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Lunar orbit question

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#1 zleonis

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Posted 10 July 2019 - 10:08 PM

I'm wondering if there's a term for the points between the nodes when the moon is at its maximum distance from the ecliptic plane. The question arises in part out of an interest in knowing/describing when a given phase will be higher/lower in the sky than average for the time of year, and in part because these sorts of terms have cool-sounding names (Argument of periapsis! Precession of the equinoxes!) Thanks!

#2 WarmWeatherGuy

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Posted 10 July 2019 - 11:29 PM

The ecliptic plane is the plane of Earth's orbit around the Sun. For an orbit around Earth you would want the maximum from the plane defined by Earth's equator. The inclination is the angle between the equator plane and the orbit plane. The point where the object crosses the equator going south to north is the ascending node.

 

Wikipedia has a good write-up here.



#3 Tom Glenn

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Posted 11 July 2019 - 02:03 AM

The point where the object crosses the equator going south to north is the ascending node.

 

Actually, in the lunar orbit, the orbital nodes are the points at which the Moon crosses the ecliptic plane, not the celestial equator.  Your reference link is referring to artificial satellites of Earth when it defines nodes the way you did, because the reference plane for an Earth orbiting satellite is typically the equator.  But the Moon is a special satellite, and the reference plane for it's orbital nodes is the ecliptic plane.  The Moon's orbit is unique because its orbital plane is inclined to Earth's equator, and is much closer to the ecliptic.  


Edited by Tom Glenn, 11 July 2019 - 02:46 AM.

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#4 Tom Glenn

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Posted 11 July 2019 - 02:41 AM

I'm wondering if there's a term for the points between the nodes when the moon is at its maximum distance from the ecliptic plane. The question arises in part out of an interest in knowing/describing when a given phase will be higher/lower in the sky than average for the time of year, and in part because these sorts of terms have cool-sounding names (Argument of periapsis! Precession of the equinoxes!) Thanks!

The Moon's maximum altitude above the horizon to an observer does have a correlation with lunar phase, but this is distinct from the Moon's elevation above the ecliptic plane.  The position of the Moon above or below the ecliptic plane determines its latitude in libration, which determines how much we can see of the North and South polar regions from Earth.  Maximum librations in latitude occur in between the nodes, and so follow a period of the draconic month, ~27.2 days.  The maximum positive and negative librations therefore occur in half that period of time.  This affects how we see the Moon, but does not tell you whether the Moon will be high in the sky. 

 

The maximum altitude that the Moon reaches in the sky is determined by its declination, or its elevation above the celestial equator.  This does correlate with the lunar phase, and cycles with the seasons.  If you are in the tropics, then the Moon is always high, but if you are at a more northernly or southerly latitude (such as you are), then the Full Moon is always highest in the winter, the First Quarter Moon is highest in the spring, Last Quarter is highest in the fall, and the New Moon is highest in the summer.  This makes sense if you think of the Sun.  The Full Moon is opposite the Sun, and the Sun is lowest in the winter, so this makes the Moon high.  The New Moon is always within a few degrees of the Sun, and so is highest in the summer.  You can't see the New Moon unless it's eclipsing the Sun, but this does make the narrow crescent phases highest in summer.  If you look at an orbital diagram with all the proper inclinations this will start to make sense. 

 

The Moon's relationship to its orbital nodes does affect declination in an interesting way, however.  The elevation above and below the ecliptic plane can either add or subtract to the declination, and this varies on a periodic cycle of 18.6 years, which is the period of nodal precession.  This leads to conditions known as major and minor lunar standstills. Some interesting links about the Moon's orbit and lunar standstill are below.  But for a basic understanding of whether the Moon will generally be high or low in the sky at any given phase, you can just use the seasons. 

 

https://en.wikipedia...bit_of_the_Moon
https://en.wikipedia...unar_standstill


Edited by Tom Glenn, 11 July 2019 - 02:43 AM.

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#5 cpsTN

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Posted 12 July 2019 - 08:23 PM

What the OP is asking is if there is a name for the points when the Moon is at it highest and lower, or farthest points away from the ecliptic. I am pretty sure he knows how the Moon's orbit works. 



#6 Tom Glenn

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Posted 12 July 2019 - 08:51 PM

 I am pretty sure he knows how the Moon's orbit works. 

It's rare to find anyone that knows much about how the Moon's orbit works, other than the most basic details, even among seasoned observers.  The OP did specifically express interest in "knowing/describing when a given phase will be higher/lower in the sky than average for the time of year", which is precisely what I answered.  The Wikipedia article on the Moon's orbit that I linked to, while short, hits the highlights and may give more of the terminology that the OP is after, or at least provide links to further reading. But you are of course welcome to add anything of substance to the discussion.  


Edited by Tom Glenn, 12 July 2019 - 08:57 PM.


#7 frank5817

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Posted 12 July 2019 - 10:23 PM

zleonis,

 

Are you asking about lunar standstill (lunistices)?

 

https://en.wikipedia...unar_standstill

 

Frank



#8 zleonis

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Posted 15 July 2019 - 12:28 PM

Thanks to everyone who weighed in, especially to Tom for the thorough overview. I'd read those wikipedia pages, but it was helpful to hear it phrased in a different way, and I think it cleared up some confusion on my part. I was aware that the orbital nodes affected the moon's declination/altitude, but it somehow hadn't clicked for me that the period between successive nodes (or maximum distance from ecliptic) is only a few days out of phase from the cycle of lunar phases. So while over a long enough timeframe there would a full moon on January 21 at a declination of roughly 25° (that occurred when the moon was mid-way between ascending and descending node) that could be higher in the sky than a full moon on some other December 21 (for northern observers), these occurrences would be many years apart. 

 

Frank5817, thanks for pointing out the article about lunar standstills. From my understanding of that article, lunistices are a special case of the phenomenon that I was asking about, when the moon's maximum/minimum deviation from the ecliptic coincides with its maximum/minimum declination for a given lunar month. Is that correct? It doesn't sound like there's a widely used term for the maximum distance from the ecliptic in other lunar months. 

 

Thanks again!



#9 Tom Glenn

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Posted 15 July 2019 - 06:45 PM

From my understanding of that article, lunistices are a special case of the phenomenon that I was asking about, when the moon's maximum/minimum deviation from the ecliptic coincides with its maximum/minimum declination for a given lunar month. Is that correct?

The way I think of it is that the inclination of the Moon's orbit to the ecliptic plane can either add to, or subtract from, the angle between the plane of the Moon's orbit and the celestial equator.  So the declination changes that the Moon undergoes throughout the month can be greater than, or less than, the changes in declination that the Sun undergoes throughout the year, if that makes sense.  I think the illustration from the Wikipedia article shows this fairly well.  

 

lunar_standstill.jpg

From Wikipedia 

 

In October 2015, we were at a minor lunar standstill, and so the declination change throughout a lunar cycle was at a minimum.  We are currently progressing towards the next major lunar standstill which will occur in April 2025.  From a practical standpoint, this means that were I live, when the Moon crosses the meridian at a period of maximum declination, then in 2015 it would have been approximately 75 degrees altitude above the horizon, but in 2025 it will be about 85 degrees above the horizon, or nearly at zenith.  


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#10 WarmWeatherGuy

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Posted 15 July 2019 - 07:43 PM

You said that the orbit of the Moon is typically referenced to the ecliptic rather than the Earth's equator. It would be possible to compute orbital elements with reference to the Earth's equator though. I am wondering why they use the ecliptic instead of the equator. Because the Earth-Moon is not an isolated system, it is a 3 body problem Earth-Moon-Sun, the orbital elements will vary over time. Is it that they are more stable over time when using the ecliptic as the reference? Are there other benefits to using the ecliptic?



#11 Tom Glenn

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Posted 15 July 2019 - 08:11 PM

You said that the orbit of the Moon is typically referenced to the ecliptic rather than the Earth's equator. It would be possible to compute orbital elements with reference to the Earth's equator though. I am wondering why they use the ecliptic instead of the equator. Because the Earth-Moon is not an isolated system, it is a 3 body problem Earth-Moon-Sun, the orbital elements will vary over time. Is it that they are more stable over time when using the ecliptic as the reference? Are there other benefits to using the ecliptic?

The Moon's orbit has a number of interesting properties related to the ecliptic.  Cassini identified several interesting aspects back in the 1600s, known as Cassini's Laws.  

 

https://en.wikipedia.../Cassini's_laws

 

One interesting aspect is that the rotational axis of the Moon is always tilted 1.54 degrees to the ecliptic.  The rotational axis of the Moon precesses at the same rate (18.6 years) as nodal precession, and so this angle is always maintained.  The nodes are also used to predict eclipses.  You can also generally predict the libration latitude if you know the position of the Moon relative to the nodes.  In contrast, the points at which the Moon crosses the celestial equator don't really have any significance that I know of, although knowing the declination of the Moon is very useful for planning observations, since higher is generally better. 


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#12 cpsTN

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Posted 13 September 2019 - 06:12 PM

It's rare to find anyone that knows much about how the Moon's orbit works, other than the most basic details, even among seasoned observers.  The OP did specifically express interest in "knowing/describing when a given phase will be higher/lower in the sky than average for the time of year", which is precisely what I answered.  The Wikipedia article on the Moon's orbit that I linked to, while short, hits the highlights and may give more of the terminology that the OP is after, or at least provide links to further reading. But you are of course welcome to add anything of substance to the discussion.  

I wasn't saying the OP knew every aspect about the Moon's orbit, just that he knows about the passage through the node points. I understand he was looking for an overview of the Moon's orbit, but he DID ask a specific question. To many times, so many of us seem to want to educate people so much that we give them an overwhelming amount of information that they don't get anything out of it.



#13 beggarly

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Posted 14 September 2019 - 10:25 AM

In Mathematical Astronomy Morsels I by Jean Meeus chapter 5 is about 'Extreme declinations of the Moon'.

An earlier version of that chapter is available here: http://articles.adsa...000192.000.html


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#14 clintmk89

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Posted 20 September 2019 - 06:01 PM

When I thought KSP taught me well I realize there’s much more to learn. 🛰👍🏼 Tom thanks for the info and diagrams I was curious about this myself recently.


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