16 replies to this topic

[Arkalius]

September marked the end of the 2005-2006 major lunar standstill season, when the variance of the moon's declination was greatest during it's phases. This week we will still get to see some evidence of the culmination of this 18.6 year cycle.

In the early mornings, before dawn, of the 11th, 12th, and 13th of this month (October), the moon will culminate very high in the sky for observers in the contiguous United States. For observers in southern Texas (Corpus Christi and southward) and in southern Florida, south of Cape Canaveral, the moon will actually culminate slightly north of the local zenith on these nights, an event which is very unusual for the US.

To all lunar observers who rise early to view these aged waning moons, the high altitude will of course provide some of the crispest views one can get, especially if your local seeing conditions are good. Enjoy it while you can. From here on out, these maximum culminations of the moon are going to start happening closer and closer to sunrise, and occuring at lower altitudes over the next months.

[67champ]

Hi, could someone explain "this 18.6 year cycle" for me.

Thanks,

dt

[Arkalius]

This site explains it fairly well. It's tough for me to explain effectively without some kind of visual aid.

http://www.starwaves...tandstills.html

[Centaur]

Hi, could someone explain "this 18.6 year cycle" for me.

I explained this cycle in my two posts withiin an earlier thread:

Am I Crazy?

The first post was fairly simple. The second one was quite detailed.

To state the case even more simply:

The Earth's orbital plane is inclined 23.44° to its equatorial plane. The points where they intersect on the Celestial Sphere are called the Equinoxes.

The Moon's orbital plane is inclined 5.15° to the Earth's orbital plane. The points where they intersect on the Celestial Sphere are called the Nodes.

The Nodes precess a full 360° relative to the Equinoxes along the Ecliptic in 18.6 years.

That means at the extreme point in the 18.6-year Nodal Cycle (2006) the Moon can move over 28° from the Celestial Equator. At other times (1997 and 2015) the Moon cannot move much more than 18° from the Celestial Equator.

Edit: link shortened.

[67champ]

THANKS! I almost understand this now. lol

I wonder if this "cycle" could be used to predict the moons orientation in the sky to the observer on Earth as to repeat
the moons altitude and azimuth, etc. on a given day 18.6 years later...? Thinking somewhat similar to how we use colongitude to know when the terminator may be located at a specific crater on the moon every month.....

?

dt

[Centaur]

I wonder if this "cycle" could be used to predict the moons orientation in the sky to the observer on Earth as to repeat
the moons altitude and azimuth, etc. on a given day 18.6 years later...?

Not after 18.6 years. The problem is that in addition to being at the same point in the nodal cycle, a nearly integer number of years and a nearly integer number of synodic months would both need to have elapsed to place the Moon near the same altitude and azimuth at the same time of day. The fractional part of the 18.6 years would mean observing the Moon during an entirely different season.

After a period of 19 years (Metonic Cycle), almost exactly 235 synodic months will have passed and it will be only a little longer than a Nodal Cycle. However, the Moon's position relative to its perigee point would be quite different. Also, 19 years does not evenly divide by the 4 years of a leap year cycle. Nevertheless, after 19 years the Moon's position will come close to repeating in the manner you describe.

[67champ]

Thank you. Maybe thats what I was thinking of... Ok, here's my problem. Is there a way to easily (or not easy) to predict the moons physical relationship to the earth and sun (phase and sunlight angles) for a future date that would most duplicate a previous date from the past? I hope that makes sense. (other than co-long)

dt

[Arkalius]

19 tropical years (the year our calendar is based on, about 365.25 days) differs from 235 synodic months (a lunation, a full cycle of the moon, about 29 days) by about 2 hours. That's best predictor of the moon's relationship to the Earth, as it will only be 2 hours different after 19 tropical years. However, 19 tropical years includes a fractional day of about 14.4 hours long, meaning after that period, it won't be the same time of day for the particular point on the planet (none of these cycles account for earth's rotational period).

The error of the Metonic cycle is one day every 219 tropical years, so that may help somewhat.

[Centaur]

Is there a way to easily (or not easy) to predict the moons physical relationship to the earth and sun (phase and sunlight angles) for a future date that would most duplicate a previous date from the past?

The 19-year Metonic Cycle of 235 Synodic (phase) Months is about as good as you’re going to find, if you want to witness near repeats of lunar positions and phases over the course of a lifetime. This assumes that the position of the Moon measured within any of the standard coordinate systems is what is important to you.

If you simply wish to know when the Sun, Moon and Earth will again be in nearly identical relative positions (with minimal regard for their positions within a particular coordinate system) then the Saros Cycle of 223 Synodic Months (6585.32 Days or 18.02963 Julian Years) is what you are seeking. The Saros Cycle was used by the ancients to predict eclipses. It is very nearly equal to 242 Draconic (node) Months or 239 Anomalistic (perigee) Months.

The important thing to know is that there are no perfect resonances (rational relationships) among the various solar, lunar and terrestrial cycles. In fact, long-term secular changes in the values of numerous factors will eventually make even the Metonic and Saros Cycles useless.

[Arkalius]

The important part of predicting the exact appearance of the moon is it's libration and it's phase, assuming you do not care about it's distance from Earth. Because the variance of this distance is so relatively small, this will not affect the moon's appearance other than it's apparant size, which probably doesn't matter in this case.

It's phase is dependant on it's elongation from the Sun, and it's distance above or below the plane of the ecliptic. However, since that distance is so miniscule compared to the distance to the sun, this can be considered insignificant in its effect on the phase. Elongation from the sun repeats it's cyle every synodic month, or lunation (there is an additional factor affecting elongation which is mentioned below).

It's lattitudinal libration depends upon it's ecliptic declination (different than it's true declination which is measured from the celestial equator). Ecliptic declination repeats every draconic month. Longitudinal libration depends really on it's distance from Earth, so here the distance to Earth comes back in to play. This distance repeats every anomalistic month.

There is no perfect integer resonance between all of these values, but one Saros cycle as Centaur mentions comes closest to one. It also throws in the anomlistic year of Earth, as solar Right Acension does not change at a static rate, but cycles once every anomalistic year. This will have an effect on the lunar phase as well somewhat as it factors into lunar elongation from the Sun.

A Saros cycle is about 18 calendar years, 11 days, 8 hours long, though the number of calendar days can vary from 10 to 12 depending on the number of leap days counted. This is calendar days/years mind you; the actual length is fixed. For example, if we started today, We'd only add 10 days, 8 hours. It's currently October 10th, 2006 at 7PM local time (for me), the current phase of the moon (and it's RA and Dec) would be almost exactly the same as it is right now at 3AM on October 21st, 2024, as there are 5 leap days in the intervening period (2008, 2012, 2016, 2020, and in Feb of 2024, the year in question) rather than the 4 assumed above. Note that the time of day is different by 8 hours, so it's altitude and azimuth from the same place on Earth will be vastly different. Three Saros cycles (called a Triple Saros) corrects this, and is 54 years, 33 days exactly (32 days when there is an extra leap day, 34 if one less). After that period of time, the moon will be nearly the exact same size, have the same position in the sky, same libration, and be at the same phase as it is right now.

I say almost, because Saros cycles are not perfect. This is because it isn't a perfect resonance. Even if it was perfect, it would be pure coincidence as all the factors involved are currently changing (very slowly), so that even a Saros cycle won't be accurate eventually, just as Centaur said.

[67champ]

Wow.... Thanks to both of you! I think this may be way more complicated than I realized. (to repeat Everything on a given night) I will look at the info you supplied and see which one looks like it will work best. Thanks!

dt

[Arkalius]

Yeah I was in the same boat as you... If the orbit of Earth and the Moon were perfectly circular, it would actually be much easier to predict such things. Since they are not, they move at different speeds through the courses of their orbits, which complicates everything.

[67champ]

I'm going to throw some terms/categories at you from a lunar program I have, please try to define them for me, and let me know which ones would be important as to duplicating sunrise illumination angles at teminator on a given feature... :-)

I assume to duplicate illumination of a given lunar feature exactly on a future date, some of these are important; as opposed to just looking at CoLong. I hope I'm using the first four categories correctly below.



Libration in latitude (geocentric)
Libration in latitude (topocentric)
Libration in longitude (geocentric)
Libration in longitude (topocentric)
PA of axis
RA
DEC
Parallactic angle

Thanks!

dt

[Arkalius]

Libration is the slight change in what area of the moon we see as it moves through it's orbit. The moon rotates such that the same side always faces us, but it's rotation speed is constant, whereas the speed at which it revolves around Earth is not. Because of this, when it moves faster the rotation falls a bit behind, and when it moves slower, it catches back up and gets ahead. Additionally, because of it's inclination to Earth, we may see a little more of the northern part or the southern part depending on it's declination. This is the Libration of the moon. The lattitude and logitude values indicate how much the moon's visible surface is shifted in the vertical and horizontal. Geocentric indicates the values as observed from the center of the Earth. Topocentric values are those as observed from a particular part of Earth's surface. Since the moon is so much closer to us than all other celestial objects, the differences between topocentric and geocentric values can be visually perceptible.

PA of Axis is the Position Angle of Axis. It indicates the angle of the moon's rotational axis as viewed from Earth. I don't fully understand how this value is represented. At any rate, it can help you understand where the poles of the moon are.

RA and DEC are the Right Ascension and Declination of course, the celestial coordinates of the moon's position.

Parallactic angle description removed in favor of Centaur's below.

[Centaur]

67champ, you received good explanations from Arkalius regarding most of your listed terms.

Regarding PA of Axis: That represents the apparent tilt of the north pole of the Moon’s rotational axis in the equatorial coordinate system measured counterclockwise from the north celestial pole (as projected upon the 2-dimensional lunar disk.)

Regarding Parallactic Angle: The term has nothing to do with parallax. I’m afraid Arkalius’ definition is incorrect. The term references the fact that a celestial body in its daily movement appears to track closely along one particular parallel circle of an observer's sky. This parallel is analagous to a parallel of latitude on Earth. As the body appears to move along this parallel, it seems to the observer to be tilting. Parallactic Angle is a measure of that tilt. When observing the Moon there is a point on its limb that is nearest to the observer’s zenith; call that point Z. There is another point on the limb that is nearest to the north celestial pole; call that point N. Call the center of the apparent lunar disk point C. The angle ZCN is the Parallactic Angle. It is negative before the Moon passes the observer’s southern meridian, and positive afterward.

[Arkalius]

Sorry... I actually was just guessing on the parallactic angle thing... seemed related to Parallax shift. I was obviously way off!

[67champ]

Thanks again! And, yes the moon was as high in the sky as I ever remember seeing it this morning 6am. Looked almost straight up.

dt