away forever.

Assuming the Earth moon system is isolated, their angular momentum will be conserved. I think what will eventually happen is that you will have a synchronous rotation where the Earth and the moon see only one face of each other. This is already true for the moon (moon rotation period=moon revolution period=one month) and it will happen for the Earth too (as seen from the moon). That can only occur at one radius and that will be the final distance between the Earth and the moon.

With the sun in the mix, it will be more complicated but I'm pretty sure we're not going to lose the moon no matter how long we wait.

 

[Ryoko]

I have a question related to this, which is "What gives satellites their right angle velocity (relative to the mass) which creates a stable orbit?

Gravity's vector is only towards the mass of the object, so what creates this additional force which allows us for the stable orbit.

You need to review Kepler's equations for your answer. In short, conservation of momentum, conservation of angular momentum and conservation of energy are why orbits are stable.

 

[Drakkith]

How does conservation of energy relate to Gravity? The moon seems to rotate around the Earth for eternity (so it seems). But intuitively I would think that the energy of Gravity would eventually deplete and the moon would drift off into space. This apparently isn't the case. I know that F_g=Gm₁m₂/r², but I can't get my pea brained head around the idea that this goes on for eternity; and the energy of gravity doesn't run out as long as their is two bodies of mass.

Gravity is one of the four fundamental forces, and as such it does not require an expenditure of energy to work. It is quite the opposite. It is the result of these forces interacting between objects that gives rise to energy.

 

[xAxis]

You need to review Kepler's equations for your answer. In short, conservation of momentum, conservation of angular momentum and conservation of energy are why orbits are stable.

It is because the force is central