PDA

View Full Version : Change in period of lunar month



dwnielsen
2009-Jun-21, 05:42 PM
Hello, all!

The Earth day (ie, solar day) gains approximately (1 s) every (62500 y), measuring years in a fixed time unit (not days). The length of the Earth year may be generally considered constant over the past few billion years, as I understand it.

My question is, is it acceptable to hold lunar revolution in fixed proportion, that is, 29.53059 days, no matter the length of day?

Gandalf223
2009-Jun-21, 06:37 PM
My question is, is it acceptable to hold lunar revolution in fixed proportion, that is, 29.53059 days, no matter the length of day?

Not really. The moon is gradually moving away from the earth. As it does so, the lunar day gets longer. The mechanism for this is the tides, which are slowly slowing the earth's rotation, thus making the days here longer. Conservation of angular momentum for the earth/moon system requires that the energy lost by the earth goes somewhere; it goes into raising the orbit of the moon.

In a few billion years, the moon's distance will stabilize and the earth's rotation will become gravitationally locked to the moon. From then on, the earth's rotation will match the moon, meaning only one side of the earth will ever see the moon.

Of course, by the time that happens the sun will have exhausted its fuel and gone giant or blown off its upper layers, and the earth and moon will be nothing but galactic cinders. Assuming there's anything left at all...

dwnielsen
2009-Jun-21, 07:47 PM
Thank you, Gandalf.

I was thinking the diminishing energy of the Earth's rotation was only radiating as heat from Earth somehow, leaving the system. But now what you say makes intuitive sense. I would suppose in general other planets do not undergo such dynamic changes in their moon systems, because they are much larger than their moons or do not contain so much fluid - that might be wrong, though. I wonder at what distance the moon might be considered another planet, although I see on a Wiki page for "double planet" a "tug-of-war" definition that already qualifies it as such, which I'd like to think it is.

An expression is already given for the length of solar day in Arbab's "The Length of the Day: A Cosmological Perspective" (2009 Jan), which I'm assuming to be accurate.

I'd very much like to obtain an expression for the lunar month (or, equivalently, a tidal day) as a function of time. Do you know of one, or a paper trail I might follow?

chornedsnorkack
2009-Jun-22, 11:27 AM
What is the official length of the month?

And what is the accumulated shift of the phases of Moon since 1582?

dwnielsen
2009-Jun-22, 03:19 PM
If one enters "lunar month in days" on Google, the answer is 29.53059 days.

Also, text at [http://www.ctan.org/tex-archive/macros/latex/contrib/calxxxx/readme.pdf] states,

"The lengths of solar (tropical) year and lunar month in days are
Y = 365.24219872, M= 29.530588.
(These are values for a period December 31st, 1900, at 12h since it slowly
decreases.)"

However, the current period used in a line of geological time papers is 29.5271 days.

That is given in these 2 papers:
http://www.mantleplumes.org/WebDocuments/GEOY-32-10-841.pdf
http://www.mantleplumes.org/WebDocuments/MazumderESR2004.pdf

They also refer to articles stating that the ratio P_synodic / P_sidereal = 1.0808 for the past 1 billion years, and that the moon likely collided with the Earth between (2 Ga) and (1.5 Ga).

In the end, I'm looking for a very accurate expression for the period of the synodic lunar month as it changes over the past 100 million years, without trying to reinvent the wheel - but any pointers or advice is much appreciated.

Hornblower
2009-Jun-22, 03:43 PM
What is the official length of the month?Try browsing the Wiki article on "month".
http://en.wikipedia.org/wiki/Month
It gives the duration is SI days for several types of month, and the secular rates of change for some of them. As I understand it the SI day is 86,400 official atomic seconds.


And what is the accumulated shift of the phases of Moon since 1582?

Relative to what?

hhEb09'1
2009-Jun-22, 04:19 PM
The Earth day (ie, solar day) gains approximately (1 s) every (62500 y), measuring years in a fixed time unit (not days). As Gandalf223 has said, this is mostly attributable to lunar tides, which also lengthens the lunar month.

However, the general increase in the length of the day over the last century was nearly wiped out in the past ten years (as was evidenced by a long absence of leap seconds), so none of it can be depended upon to be a constant, including the change.

chornedsnorkack
2009-Jun-22, 04:26 PM
Found the data.

70 499 183 months are supposed to be exactly 2 081 882 250 days.

So three questions:

1) What was the error of this length compared to the true speed of Earth rotation and Moon revolution as they moved in 1581?

2) What has been the change in the true length of month between 1582 and 2009 (due to both changes of Earth rotation and Moon revolution)?

3) What is the accumulated phase difference in the phase of the Moon, between 1582 and 2009, due to both of the above errors?

hhEb09'1
2009-Jun-22, 04:59 PM
So three questions:

1) What was the error of this length compared to the true speed of Earth rotation and Moon revolution as they moved in 1581?We don't really know, because they are so variable.

And why 1581 (or is it 1582?)

chornedsnorkack
2009-Jun-22, 05:07 PM
We don't really know, because they are so variable.

And why 1581 (or is it 1582?)
The Gregorian calendar was proclaimed in February 1582. So 1581 was the last full year before proclamation of Gregorian calendar.

With the observations and measurements of four centuries, precise tools and theory of heavenly mechanics, are we more precise now in estimating the true length of month in 1581 than the people then observing were? Remember, we are using all the same historical records - the only thing we lack is live eye observing in 1581.

hhEb09'1
2009-Jun-22, 05:21 PM
Offhand, I'd say "yes," if I understand your question, and I'm not sure about that.

But still, why 1582, why the phase shift?

chornedsnorkack
2009-Jun-22, 06:07 PM
Offhand, I'd say "yes," if I understand your question, and I'm not sure about that.

But still, why 1582, why the phase shift?
The original question was about holding the ratio of synodic month to solar day to a fixed (and rational) number.

This is being done, and being done since 1582.

Thus my question is: how big was the error by measuring wrong value back in 1581, and how big is the error due to the ratio itself having changed between 1581 and 2009? Also, how big is the accumulated difference, from both sources, between full moon and true opposition of moon?

hhEb09'1
2009-Jun-22, 06:17 PM
The original question was about holding the ratio of synodic month to solar day to a fixed (and rational) number.

This is being done, and being done since 1582.I did not know that. I did not know that was possible.

Thus my question is: how big was the error by measuring wrong value back in 1581, and how big is the error due to the ratio itself having changed between 1581 and 2009? If the ratio being held constant, how could it change?

chornedsnorkack
2009-Jun-22, 07:12 PM
I did not know that. I did not know that was possible.
Being done by Inter gravissimas - not only by Papists, but by Protestants, many Orthodox and even heathens.

If the ratio being held constant, how could it change?

The calendar is held constant. The underlying movement of Earth, Sun and Moon changes.

hhEb09'1
2009-Jun-22, 07:49 PM
Being done by Inter gravissimas - not only by Papists, but by Protestants, many Orthodox and even heathens.Why does Inter Gravissimas (http://en.wikipedia.org/wiki/Inter_gravissimas)have anything to do with the synodic month at all?

dwnielsen
2009-Jun-22, 08:14 PM
However, the general increase in the length of the day over the last century was nearly wiped out in the past ten years (as was evidenced by a long absence of leap seconds), so none of it can be depended upon to be a constant, including the change.

Really?! I assume this is due to high-order astronomical effects (not to global warming or something). The Arbab article I cited shows a smooth trend when considered over past billions of years, but states, "The slowing down in the rotation is not uniform; a number of irregularities have been found".

To correct an earlier statement I made: Apparently the Moon-Earth collision would have occurred ca (4.5 Ga), which has been common knowledge since 2001 (http://www.nature.com/nature/journal/v412/n6848/abs/412708a0.html), not at (2 Ga) thought in 1980 (and for some reason cited in the 2004 Mazumder article).

chornedsnorkack
2009-Jun-22, 10:32 PM
Why does Inter Gravissimas (http://en.wikipedia.org/wiki/Inter_gravissimas)have anything to do with the synodic month at all?

It deals with determining the time of synodic new moon and full moon.

hhEb09'1
2009-Jun-23, 02:19 AM
Ah for determing Easter.

The moon itself is not really that important, right?

dwnielsen
2009-Jun-23, 03:58 AM
Of course it is. As a symbol of the resurrection of the almighty Lord, whose body is bread, like fields of wheat growing under the ever-renewing moon. Well, maybe it is for some, but sorry, Chornedsnorkack, I'm a little confused. I think you said it here:
"Thus my question is: how big was the error by measuring wrong value back in 1581, and how big is the error due to the ratio itself having changed between 1581 and 2009?"

I still don't really get any of it, but perhaps something like that might be able to provide some data for the past few centuries, which would be nice. But it doesn't really seem to make sense, because knowing the error implies that you know the actual value, it would seem. Even if it works nontrivially, it sounds incredibly painful.

chornedsnorkack
2009-Jul-06, 08:05 PM
Ah for determing Easter.

The moon itself is not really that important, right?

It probably is.

After all, the aim of the Gregorian calendar is to get the movement of the equinoxes right AND get the movement of Moon right.

400 years are precisely 146 097 days (365,2425). And the ratio of 70 499 183 months equalling 2 081 882 250 days means a month is 29,530 461 237... days.