Lunar and Solar Period Locking

[jjalexand]

The average synodic rotational period of the Sun is approximately 27.27 days. (synodic means 'relative to an observer on earth')

The sidereal orbital period of the moon around the Earth is known accurately and is 27.321661 days. (sidereal means 'relative to an observer fixed in space' i.e. 'relative to the stars').

These two figures are remarkably close, and suggest there might be some kind of tuning relationship between them.

As pointed out by Janus in another thread, it is not easy to see why there should be a relationship between the sun's apparent rotational period relative to the Earth, and the time it takes the moon to orbit the Earth relative to the fixed stars.

However, there is another lunar period which is very close to the moon's synodic orbital period, and that is the moon's nodical period. The length of the nodical period is 27.2122 days, which is also very close to the solar synodic period of 27.27 days approximately. The nodical period is the period between two crossings of the ecliptic in the same direction.

Here is a feasible method here for tuning to occur, as the sun's gravity tries to pull the orbital plane of the moon into the plane of the ecliptic. Solar asymmetries or tidal effects could possibly act over long periods to tune the moon's nodical period (and thus also its sidereal period) to the solar synodic period.

(Since the sun is a fluid body, it's rotation rate varies depending on latitude, and the 'average' rate may not be directly measurable. I am not sure exactly what method is used to determine the above figure of 27.27 days, but it would seem logical to me to define it as follows: The synodic period of rotation of an equivalent rigid body of the same mass, radius, mass distribution and angular momentum as the sun. Since this 'average' period is preumably difficult to determine and conceptualise, it may only have become known relatively recently in relation to other simple orbital periods, and the co-incidence between these two periods may not have been noticed before)

Since the sun's average synodic rotational period is clearly difficult to define and deduce, the small apparent variation between 27.21 and 27.27 may be due to the methods by which it is defined and derived. The effective period for the purpose of tuning the nodic period may in fact be 27.21 days.

The following web page has a thorough discussion of the various periods of the lunar orbit:

http://www.astronomy.org/astronomy-survival/eclipse.html

(This thread is a continuation of a sub-discussion that arose in the "Why doesn't the Moon spin? thread". I thought it deserved its own thread)

Any comments?

 

[russ_watters]

Originally posted by jjalexand
Any comments?

Two unrelated numbers have similar values: that's a coincidence.

 

[jjalexand]

Reply to Russ Watters

Here is a quotation from the previously mentioned web page:

"The regression of the moon's nodes results from the sun's gravity trying to pull the orbital plane of the moon into the plane of the ecliptic. The result of this force however, acts at a right angle to it, thus causing the moon's orbit to wobble (regress or precess) to the west. One complete wobble takes 18.61 years."

Therefore, these two numbers may not be unrelated, because there is already a recognized known relationship between the sun's gravity and the moon's orbit expressed in the above relationship.

I have adapted my argument to the NODIC period, not the SIDEREAL period. Did you see that? How about adapting your thinking, and giving a slightly more substantial response?

 

[jjalexand]

Moon moving away from Earth argument

There is an argument against the above possibility, put forward by Janus, that says:

"The moon is moving away from the earth, therefore this must be coincidence, as it was not true in the past, and will not be true in the future"

However, whilst the moon is moving away from the Earth (and thus it's orbital period is increasing), the period of rotation of the sun is also presumably increasing, as the sun is probably slowing down also due to tidal forces, internal frictions between matter moving at different speed in different latitudes, etc.

If there was any sort of match between these two rates, then the relationship could hold for perhaps a considerable period, and may well be holding now, even if it did not hold in the distant past and will not hold in the distant future. Different lockings may appear every now and then as the relative periods come close to being integral multiples.

(The sun has probably been slowing down ever since the formation of the solar system. Rapid initial rotation would have been caused by conservation of momentum as the gas cloud that formed the solar system collapsed under it's own gravity, rotated faster, forming a disk due to spin, then rings (a form of gravitational collapse of the disk to a lower potential energy state), then planets (gravitational collapse AROUND the rings) with a rapidly rotating star at the centre.)

 

[selfAdjoint]

Excuse me, "The period of the Sun"? Period about what? I hesitate to even ask, but you do know, don't you, that the Sun doesn't go around the Earth?

 

[russ_watters]

Originally posted by jjalexand
I have adapted my argument to the NODIC period, not the SIDEREAL period. Did you see that? How about adapting your thinking, and giving a slightly more substantial response?

I doublechecked, but unless I misread again, you're comparing one's synodic period to one's siderial period. Maybe if you compared sidereal to sidereal or synodic or synodic I'd find that an interesting coincidence, but what you have can barely even be considered a coincidence.

Hey, did you know that pi^2 differs from G by less than 1%? Interesting coincidence?

Have you ever noticed that the numbers 69 (yes, I'm a pervert) and 666 (yes, I'm satanic) appear with an abnormal frequency in your everyday life? That's your brain's highly evolved instinctive pattern recognition software looking for patterns in everything you see. What is not instinctive is the ability to recognize if the pattern is real or just a coincidence. In the case of the numbers 69 and 666, you don't actually see them more often than other numbers, you just notice them when you see them. In the case of the periods you mentioned, there is no relationship, just a coincidence that they are near each other in value.

 

[jjalexand]

Reply to SelfAdjoint

Please read the original post, I'm talking about the period of ROTATION of the sun. I explained two different types of period of roation, synodic and sidereal in the post. Thge term 'period of the sun' is shorthand in the context of a number of different periods, some of them orbital periods, and in the case of the sun, it's rotational period.

 

[jjalexand]

Reply to Russ Watters

Russ, please read the post at the top of this thread. Have you heard of the NODICAL period of rotation of the moon? Do you know it is a different thing from the sidereal period?

I explained it all in the post. It is also well explained in the HTML reference I gave.

I am NOT comparing the solar synodic rotation period with the sidereal orbit period of the moon anymore.

That was in the previosu thread. This is a _new_ idea :) It is all clearly explained in the post. Maybe you skimmed it too quickly.

 

[russ_watters]

Originally posted by jjalexand
Maybe you skimmed it too quickly.

Maybe. This is what I see:

...synodic rotational period of the Sun...

...sidereal orbital period of the moon around the earth...

What I don't see is a basis for thinking that sidereal anything and synodic anything should be related. Sidereal and sidereal or synodic and synodic, maybe.

 

[Janus]

Originally posted by jjalexand


Here is a feasible method here for tuning to occur, as the sun's gravity tries to pull the orbital plane of the moon into the plane of the ecliptic. Solar asymmetries or tidal effects could possibly act over long periods to tune the moon's nodical period (and thus also its sidereal period) to the solar synodic period.

No it isn't a feasible method. There is no mechanism through which the rotation of the Sun can "tune" the nodical period. The nodical period is just a combined effect of the Moon's Sidereal Period and the period of the regression of the Nodes (18.61 years).
The fact that the Sun is spinning can have no effect on this.


Coincidences happen. This just happens to be one, and there is no physical connection that causes it.

 

[jjalexand]

reply to russ watters

Russ, I have extracted paragraphs 5 and 6 from the post at the top of this thread, I think you are still missing seeing these, or you are looking at some older post.

"However, there is another lunar period which is very close to the moon's synodic orbital period, and that is the moon's nodical period. The length of the nodical period is 27.2122 days, which is also very close to the solar synodic period of 27.27 days approximately. The nodical period is the period between two crossings of the ecliptic in the same direction.

Here is a feasible method here for tuning to occur, as the sun's gravity tries to pull the orbital plane of the moon into the plane of the ecliptic. Solar asymmetries or tidal effects could possibly act over long periods to tune the moon's nodical period (and thus also its sidereal period) to the solar synodic period."

 

[jjalexand]

Reply to Janus

We could keep on contradicting each other all week, but I will leave it for others to judge who is the bigger fool. This really seems to be more a problem in Psychology than Physics.

I have given clear reasons why the sun's gravity _can_ and does affect the nodical period of the Moon, quoted from the website reference I gave above, which was produced by astronomers. I will clarify it for you:

If we take the top of the moon's orbit in relation to the ecliptic, i.e. the moons maximum height above the ecliptic (A), then draw a line down vertically from (A) to the ecliptic (call the point of intersection (B), then make a right angled triangle between these two points and the center of the sun (C), we have a force vector from the (A) to (C) caused by the sun's gravitational attractive force on the moon. This force vector has a small component in the direction from A to B. That force vector from A to B has a component tangential to the moons orbit which is inclined to the ecliptic. Any asymmetries in the sun's gravity caused by small mass imbalances can exert smaller proportional effects on the moon's orbit via this force vector from A to B and then via tangential component of AB to the moons orbit. When the moon is rising up to the maximum point, any small increase in the sun's effective gravitation attraction at that point will act to slow it in its orbit. When the moon has passed it's maximum point and is falling back to the ecliptic, the same increase will act to speed it up in it's orbit. This is the synchronizing mechanism I am talking about. Let me know if you would like a diagram and I will put one up on the web for you. We are basically looking at a sundial-like structure, with the ecliptic being the base of the sundial.

This is just very simple physics, which I think most people who view these forums can clearly understand.

 

[jjalexand]

Second thoughts

Actually, I don't really like the above explanation, and my reply is a slightly rude too, sorry. Anyway I can accept being the fool if it turns out that way.

My explanation did not mention the precession, which I believe is caused by the 'tilting' effect of the AB vector and it's double mirror image, which point in the opposite directions above and below the ecliptic, and on opposite sides of the lunar orbit. It also ignored a more powerful effect discussed below.

A strong objection to my theory seems to be that there actually a much bigger effect of the solar gravity, and that is to directly act on the orbit with the almost horizontal AC vector who tangential component to the orbit would be much stronger.

Presumably it is already recognised that the moon's orbit receives a speedup as it heads towards the sun, and a slowdown as it heads away again.

If there were mass asymmetries in the sun, they would show themselves there in a much stronger way, but this would possibly be a synodic to synodic relationship (although it would be symmetrical with respect to the nodical orbit, so I'm not sure), which we don't have because there are no common numbers.

In summary I would say that of course it could be a coincidence that these two numbers are close, perhaps say 60% for example.

But I also think there are very many complexities, for example tidal interations, including actions from Jupiter on the sun that might be enough to create detectable solar gravity variations. Also, every orbit in the solar system is in a sense affected by every other orbit, by the changes in gravitational force that are broadcast out at the speed of light from the body in that orbit. (Are these orbits still perfect ellipses after that? Could we detect all nearby masses by observation of these variations? - would require two preferably orthogonal orbits. A sort of graviational observatory?. Could we have answered this question with a really good simulator of the solar system by speeding up the sun's rotation and running it forward for a few millenia. Do we have such a simulator? If not, would it be good to have one?)

I think the idea did not really get a fair hearing from the mentors from my point of view as a poster, and one or two objections were definitely over-hasty or mistakes in my opinion.

A couple of other interesting ideas have come out of this which I might follow up in other posts.

 

[Nereid]

The rotation rate of the Sun's surface is fairly easy to determine, from sunspots for example. It varies from ~25 days at the equator to >30 days at the poles. Determining the rotation period(s) of the Sun is a science project which high school kids are encouraged to do by some teachers; there are packages on the internet which a teacher can use easily. An example:
http://www.sciencebuddies.org/mentoring/plugin_soho1_abstract.shtml

The Sun doesn't have 'mass asymmetries' - other than differences in density with radius, and a small oblateness due to its rotation. If there were significant asymmetries, they'd've long since been detected, through deviations in orbits of solar system objects, especially Mercury and Earth-crossing asteroids, from those predicted from Newtonian celestial mechanics (with the appropriate relativity corrections).

How does the Sun's rotation period vary with depth? At first glance this might seem an impossible question to answer. However, helioseismology is sufficiently advanced that it can be measured, at least for the outer parts of the Sun. Here's an interesting paper on the topic:
http://www.sp.ph.ic.ac.uk/~mjt/pr03a.html

A really cool pic is Figure B, near the bottom of the page: "The time-averaged rotation in the interior of the Sun, as deduced from helioseismic measurements by the MDI instrument on board the SOHO satellite. The Sun's equator is along the bottom of the plot, the pole at the top. The rotation in the convection zone (i.e. the outer 30 per cent) shows vivid contrast with faster rotation near the equator (red colours) and slower rotation near the pole (blue colours). The deeper interior appears to rotate at a nearly uniform rate with a period of about one month."

If we take this deeper, nearly uniform rate as the 'true' rotation period of the Sun, the near coincidence with the Moon's nodical period becomes less coincidental.

 

[jjalexand]

reply to nereid

Thanks Neried, you obviously know something about this.

A couple of points:

(a) It would be more accurate to say "there are no mass asymmetries in the sun above a certain limit" rather than "there are no mass asymmetries at all". Clearly there are mass asymmetries below some limit, starting with quantum effects, and perhaps going up to sunsport effects. And certainly there are tidal bulges caused by Jupiter for example, that alos create asymmetries of a form.

(b) There are clearly several different ways of defining the "average rotaitonal period of the sun". Any method based on averaging out the speeds at different levels may not give an average that is based on the overall angular momemntum. We would need to integrate each slice speed x it's mass at least to get the sort of average period I am talking about, and that may not be the standard high-school method.

 

[Nereid]

Originally posted by jjalexand
(a) It would be more accurate to say "there are no mass asymmetries in the sun above a certain limit" rather than "there are no mass asymmetries at all". Clearly there are mass asymmetries below some limit, starting with quantum effects, and perhaps going up to sunsport effects. And certainly there are tidal bulges caused by Jupiter for example, that alos create asymmetries of a form.

Yes; a more accurate statement might be: "no mass asymmetries detectable from orbits of solar system objects." Note that this mass asymmetry limit may be far below that which would give rise to your proposed 'solar-nodical period' lock.

Originally posted by jjalexand
(b) There are clearly several different ways of defining the "average rotaitonal period of the sun". Any method based on averaging out the speeds at different levels may not give an average that is based on the overall angular momemntum. We would need to integrate each slice speed x it's mass at least to get the sort of average period I am talking about, and that may not be the standard high-school method.

Yep, and that's fairly easy to do (at least in principle) because the solar models are now so good. Figure B in the link gives you the rotation rates, by radius and latitude; once you get a mass fraction (or equivalent) by radius (latitude is a cinch; assume constant density at any given radius), you can do the calculation to get an estimate for whatever 'average' rotational period you choose to define. However, you will need to be quite clear what your definition is, and you should write this out BEFORE performing the calculation!

[Edit: thanks for the bouquet, but no, I don't think I know very much about this subject; I wish I did. ]

 

[Janus]

Originally posted by jjalexand
And certainly there are tidal bulges caused by Jupiter for example, that alos create asymmetries of a form.

These tidal bulges follow Jupiter around the Sun, and don't rotate with the body of the Sun. This gives them a synodic period of 1.09 years. This in no way relates to your attempts to show a sychronization between the Moon and Sun.

On another note, concerning your, 'Moon speeds up heading towards the Sun and slows down moving away' statement. This doesn't happen.

The Earth Moon system is in orbit around the Sun, and thus is in freefall with respect to it. As a result there is no net pull of gravity on the Moon by the Sun wrt to the Earth, as you describe in your post.

That is not to say that the Sun has no effect on the Moon's orbit. There is the Tidal effect caused by the fact that the Moon moves slighty closer and further from the Sun than the Earth does.
The result of this is a net force that points away from the Earth, inwards towards the Sun, and outwards away. it is weakest near the Earth's line of orbit and stronger further away. The net effect of this is to stretch the Moon's orbit along the radius vector of the Earth. (It also supplies the force that attempts to align the Moon's orbit with the ecliptic and causes the recession of the nodes.)

Now the Moon has an eliptical orbit itself, therefore, over the course of a year, this stretching effect increases and decreases the eccentricity of the orbit, depending on the time of the year.

Thus, any "small variations" in the Sun's gravity only effect on the Moon's orbit would be this tidal effect. Since tidal effects fall of by the cube of the distance, this would be very, very, very small. Many orders of magnitude smaller that the tidal interaction between the Earth and Moon that is causing the Moon to increase its period. (The full tidal effect of the Sun of the Earth itself is 1/2 of that of the Moon.)

Thus there is no way that this could overcome the natural tendency of the Moon to increase it period.

 

[jjalexand]

Reply to Nereid

Solar Mass Anomalies:

Sunspots and solar flares are definitely detectable visually from Earth. Perhaps their graviational effect is also detectable?

Definition of average mass of sun:

I did provide what I consider to be a fair definition for these purposes in a prior post, it may have been in this thread of the "Why doesn't the moon spin thread".

Thanks for the info re measuring and calculating these items, I might give it a go.

Do you have any interest in the putative circular waveform that may have occurred leading up to the formation of the sun, its rings and planets as the solar system formed from a contracting cloud of gas.

Do you know if it is regarded as possible that this waveform may indicate something about the shape of the original gas cloud which was perhaps centered on a previous stellar explosion (ie supernova)? I mean that if rings formed, they were possibly preceded by distributed semi-toroidal bulges/densities in the cloud forming a kind of circular ripple effect like dropping a stone vertically into a pond.

Do you think it would be worth starting another thread on this, which to me seems to be quite an interesting topic? We could also look at the distribution of different elements, whether there is any indication of any wavepattern here, whether one would expect one theoretically, or whether such a wave had only a single peak for each element (ie some sort of circular pattern with a histogram-like cross section). I know vaugely that there is a fair bit of thinking about the distribution of elements at different distances from stars.

 

[Nereid]

I'd be quite surprised if the gravitational effects of sunspots and flares were detectable any time in the next 50 years (unless, perhaps, there's a breakthrough from some left field, like SUSY or neutrino detection).

Regarding the formation of the solar system - any solar system: AFAIK, this is also an area of active research, from the collapse of something like a Bok globule to the formation of planetisimals to the abundance gradients of elements and molecules.

You may have heard of the book "Rare Earth", by Ward and Brownlee; it has some good chapters on factors involved in the formation of solar systems.