As most know, the moon is moving away from us at about 3cm a year. after millions of years, will the earth let go and it flys away, or will it keep its grip until it hits Venus or Mars (probaly not). or will it fly off to be a planet or get stuck in the sun.

Well i cannot say if this drift will continue, because no one knows when it has started and if this drift is really a constant /we don't know where moon actually came fromso now we can only calculate when it was set off from Baikonur and this would be... probaly just as wrong as to calculate when moon will set itself free/. It won't reach Mars being im the orbit of Earth simply because Earth's gravity grasp would have let her go a loong time before that. But it will take a really long time - few simple calculations show that for 20 mil years the distance moon would make at this rate is 60000 km.

Cheers,
h34r:

Currently the moon is moving away from the Earth because it receives orbital kinetic energy from its tidal interaction with the Earth because the Earth rotates faster than the moon revolves. The moon also gives up orbital energy to the process which inelastically deforms and heats the Earth's mantle and the tidal effects on the Earth which speed up the Earth's rotation. Eventually the interplay of these forces will stop the recession of the moon and cause it to approach the Earth and either crumble into a ring of dust and small rocks or crash into the Earth.

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MY GOD... we're all doomed! No one can escape this the apocolypse of the moon. WE MUST FLEE TO MARS!!!
excuse my over reacting, but this seems a fair logical explanation to it. As to jayfb's say, if the moon did continue to drift off, (the sun still has another 5billion years of life left), it would porbaly we quite great how far it drifts away.

Hurtling away from us at 3cm per year. . . its going to be a very long time befor the Moon escapes Earths gravational grasp. As Gourhead said, It wont. . . It will look smaler, and Earths ociens will be less affected by its gravaty, Is this cousing the weather changes we are percieving to be apon us?. . . Hmmm...3cm/year. . .wow thats over an inch. gosh NASA had better get back there soon. Its ferther away as we speek. Two feet in just twenty four years. Yawn. . . .

That's almost one step away. Small step for humanity, huge one for the moon.

Hang on...so, will the moon crash/become a ring or reach a critical getaway point?

Actually, is possible that Phobos will crash on mars also in the future. I recommend you that you look a better place

With respect GOURDHEAD's post, there's no consensus about the fact that Moon will approach Earth again. Some theoreticians speculate this, but others say that will simply stop receding, and will maintain a constant distance thereafter

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It would be 600,000m or 600km.

The moon is receeding as was stated, due to the earth rotating faster than the moon orbits. This cuases the tidal bulges in the ocean to be dragged slightly ahead of the moons position (instead of directly below), causing an offset in earths gravitational attraction to the moon. This pulls hte moon forward, adding energy to it, and allowing it to shift outwards.

This will slow, as the tidal bulges weaken and earths rotation slows.

It will not cause the moon to disentigrate, nor come closer to the earth.

It will reach equilibrium at some point (earth day = 1 lunar orbit). If it reaches equilibrium before the moons orbit is beyond the "Roche Limit" it will be retained. If not, the other gravitational forces in the solar system will strip it from the earth, and allow it to wander around on it's own.

Now, IIRC, I heard of a simulation stating an equilibrium duration of ~50 days for the moons orbit and earth's single "daily" rotation.

For an example of a tidaly locked planet-moon system look at pluto and it's moon charon. The moon is currently locked to show only one face to us atm.

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If you seriously want the moon to go away and wander the universe at relativisitic speeds, all you have to do is build a moonbase, call it Alpha . . .

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I think you're mistaken about the meaning of the "Roche limit". It's the orbital distance inside which a satellite will be tidally disrupted (torn to bits), not the distance beyond which it will be lost.

The definition of "Roche limit" assumes the satellite has no structural integrity. Thus an artificial satellite made of sturdy materials can survive happily well inside the Earth's Roche limit. So could the Moon, but not nearly as far inside -- rock doesn't have the tensile strength of metal.

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I'm guessing the term Ricimer was looking for was the Instability Limit (Hill Sphere.) The Hill Sphere for the Earth has a radius of about 1.5 Million km (the moon is currently about 380,00 km away.) If the moon ever moves farther from the Earth than 1.5 Million km, it will be lost and assume it's own orbit about the sun.

Possibly Ricimer meant Roche sphere, given that Hill sphere and Roche sphere are synonyms

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As noted above, the Moon will continue to pull away until the Earth's rotation is tidally locked with the Moon's revolution around the Earth, and then the moon would slowly start coming back toward the Earth until reaching the Roche limit...

However, this will take a while, and it is possible that the Moon will be vaporized by the expanding Sun before it gets a chance to turn into a really amazing ring system around the Earth.

It is also possible that the Moon will be completely disassembled and used for parts by us before the tidal locking thing happens. We have to be realistic about these things.

Bad news for whomever happens to be on a moonbase at that time :-)

The mechanism of the moon's expanding orbit, as I understand it, is that it is gaining orbital energy due to tidal stretching of Earth's oceans. The moon gains a little bit of orbital energy (and moves a bit further out) with each pass whereas the Earth rotation slows down a little bit. For this process to continue inefinitely assumes that the Earth's oceans have not boiled off or been subducted gradually by continental drift without adequate replenishment from the other geologic/volcanic means or by suspected extra-terrestrial sources (assimilation of water from micro-comet absorbtion in our atmosphere.) Of course any process that would effect the oceans to this degree would have to take place over a vast timescale of hundreds of millions to billions of years.

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Not just the oceans, but the crust and mantle are lifted slightly and contribute. There is no need for liquid oceans to make this happen, as evidenced by the large number of dry tidally locked bodies in the solar system.

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Antoniseb's reply got me thinking about a similar future interaction between Triton and Neptune. Will Triton maintain its integrity and simply collide with Neptune, or will it break apart and form a spectacular ring beforehand? I guess either way a ring system will form since the ejecta from a collision will do the same thing.

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Um, you changed moons on us there in the middle, didn't you? I got confused for a few seconds, since I'm not on Pluto and I don't think you are either...

What mechanism would pull the Moon back towards the Earth once they are locked together? Does this mean that Charon is falling back towards Pluto as well?

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Actually that's not quite right.

I did mean the Roche "instability" limit, as opposed to the one that measures the minimum distance away from the planet before gravitational tidal forces cause the object to fall to pieces.

Also, the Roche limit calculations do not assume "no structural integrity", as they include a constant to address just such a thing. I've seen values for solid vs "liquid" objects, and while the actual value may be in contention, the calculations do take them into consideration.

And also note: The mooon will not come back. It will only continue to receed until it stops. There is no mechanism, short of earth getting walloped hard enough to rotate the other direction, (or the moon just plain being smacked like a billiard ball) that will cause the moon to approach earth again.

I was very confused by the original claim, and actually started to type a reply, but decided to think about it some more first. But an object with literally no structural integrity would, I suppose, be a collection of loose particles, and then the only thing keeping them from separating would be their own gravity. And then it seemed to me the limit would not be independent of the number/mass/density/etc. of the particles...

It would break up.

The Roche limit is based on the "liquid" assumption: that the satellite has no structural integrity. A rocky or icy moon has somewhat more tensile strength than a big water blob, but not much more. So a moon will break up before it impacts. (Another assumption here is that the satellite is significantly smaller than the parent body. I'm not sure what would happen to, say, Pluto-Charon if they ever came close; I'd guess that they'd both break up.)

The only way to avoid this is to approach very, very fast and/or directly. A "big splat" type impactor would remain pretty much intact until contact. But a slow sparalling-in event will cause breakup and ring formation.

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Well, I have a vague recollection that the mechanism was solar tides. Ricimer seems to think it will never happen. I've read other opinions, but even the most supportive ones say this would not take place until after the Sun runs out of hydrogen and turns into a red giant, making the issue moot.

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It will stay in Earth orbit. See my next post on why it is receeding.

PART 1:

First let us start out with some precursor information.

Historically timekeeping and calendars have been tied to the motions found in the heavens. These have been primarily the stars, our Moon, and the Sun. To get a rudimentary understanding of how time is measured and where we got our units of time, we must first talk about the motions of these heavenly bodies referenced back to our Earth. The background for this post will start with the Celestial Sphere, followed with a description of the Earth Sun relationship, and finally with the Earth Moon relationships/system.

The Celestial sphere:

When we look up at the stars in the night sky they appear to be stationary relative to each other. As the Earth moves from one side of the Sun to the other, the displacement of those stars due to parallax is less than one second of arc even for the nearest star (Proxima Centauri). One way of looking at this is a fixed sphere of stars surrounding the Earth/Sun system. This is often referred to as the Celestial Sphere. This is why some of the ancient civilizations considered the stars to be holes in a tapestry.

Since we are talking distances and parallax, lets briefly take a moment and describe such. The more familiar term for the layman when referring to stellar distances is called a light year. This is the distance light will travel in one calendar year. For example the star Proxima Centauri is approximately 4.22 light years from our solar system. Astronomers use another term that may be not so familiar called the Parsec. The Parsec (parallax-arcsecond) is the distance needed for an object (star) to have a shift of one arcsecond referenced to one astronomical second (AU), the average distance from the Earth to the Sun or approximately 93 million miles. An arcsecond is 1/60 of an arcminute, which is 1/60 of a degree. However, there are no stars that are close enough to exhibit this large a shift. The distance of a Parsec is about 3.26 light years and the nearest star is 4.22 light years.

Even though it appears the stars remain in “fixed” locations in the night sky, over a period of time the stars do move relative to each other and relative to the Earth. This is why the right ascension and declination (star location) changes over the years. If you look at a star catalogue based on the epoch B1950 and one base on the epoch J2000, you will notice some differences.

Another interesting item of note is that the constellations we see are made up of the brightest stars. Even in the same constellation these stars are at different distances from the Earth. Some may be dimmer than the others, however, being closer they are just as bright as a larger one further away. The brightness of a star is called its magnitude. There are two ways astronomers measure magnitude: Apparent Magnitude and Absolute Magnitude.

The Apparent Magnitude is how bright a star appears to us here on the Earth. The Absolute Magnitude is how bright a star would appear if it were exactly ten parsecs away from the Earth. (Close to 33 light years).

Two notes:

1) Apparent magnitude is usually denoted with a small “m” and absolute magnitude uses a capital “M”.
2) The magnitude scale is backwards of what you might think, the larger the number the fainter the object.

Since the Earth is tilted (23.5 degrees) in reference to the path it sweeps out in its orbit about the Sun, this path projected onto the celestial sphere does not fall on the celestial equator. This imaginary plane is called the ecliptic. Note: This angle between the ecliptic and the equatorial plane is called The Obliquity of The Ecliptic.

This imaginary plane crosses the celestial equator in two places (called the equinoxes). The Vernal Equinox falls in the spring as the Sun appears to cross the ecliptic going north and the Autumnal Equinox falls in autumn when the Sun again crosses the ecliptic, this time going south. Note: Vernal comes from the Latin vernalis, meaning spring. Also the term equinox relates to the word equal since both day and night are close to the same, 12 hours during the equinox.

The points where this plane is the farthest above (north) and below (south) the celestial equator is called the solstices. In the northern hemisphere of the earth, the most northern point of the ecliptic is called the Summer Solstice and the southern most is called the Winter Solstice. In the Southern hemisphere of the Earth the reverse is true.

The zodiac lies along the plane of the ecliptic. Since the Earth is orbiting the Sun, the Sun appears to follow the plane of the ecliptic, making one complete circle in one calendar year. The name “zodiac” comes from the Greek meaning animal circle. Note: The path of the Moon and the other planets fall pretty much on this plane as well. Since it takes 365 days for the Earth to orbit the Sun and there are 360 degrees in a circle, the Sun moves pretty close to 1 degree per day.

If you were to draw a line out from the Earth intersecting the Vernal Equinox, that line would be referred to as The First Point of Aries. The reason it was called this is that this line pointed to the first star in the constellation of Ares in March of 1950.

The celestial sphere is tied to the Earth for its coordinate system. Project the Earth’s equator out to infinity and you have the equator of the celestial sphere. Likewise the north and south poles of the Earth points to the north and south poles of the celestial sphere respectively. This makes it very easy to map the sky referenced to the Earth. This coordinate system is called the Equatorial Coordinate System. It ties in closely with our own geographic coordinate system here on the surface of the Earth.

There is one fundamental difference however. The geographic coordinate system is fixed upon the surface of the Earth (Lat Long) so it rotates with the rotation of the Earth. The celestial coordinate system is fixed to the celestial sphere and appears to rotate due to the Earth’s rotation. The “latitude” of the celestial sphere (the angle of an object above or below the celestial equator) is called declination with zero being on the equator. This is pretty easy since the celestial’s equator and poles appear to be fixed like our own earth. Unlike the Earth, since the celestial sphere appears to be rotating, the “longitude”, called right ascension, is not a “fixed” reference to the Earth. So instead of using degrees, hours were used for this measurement. First there needed to be a “fixed” direction to measure from. The Vernal Equinox was selected as the zero reference for the right ascension. Since there are 360 degrees in a circle, the Earth rotates about 15 degrees every hour. So you will note right ascension is measured in hours/minutes/seconds as apposed to degrees. Remember that for declination Zero is on the equator and for right ascension zero is at the Vernal Equinox. So the Vernal Equinox will have the coordinates of 0 degrees and 0 hours. This then becomes the center point for an Equatorial Sky Chart.

On to the Earth-Sun system: It takes one year for the Earth to rotate around the Sun one time and 24 hours to rotate on its axis. Think about this relationship. Not only is the Earth revolving on its axis, it is in motion about the Sun. (I know this is really basic grade school stuff, however, it will help in visualizing the concepts I am about to explain) Therefore the Earth moves 1/365th of its orbit about the Sun every day.

Ok, here is where that visualization will come in handy. Since a “day” is described by one complete rotation of the Earth on its axis, this equates from noon to noon (when a point on the Earth is directly pointed at the Sun). The term for this is called the Mean Solar Day. But here is the rub; the Earth has moved during this period of time we called a day. So the Earth must turn a tiny bit more to have the same spot facing the Sun every day.

PART 2

Now let us think of this celestial sphere we have been chatting about.

Remember the stars appear fixed in one location (at least on a daily basis). This means that one complete revolution of the Earth referenced to a star does not take that little bit of extra time to be over the same spot on the Earth. This “day” is referred to as a Sidereal Day. It takes approximately four extra minutes for the Earth to have the Sun over the same location on the Earth than a star.

This is the difference between a Sidereal Day and a Mean Solar Day.
Also the Earth is tilted on its axis from the plane of the ecliptic by 23.5 degrees. That tilt causes the North Pole to be currently pointed towards Polaris. As the Earth moves around the sun its pole stays pointed at Polaris. This is the cause of the seasons we experience. Note. This tilt varies back and forth from 21.6 degrees to 24.5 degrees approximately every 41,000 years.

There is also a precession of our pole and it sweeps a complete circle in the sky (think of the Earth as a top wobbling as it rotates) about every 26,000 years. This gives us different pole stars as the north pole of the Earth sweeps out a circle on the celestial sphere.

There are also a number of other motions that must be taken into consideration over the years such as the precession of the aphelion. Our Earth’s orbit around the Sun is not a perfect circle. It is an ellipse with the closest point of the orbit called the perihelion and the furthest point the aphelion. Currently the aphelion falls on the fourth of July. However, this is not always the case. The aphelion and perihelion change over the centuries and sweeps thru the calendar year with a periodicity of around 22,000 years.

The amount of “squishing” of an ellipse is called its eccentricity. If the eccentricity is equal to zero the orbit will be a perfect circle. Between zero and one the path of an orbit is an ellipse. Note: A circle is also known as a degenerate ellipse. However, should the eccentricity equal exactly one, the path becomes a parabola and finally, if the eccentricity is greater than one, the path then becomes a hyperbola.

The Earth’s eccentricity is very small. However, even this changes over time. Its eccentricity varies periodically about every 100,000 years. There are also other motions caused by the Moon, Jupiter and the Sun called Nutations. One of the major nutations has a period of 18.6 years.

Now that we have taken a cursory look at the Earth/Sun system, there is another big factor in all of this. It is called the Moon. The reason the Moon keeps one face to the Earth (Its rotation on its axis matches the period of its orbit) is it is tidally locked to the Earth. This tidal locking will eventually cause the Earth and Moon to keep one face to each other
.
Here is a more in depth explanation.

The total angular momentum of the earth moon system, which is spin angular momentum plus the orbital angular momentum, is constant. (The Sun plays apart also) Friction of the oceans caused by the tides is causing the Earth to slow down a tiny bit each year. This is approximately two milliseconds per century causing the moon to recede by about 4 centimeters per year. As the Earth slows down, the Moon must recede to keep the total angular momentum a constant. In other words as the spin angular momentum of the earth decreases, the lunar orbital angular momentum must increase. Here is an interesting side note. The velocity of the moon will slow down as the orbit increases.

Another example of tidal locking is the orbit period and rotation of the planet Mercury. What is interesting about this one is that instead of a 1:1 synchronization where Mercury would keep one face to the Sun at all times, it is actually in a 2/3:1 synchronization. This is due to the High eccentricity of its orbit.

There also can be more than one body “locked” to each other. Lets take a look at the moon Io. Io is very nearly the same size as the Earth’s moon. It is approximately 1.04 times the size of the moon. There is a resonance between Io, Ganymede, and Europa. Io completes four revolutions for every one of Ganymede and two of Europa. This is due to a Laplace Resonance phenomenon. A Laplace Resonance is when more than two bodies are forced into a minimum energy configuration.

And finally a look at the asteroid belt:

The asteroid belt has an estimated total combined mass of less than 1 tenth of the Earth’s moon. Jupiter also has a profound effect on the asteroid belt. Since Jupiter has a semimajor axis of 5.2 AU (I AU is the distance from the Sun to the Earth) it has an orbital period of 11.86 years. Since the asteroids are not all at the same distance from the sun, some of them have an orbital period of one half of Jupiter. This puts that asteroid in a 2:1 orbital resonance with Jupiter. The result of this resonance is gaps called Kirkwood’s gaps. So here is the rub; why did not these asteroids for a planet? The reason is the gravitational force of Jupiter. It perturbs the asteroids giving them random velocities relative to each other. Another effect of both Jupiter and the Sun on the asteroid belt is a group of asteroids that both precede and follow Jupiter in its orbit by 60 degrees. These asteroids are known as the Trojans.

Since we are now talking about orbiting bodies, let us digress just a wee bit further and briefly talk about orbits:

There are different sizes and shapes of orbits. We use the term Semi-Major Axis to measure the size of an orbit. It is the distance from the geometric center of the ellipse to either the apogee or perigee (The highest (apo) and the lowest (peri)). Apoapsis is a general term for the greatest radial distance of an Ellipse as measured from a Focus. Apoapsis for an orbit around the Earth is called apogee, and apoapsis for an orbit around the Sun is called aphelion.

Periapsis is a general term for the smallest radial distance of an Ellipse as measured from a Focus. Periapsis for an orbit around the Earth is called perigee, and periapsis for an orbit around the Sun is called perihelion.

The terms Gee and Helios comes from the Greek words “Ge” (earth) and “Helios” (Sun) respectively.

First lets talk a bit about “where it is”. An orbit is a nothing more than an object falling around another object. Both Kepler and Newton came up with a set of laws that describe this phenomenon.

Kepler’s three laws of planetary motion:

1) The orbit of a planet is an ellipse with the sun at one of the foci
. 2) The line drawn between a planet and the sun sweep out equal areas in equal times.
3) The square of the periods of the planets is proportional to the cubes of their mean distance from the sun.

So what is that telling us? In a nutshell, all orbits are ellipses, the close to the body you are orbiting the faster you go (e.g. if you have a highly elliptical orbit the satellite or planet’s velocity will increase as it approaches the object being orbited and decrease as it get further away).
These laws not only apply to planets and satellites, but to any orbiting body.

Note: Super geek alert #1:

For an orbiting body this is not entirely correct. It turns out that both bodies end up orbiting a common center of mass of the two-body system. However, for satellites, the mass of the Earth is so much greater than the mass of the satellite, the effective center of mass is the center of the Earth.

Newton’s three laws (and law of gravitation):

1) The first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. (Commonly known as inertia)
2) The second law states that force is equal to the change in momentum (MV) per change in time. (For a constant mass, force equals mass times acceleration F=ma)
3) The third law states that for every action there is an equal and opposite reaction. In other words, if an object exerts a force on another object, a resulting equal force is exerted back on the original object.
Newton’s law of gravitation states that any two bodies attract one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Note: Super geek alert #2:

Actual observed positions did not quite match the predictions under classical Newtonian physics. Albert Einstein later solved this discrepancy with his “General Theory of Relativity”. There are four classical “tests” that cemented General Relativity:

1) In November of 1919, using a solar eclipse, experimental verification of his theory was performed by measuring the apparent change in a stars position due to the bending of the light buy the sun’s gravity.
2) The changing orientation of the major axis or Mercury not exactly matching classical mechanics.
3) Gravitational Redshift
4) Gravitational Time Dilation

So what is all this trying to tell us? Planets, satellites, etc orbit their parents in predictable trajectories allowing us to “know” where they will be at any given time. A set of coordinates showing the location of these objects over a period of time is called its ephemeris.

PART 3 (last part)

Historically, time has been measured by the rotation of the Earth on its axis and the time it takes to rotate once about the Sun (a year). However, both of these are not uniform enough for precise calculations.

One of the units of time is called the second. It used to be defined as 1/86,400 of a Mean Solar Day. This was good enough for early calculations, but don’t forget that the Earth is slowing down due to tidal forces so that ends up changing over time. After a number of intermediate steps the second was finally redefined as:

The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. (Atomic time), also known as Coordinated Universal Time (UTC).

Since the Earth is slowing down approximately 1.4 milliseconds per day per century, this deceleration causes the Earth’s rotational time to vary from atomic time. The current true (instantaneous) rotation rate of the Earth is called UT1 (which is a non-uniform rotation). Over a period of a year the difference between it and UTC can approach a full second. However, since the Earth’s rotation is non-uniform, it is monitored continuously. If the difference between UT1 and UTC approaches 0.9 seconds, a leap second is added or subtracted from UTC to keep it uniform with the Earth’s rotation. So far all of the leap seconds have been positive. This tallies with the slowing of the Earth from tidal braking.

Note: Since the GPS time does not have leap seconds added or subtracted, it is diverging with UTC with every second added to UTC. Currently it is different by 13 seconds. This can cause some consternation when flying a satellite or spacecraft that uses GPS. If your ephemeris is calculated in GPS time and you receive a “vector” in UTC time, it will be off by 13 seconds. You just cannot add 13 or subtract 13 seconds and press on. The rub is that not only has the satellite moved 13 seconds (in-track), the Earth has rotated underneath by 13 seconds (cross-track) as well. This is especially noticeable for the high inclination orbits. Vectors have to be recalculated when translating between GPS and UTC.

The interesting note is that the last time a leap second was needed was clear back in 1999. Remember, the deceleration of the Earth is not uniform. There may be a number of factors that cause this non-linearity such as snow and ice loads, earthquakes and others we haven’t even thought of. This could account for this long delay between leap seconds. This certainly is not a permanent condition. The Earth will continue to slow down and the deceleration will still vary.