[Vector169]

Vector169 asked the Naked Scientists:
   
Hi gang! 

Love you all and love the show. 

I am a mechanical engineer in Fort Wayne Indiana.  I just recently (a few months back) found your show on Itunes and I have raced back as far as Itunes would let me go in episodes and am feverishly trying to catch up.

I am in your section now with the year of astronomy and have a question that I have wondered about.  I heard years ago on a tv show that reflectors on the moon and lasers have shown that the moon is moving away from the Earth.  My question is in multiple parts.

1) Will we eventually loose the moon, or is the rate at which it is moving away decelerating.
2) If we loose the moon, will it enter a Earth crossing orbit or will it spiral towards the inner solar system?

If you have already answered this than I look forward to hearing it when I get to that episode. 

Thanks Naked Scientists!

What do you think?

[Soul Surfer]

The moon is moving away from us because it is gaining orbital energy from the tidal friction of the rotating earth. This is slowing down the earths rotatation eventually this will stop when the earth and moon always face each other. However the sun will go red giant before this happens.

[graham.d]

SS, do you mean "when the earth and moon always face each other"? I would say they do that now. One side of the moon always faces the earth. Do you mean when the moon is also fixed over one point on the earth's surface?

[Soul Surfer]

Yes

[graham.d]

I assume the "yes" is to the second of the 2 questions.

[chris]

Just bumping this topic to the top, because we could really do with a clear explanation for this.

Can anyone help?

Chris

[chiralSPO]

The Earth is transferring angular momentum to the moon, so the moon is moving away from the Earth (very slowly, it's on the order of 4 cm/year) and the Earth's rotation is slowing down (the day is getting longer--about 2 ms per 100 years). Eventually the length of the day will be equal to the length of the month (doubly tidally locked system).

https://en.wikipedia.org/wiki/Tidal_acceleration#Quantitative_description_of_the_Earth.E2.80.93Moon_case

But this is when things get a little more interesting. The moon is moving away from us because it is further than the distance of the geosynchronous orbit, but as the Earth's day slows down, the geosynchronous orbit grows, and it is growing faster than the moon is shifting, so eventually they will be the same. (when the length of the day will be equal to the length of the month). After this point, any loss of energy from the system will result in the moon moving CLOSER to the Earth, as it will be lower than a synchronous orbit. So ultimately the moon will crash into the Earth. (but don't worry, the sun will turn into a red giant first, so the moon probably won't kill anybody)

EDIT: this all assumes no intervention and no major asteroid impacts that would distrub the system. A large enough impact could cause the moon to crash earlier, leave orbit (away from Earth), or be completely destroyed (depending on magnitide and direction of impact)

[evan_au]

ultimately the moon will crash into the Earth

...but it won't crash as a single piece (barring external influences).
The Moon will start to disintegrate when it passes within Earth's Roche limit.
So, for a while, Earth would have some rocky rings (if the expanding Sun hadn't melted it all first).

[PmbPhy]

The moon is moving away from us because it is further than the distance of the geosynchronous orbit, ...

What does the distance of geosynchronous orbit have to do with the moon moving away?

...but as the Earth's day slows down, the geosynchronous orbit grows, and it is growing faster than the moon is shifting, so eventually they will be the same. (when the length of the day will be equal to the length of the month). After this point, any loss of energy from the system will result in the moon moving CLOSER to the Earth, as it will be lower than a synchronous orbit.

What does the distance that an object will be in geosynchronous orbit have to do with the moon moving closer to the Earth? It's not as if the slowing of the Earth's rotation slowing down changes the strength of its gravitational field.

[chiralSPO]

No, no one is suggesting that the gravitational field is changing. The issue at hand is how the system responds to a mismatch between the orbital period (OP) of the moon and the rotational period (RP) of the Earth.

For any object in orbit above the synchronous orbit (OP>RP) tidal interactions transfer angular momentum from the rotating planet to the orbiting body--slowing the rotation of the planet, and increasing the altitude of the orbiting body (OP and RP both increase, but RP increases faster)

For any object in orbit below the synchronous orbit (OP<RP) tidal interactions transfer angular momentum the other way, decreasing the rotational period of the planet, and decreasing the altitude of the orbiting body. (like the Martian moons)

I don't have time to crunch the numbers now, but my recollection from my orbital dynamics course (so many years ago), was that the stability of the synchronous orbit is dependent on the relative sizes of the planet and moon. The closer in mass the two are, the more stable the orbit will be (like pluto and charon), whereas when the masses are very different (like Mars and its moons), the system does not self-correct. Our case is intermediate, and my recollection was that the OP>RP case converges to OP=RP, but that the OP<RP case decays...

http://assets.zombal.com/7f59e7d3/TidalEquations.pdf
http://www.askamathematician.com/2015/05/q-why-is-our-moon-drifting-away-while-mars-moons-are-falling/

[jeffreyH]

Can this tell us anything about gravitational interactions at the atomic level? The probability distribution of the electron may well have a gravitational component, although very small in magnitude. The electron can sometimes be regarded as being coincident with the nucleus where the effects of gravitation may be much more significant.

[chiralSPO]

Unfortunately, I don't think we gain much information about atomic scale physics from studying astronomic interactions...


There is definitely a relationship between mass and probability of being very close (or in) the nucleus. If you replace an electron with a muon (also negatively charged, but more massive) the average distance falls significantly. I don't think this is an effect of gravity though, as it can be modeled perfectly (for hydrogen-like atoms) by wave functions generated without including gravitational terms. There probably is some extremely tiny contribution that gravity has at the subatomic scale, but I don't know how we would go about testing that...

[jeffreyH]

Unfortunately, I don't think we gain much information about atomic scale physics from studying astronomic interactions...


There is definitely a relationship between mass and probability of being very close (or in) the nucleus. If you replace an electron with a muon (also negatively charged, but more massive) the average distance falls significantly. I don't think this is an effect of gravity though, as it can be modeled perfectly (for hydrogen-like atoms) by wave functions generated without including gravitational terms. There probably is some extremely tiny contribution that gravity has at the subatomic scale, but I don't know how we would go about testing that...

I have been looking at the Compton equations. Especially the Compton wavelength. Something is nagging me about them but I can't put my finger on it. I know that it is concerned with photons and nothing to do with gravity.

[rmolnav]

Not long ago I saw a very interesting tv program, where a Scientist compared the physical effect to what happens at hammer throwing. Though firstly I did not agree, after a couple of emails he convinced me.
It´s equivalent to what said on #1 in terms of energy.
He explained it in terms of forces. The tidal bulge due to Moon pull, as Earth is rotating at a big pace (tangential speed at equator is 40,000 km/24 h), cannot catch up with Moon´s vertical meridian. We can see that comparing high tide time with Moon´s position. That causes a relatively small tangential component of the total Earth´s pull on the Moon, due to the fact that the huge mass of water of the tidal bulge continuously has its C.G. eastwards from the Moon. And that, though very slowly, is increasing Moon´s speed of rotation.
 

[evan_au]

" And that, though very slowly, is increasing Moon´s speed of rotation."
It's not obvious, but as the Moon moves farther from the Earth, it's rotational velocity decreases.

The correct terminology is that the Moon's angular momentum increases, to compensate for the reduction in the Earth's angular momentum.

[zx16]

The Moon is kept close to the Earth, by our planet's gravitational field.  This field is much stronger than any competing planetary field.
For example, our very nearest neighbouring planet, Venus, is about 100 times further away from the Moon than the Earth is.

Consequently, when we apply the inverse-square law, we find that the Moon is attracted 1,000 times more strongly to the Earth, than to Venus.
Doesn't this provide a sufficient safety factor for permanent retention of the Moon in Earth orbit? 

[rmolnav]

#14 evan_au says:
"... as the Moon moves farther from the Earth, it's rotational velocity decreases". [/size]
Sorry, but that is erroneous. With a pull exactly towards Earth´s C.G., the whole pull would be centripetal, and it would keep the Moon following an exactly circular orbit. But mentioned misalignment of tidal bulge originates a relatively small tangential component of Earth´s pull.
And according to Newtons´s 2nd Principle, a tangential acceleration occurs, tangential velocity increases, and so does its square divided by the radius at considered instant. And that is the centripetal acceleration necessary to have a circular movement at that increased speed ...
But Earth has not increased its pull at that distance, and cannot produce the necessary centripetal force.
The result is that Moon´s orbit cannot be kept exactly circular: it is a kind of very, very "closed" spiral.
Eventually, Moon´s distance from Earth gets perceptibly bigger.
 

[Janus]

#14 evan_au says:
"... as the Moon moves farther from the Earth, it's rotational velocity decreases". [/size]
Sorry, but that is erroneous. With a pull exactly towards Earth´s C.G., the whole pull would be centripetal, and it would keep the Moon following an exactly circular orbit. But mentioned misalignment of tidal bulge originates a relatively small tangential component of Earth´s pull.
And according to Newtons´s 2nd Principle, a tangential acceleration occurs, tangential velocity increases, and so does its square divided by the radius at considered instant. And that is the centripetal acceleration necessary to have a circular movement at that increased speed ...
But Earth has not increased its pull at that distance, and cannot produce the necessary centripetal force.
The result is that Moon´s orbit cannot be kept exactly circular: it is a kind of very, very "closed" spiral.
Eventually, Moon´s distance from Earth gets perceptibly bigger.
 

This is orbital mechanics, so you have to take the change in gravitational potential into account.  As the tangential acceleration affects the Moon, in climb away from the Earth, this involves an increase in gravitational potential energy. This increase is actually greater than the energy it gained from the tidal acceleration, and this is made up for by a loss of kinetic energy for the Moon; it decreases its orbital speed.  This continuous process is akin to the two step process you would use to raise a orbiting space craft to a higher orbit.  First you fire your engines which changes your orbit to an elliptical one with an apogee higher than your present altitude and at the altitude to your desired orbit.  As you climb to apogee, you will exchange kinetic energy for potential energy and slow down.  At reaching apogee, your are moving too slow to stay there and would complete the other half of the orbit and return to perigee if you did nothing. So you fire your engines again in order to achieve the needed speed to maintain a circular orbit at your new altitude.  But the circular orbital speed at this altitude is less than that of your original orbit.   You accelerated twice but ended up moving slower than what you started at.   The tidal acceleration of the Moon behaves the same way except that instead of two separate engine burns and two short intervals of high acceleration, you have a constant low level acceleration.   The result is the same, the Moon ends up higher and moving slower.

[syhprum]

I think this makes it all the more imperative to get one or both of the schemes that Alan and I devised working to restore the Earths rotation speed to what it was in 1900

[rmolnav]

#17 Janus says:
"... As the tangential acceleration affects the Moon, in climb away from the Earth, this involves an increase in gravitational potential energy. This increase is actually greater than the energy it gained from the tidal acceleration, and this is made up for by a loss of kinetic energy for the Moon; it decreases its orbital speed".
I had not seen your post until now ... I have to ruminate it more quietly.
It´s clear that Moon´s angular speed has to decrease, but I´m now not quite sure about tangential speed.
In any case, I can´t actually  understand your reasoning: how if Moon continuously suffers the tangential acceleration due to Earth tidal bulge tangential attraction, it climbs away from the Earth, and it gets "too high" potential energy increase, and then it has to decrease its kinetic energy and velocity, to compensate ...
I´m realizing now that gravitational energy should actually decrease with the "climb away from the Earth", because it is mass times g and times distance. Distance increases, but g decreases inversely to the square of the distance, doesn´t it?