# Moon is getting away from earth

Hello

why is moon getting away from earth about 2-3 centimeter/year ?

Because the Martians are pulling harder!

chroot
Staff Emeritus
Gold Member
The Moon generates tides, which involve the movement of vast quantities of water. The movement of all that water causes friction, which leads to the release of energy as heat. The energy actually comes from the Earth's rotational inertia. The tides are literally slowing down the Earth's rotation.

Because the Earth's rotation is slowing, the Moon is moving further away. It must do so to converse angular momentum.

- Warren

can we estimate when the moon will have flown out of its orbit?

The friction mentioned by chroot causes the tidal bulges to move forward relative to the Moon. The gravitational force exerted on the Moon is then a bit larger because of these bulges that are propelled a bit ahead of the Moon. This causes the Moon's velocity to be a bit higher than it should be, causing the Moon to move further away from the Earth.

Note that by action is minus reaction, the Moon pulls has hard on the bulges as the bulges pull on the Moon. This means that in addition to the friction forces exerted by the Earth on the bulges there are the tidal force exerted by the Moon on the bulges as well. Because the bulges are moving at constant velocity with the Moon, there is equilibrium: The tangential component of the gravitational force exerted by the Moon on the bulges is the negative of the friction force exerted by the Earth.

Janus
Staff Emeritus
Gold Member
can we estimate when the moon will have flown out of its orbit?

We wouldn't to ever do so. Before that, the Earth's period of rotation will match the period of the Moon's orbit. The Earth will keep one face pointing at the Moon, The tidal friction that causes the Earth's slowing will no longer be there (The tides no longer move across the face of the Earth), and the Moon's recession will stop.

Chronos
Gold Member
The sun will enter its red giant phase before the moon escapes earth orbit. After that, all bets are off.

it seems the sum will die before lots of interesting events occure.

I heard that dark matter is supposed to keep everything together and dark energy is supposed to separate everything. Is any of that true?

If its true then how does the dark matter and dark energy affect our solar system, if it does in anyway? Also if its true, then is it possible that dark energy is what is pulling/separating the moon away from the earth?

can we estimate when the moon will have flown out of its orbit?

It won't occur on a monday as monday is named after the moon!!

The Moon generates tides, which involve the movement of vast quantities of water. The movement of all that water causes friction, which leads to the release of energy as heat. The energy actually comes from the Earth's rotational inertia. The tides are literally slowing down the Earth's rotation.

Because the Earth's rotation is slowing, the Moon is moving further away. It must do so to converse angular momentum.

- Warren

Tidal energy systems would also add to the problem I beleive?

Matterwave
Gold Member
The friction mentioned by chroot causes the tidal bulges to move forward relative to the Moon. The gravitational force exerted on the Moon is then a bit larger because of these bulges that are propelled a bit ahead of the Moon. This causes the Moon's velocity to be a bit higher than it should be, causing the Moon to move further away from the Earth.

Note that by action is minus reaction, the Moon pulls has hard on the bulges as the bulges pull on the Moon. This means that in addition to the friction forces exerted by the Earth on the bulges there are the tidal force exerted by the Moon on the bulges as well. Because the bulges are moving at constant velocity with the Moon, there is equilibrium: The tangential component of the gravitational force exerted by the Moon on the bulges is the negative of the friction force exerted by the Earth.

The moon does not move faster in higher orbits, it moves slower. The circular orbit equation: $$\frac{v^2}{r}=\frac{GM_e}{r^2}$$ therefore $$v=\sqrt{\frac{GM_e}{r}$$ clearly shows this.

This is because of the virial theorem. The energy boost given to the moon by the tidal forces increases its total energy (remember total energy is negative). According to the virial theorem: <V>=-2<T> so that E=<V>+<T>=-<T>. As E increases (gets less negative), <T> must decrease - i.e. it gets slower. Twice the energy boost is going to the potential energy so the kinetic energy must decrease by one times the energy boost for energy to be conserved.

The moon does not move faster in higher orbits, it moves slower. The circular orbit equation: $$\frac{v^2}{r}=\frac{GM_e}{r^2}$$ therefore $$v=\sqrt{\frac{GM_e}{r}$$ clearly shows this.

This is because of the virial theorem. The energy boost given to the moon by the tidal forces increases its total energy (remember total energy is negative). According to the virial theorem: <V>=-2<T> so that E=<V>+<T>=-<T>. As E increases (gets less negative), <T> must decrease - i.e. it gets slower. Twice the energy boost is going to the potential energy so the kinetic energy must decrease by one times the energy boost for energy to be conserved.

That's right, the Moon is indeed slowing down as it moves away from Earth, but that happens because of the extra energy added which leads to the Moon always moving a tiny bit faster than the speed it should move at if it were not for the tidal bulges.

Matterwave
Gold Member
I suppose on short enough time scales, the moon may not be in virial equilibrium and "speed-up" a little bit before being slowed back down again. On longer time scales, though, the moon should be slowing.

I suppose on short enough time scales, the moon may not be in virial equilibrium and "speed-up" a little bit before being slowed back down again. On longer time scales, though, the moon should be slowing.

The Moon is slowing down, not speeding up. But this is because the Moon is always moving at a tiny, tiny, higher speed than it should move at if you ignore the tidal bulges pulling on the Moon.

D H
Staff Emeritus
That's right, the Moon is indeed slowing down as it moves away from Earth, but that happens because of the extra energy added which leads to the Moon always moving a tiny bit faster than the speed it should move at if it were not for the tidal bulges.
That's not quite right. Yes, the Moon is moving a bit faster than it would if the bulges were not present. However, that is not what is causing the Moon to recede. Suppose the Earth was tidally locked to the Moon and was covered with an all-encompassing ocean. The tidal bulges would be perfectly aligned with the line between the Earth and Moon. The Moon would still be moving a bit faster than it would were the bulges not present -- and the Moon would not be receding.

The reason the Moon is receding is because the bulges lead the line between the Earth and Moon. This gives the Moon a transverse component to the acceleration vector. It is this transverse acceleration that makes the Moon recede.

Yes, I agree, it is caused by the tangential acceleration (I did mention this in post nr. 5)

Because the Martians are pulling harder!

:rofl:

This might be for another thread, but what were the effects on the moon's "drift", if any, caused by the LCROSS and LRO missions? Was the libration of the moon affected at all? If you have an answer for any of these questions (whether it be yes or no or whatever) can you please give me a detailed answer, including any magnitude of force and important equations which may be involved. Thx!

I'll leave a better explanation to someone else, but by simply looking at the size of the craters on the moon and thinking about the size of the objects that caused them, do you think LCROSS would have a noticeable effect?

I'll leave a better explanation to someone else, but by simply looking at the size of the craters on the moon and thinking about the size of the objects that caused them, do you think LCROSS would have a noticeable effect?

I started another thread on this. https://www.physicsforums.com/showthread.php?t=406050" I'm actually looking for the "better explanation" that someone else can offer. Someone else answered me in the same manner you have which tells me nothing in essence. I am looking for a more scientific answer with equations and the like.

But I will answer the question you posed to me. Simply looking at the moon does not give me any data about past impacts and the effect those impacts had. I can look at the moon and imagine the size of the objects that hit them, I can even research that some craters filled with lava and left only a rim and imagine just how enormous the object was that hit the moon in that particular region, but to be honest, that gives me no information of how the moon was affected by those past impacts, if at all. So it is the same with the LCROSS ...I do not know the velocity at which the centaur rocket or the shepherding spacecraft was traveling at before impacting the moon, I do not know how much matter was displaced or how big the crater was that it left, I do not know the force of impact. I do not know how to calculate what effect objects x and y traveling at a velocity of z Km/h impacting an object such as the moon which is about two percent the volume of the earth would have on said object's orbital path or libration if any. I am not asking for a "noticable effect," If the libration or orbit was affected at all I would like to know by what percentage and if there was none I would like to know how the calculation was made, same as if there was an effect.

BUT I resolve to continue study on my own as only 1 person has answered me seriously thus far. I should be having some classes regarding this in the future so perhaps at that time it will be better explained to me. I know that there are people here who are specialised in these areas of physics who could explain it to me which is why I asked.

The LCROSS mission is a search for water on the moon. The LCROSS mission is going to do this by sending a rocket crashing into the moon causing a big impact and creating a crater, throwing tons of debris and potentially water ice and vapor above the lunar surface.
^^Here is this from the Nasa site. How can I reasonably deduce what effect the mission had on the moon by just thinking of all the other "big impacts" which created a creater?

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Janus
Staff Emeritus
Gold Member
I started another thread on this. https://www.physicsforums.com/showthread.php?t=406050" I'm actually looking for the "better explanation" that someone else can offer. Someone else answered me in the same manner you have which tells me nothing in essence. I am looking for a more scientific answer with equations and the like.

LCROSS masses about 585 kg. It hit at about 9000 kph. This equates to a momentum of 1462500 kgm/s The Moon masses 7.35e22 kg. If we divide the Moon's mass into the momentum of LCROSS, we get a fair estimate of what type of velocity change the impact could have on the Moon. It works out to be 2e-17 m/s. This is the equivalent of 1 meter per 1,000,000 yrs. Pretty darn insignificant.

And that's not all. You can't even count all of that 9000 kph impact speed. The vast majority of it is due to The Moon's gravity pulling the craft in. Since gravity is a two way street, as the Probe falls toward the Moon, the Moon falls toward the probe. The upshot is that any part of the probe's momentum on impact that is due to the gravitational attraction between it and the Moon is canceled out by the moon's own momentum. That means that any momentum change to the Moon is due to the small amount of the probe's momentum that is in excess of that. This makes the change in velocity to the Moon is even smaller than the last figure I gave.

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OMG Thank you so much for the calculations!!!! D H also provided me a link to NASA's site with the information on the other thread. Thanks so very very much. I love you guys!!!! You have no idea how happy this makes me!
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Also pls forgive my many grammatical errors above...had a full day and just had my first cup of coffee!

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