# Earth - Moon - Sun are in orbital resonance ??

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In round numbers, a lunar sidereal month (360 degrees rotation, not the same as New Moon to New Moon), is 28 days, and there are almost exactly 13 such sidereal months per Earth orbital year.

Might this mean, that the Earth-Moon system, is "semi-locked", into some sort of "orbital resonance", between their mutual orbit (4 weeks), and mutual solar orbit (52 weeks) ??

No.

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So the near-integral relationship between Earth-system's (sidereal) months & years is purely coincidence ?

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Yes. First off, you fudged the numbers (i.e., you cheated) to make the ratio look closer to an integer than it is. The sidereal year is (or was, epoch J2000.0) 365.256363004 days long. The sidereal month is, on average, 27.321661 days long. That is a ratio of 13.3687466. If you want to pretend that that is "almost exactly 13", have at it.

Second, there is no reason for such a coupling. The number of months per year is a function of the distance between the Earth and the Moon. The Moon is retreating from the Earth and has been since it first formed due to angular momentum transfer from the Earth's rotation to the Moon's orbit. The mechanism that drives this retreat is the tides. The Earth tides are responsible for some of the transfer, but the bulk of the transfer is due to the ocean tides. The transfer rate due to the ocean tides is not constant. It depends a lot on the configuration of the continents.

You are playing numerology, and doing so badly. The ancients did a much better job than you. They saw that there are almost exactly exactly equal to 235 synodic months in 19 tropical years (1 tropical year is 365.24219 days). This is the Metonic cycle. They also saw that 223 synodic months, 242 draconic months, and 239 anomalistic months are almost all the same length of time, to within a couple of hours. This is the Saros cycle. Numerology still, but very useful numerology (at least for mystics).

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The Sun gravitationally influences the Earth-Moon system. The Sun may not be the dominant influence, but perhaps it tends to "pin" or "stick" sidereal months at or near (integer) orbital resonances, so that the Moon's month spends more time in orbital periods corresponding to the same, than it would, were the Earth-Moon an isolated system, in Deep Space.

(NOTE: I simply asked a question...)

Edited by Widdekind

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The Sun gravitationally influences the Earth-Moon system. The Sun may not be the dominant influence, but perhaps it tends to "pin" or "stick" sidereal months at or near (integer) orbital resonances, so that the Moon's month spends more time in orbital periods corresponding to the same, than it would, were the Earth-Moon an isolated system, in Deep Space.

The transfer of angular momentum to the moon is due to tidal coupling with the earth, and the strength of that has a lot to do with the configuration of the continents and oceans.

(NOTE: I simply asked a question...)

You asked a loaded question. It seems that you want the answer to be yes, but the answer is no.

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You are playing numerology, and doing so badly. The ancients did a much better job than you. They saw that there are almost exactly exactly equal to 235 synodic months in 19 tropical years (1 tropical year is 365.24219 days). This is the Metonic cycle. They also saw that 223 synodic months, 242 draconic months, and 239 anomalistic months are almost all the same length of time, to within a couple of hours. This is the Saros cycle. Numerology still, but very useful numerology (at least for mystics).

Great, now I have to pay to change my license tag AGAIN! Well, at least I know why I've been losing the lottery now.

Edited by lemur

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You asked a loaded question. It seems that you want the answer to be yes, but the answer is no.

No -- I meant what I said, I asked a question... that's what I did, seriously, I asked a question, on a "Science" forum...

Yeah.

I thought the answer might be yes, maybe not. Thanks.

I would like to know, what the grav. influence of the Sun is, on the E-M system. Surely, it exerts some sort of influence, that an 'ideal' isolated E-M system, "in deep space", would not experience. 2e30 kg, at only 1 AU, I would naively guess something would happen.

Apparently, 13:1 is "too big" to be a resonance... why would that be ? Note, tho, that I thought the sidereal month was much closer to 28 days, at 13.4:1, the alleged "resonance number" (13.4) is "right in the middle" between 13-14... which looks rather random.

(Sorry if I hit "a nerve", on an alleged 13:1 ratio... oops.)

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No -- I meant what I said, I asked a question... that's what I did, seriously, I asked a question, on a "Science" forum...

Yeah.

I thought the answer might be yes, maybe not. Thanks.

OK. One of the limitations of written communication is a loss of nuance. Sorry that I misinterpreted your tone and that my response was heavy-handed.

I would like to know, what the grav. influence of the Sun is, on the E-M system. Surely, it exerts some sort of influence, that an 'ideal' isolated E-M system, "in deep space", would not experience. 2e30 kg, at only 1 AU, I would naively guess something would happen.

Apparently, 13:1 is "too big" to be a resonance... why would that be ? Note, tho, that I thought the sidereal month was much closer to 28 days, at 13.4:1, the alleged "resonance number" (13.4) is "right in the middle" between 13-14... which looks rather random.

(Sorry if I hit "a nerve", on an alleged 13:1 ratio... oops.)

In order to change any of these periods you have to change the energy (and angular momentum), and as D H has already said, that happens via tidal interactions, which vary as r^3. So while the sun has an influence, because the effect drops off more rapidly than the force of gravity, the earth and moon influence each other more strongly. D H has a recent post on the subject.

The second part of all of this is why the 13:1 ratio would be a resonance (or anti-resonance); in order to keep that ratio you'd have to stop transferring energy between the bodies. Why would that happen?

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No -- I meant what I said, I asked a question... that's what I did, seriously, I asked a question, on a "Science" forum...

You asked a question that you could have answered yourself had you spent even a minute researching it. http://www.wolframalpha.com/input/?i=1+year+%2F+1+sidereal+month

Edited by D H

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In order to change any of these periods you have to change the energy (and angular momentum), and as D H has already said, that happens via tidal interactions, which vary as r^3. So while the sun has an influence, because the effect drops off more rapidly than the force of gravity, the earth and moon influence each other more strongly. D H has a recent post on the subject.

The second part of all of this is why the 13:1 ratio would be a resonance (or anti-resonance); in order to keep that ratio you'd have to stop transferring energy between the bodies. Why would that happen?

Astronomers define the Hill Sphere Radius, about a gravitating planetoid, to be that orbital distance, beyond which, any satellites will be tidally stripped by the central star:

A full derivation of the Hill Sphere Radius involves solving the restricted 3-body gravitational problem. A simpler, approximate, derivation involves recognizing that RH is the distance from an object at which the orbital period of a small test particle equals the orbital period of the object itself around the star (Scharf. Extrasolar Planets & Astrobiology, p.127).

So, seemingly, until the Earth's Moon's period is ~1 year (1:1 resonance), it will remain more tidally influenced by the Earth, than by the Sun, and remain bound to the former. So, seemingly, also, the Moon orbits the Earth >13x too quickly, to begin being affected / afflicted by tidal interactions w/ the Sun.

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Astronomers define the Hill Sphere Radius, about a gravitating planetoid, to be that orbital distance, beyond which, any satellites will be tidally stripped by the central star:

So, seemingly, until the Earth's Moon's period is ~1 year (1:1 resonance), it will remain more tidally influenced by the Earth, than by the Sun, and remain bound to the former. So, seemingly, also, the Moon orbits the Earth >13x too quickly, to begin being affected / afflicted by tidal interactions w/ the Sun.

The Hill sphere of a planet is $r_H = \sqrt[3]{\frac {m_p}{3m_s}}$. This makes the Earth's Hill sphere about 1/100 of an AU. An object of negligible mass orbiting the Earth at the Hill sphere radius will have a period of about 7 months. However, the Hill sphere is but an approximation. As a rule of thumb, stable prograde orbits have a semi-major axis that is half the Hill sphere; for retrograde orbits the stable orbital radius increases to about 2/3 of the Hill sphere radius. The Moon is orbiting the Earth at about 1/4 of the Hill sphere radius, so its orbit is currently stable. The Moon will have to retreat to about twice its current distance before it is at risk of being stripped from its orbit about the Earth.

However, this has nothing to do with whether the Sun has a perturbing influence on the Moon's orbit. The Sun has a marked perturbing influence on the Moon's orbit.

Regarding resonances: Even though the current ratio of the Moon's orbital period about the Earth to the Earth's orbital period about the Sun is not an integer, there have been many times in the past where the period was an integral number. Just because such events have occurred does not mean that there were any resonating consequences of those events. You need to find some coupling between the perturbative effects and the fact that the Moon's orbital period about the Earth and the Earth's orbital period about the Sun are related by some simple integral (or rational) ratio. As far as I can tell, you won't find any.

What you will find is that some claim that perturbations induced by various planets have resulted in some resonant feedbacks that acted to change the Moon's eccentricity. In particular, two events in the past may have had the evection coupled with the planetary perturbations caused by Jupiter and Venus.

Matija Ćuk, "Excitation of Lunar Eccentricity by Planetary Resonances", Science, 318:5848 (12 October 2007)

http://www.people.fas.harvard.edu/~cuk/papers/eccentricity.pdf

But maybe not:

Ian Garrick-Bethell and Maria T. Zuber, "A primordial origin for the lunar eccentricity", in preparation

http://web.mit.edu/iang/www/pubs/primordial_eccentricity_rev14.pdf

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