18. Lunar and Solar Declinations  
   


Like most folks today, I was born into a culture where the dark of night has been banished. The faint signatures of the celestial sphere have little relevance to our daily (and nightly) lives. Other than an occasional glance at the sky we seldom note the procession of lunar phases.

Of course, there are exceptions. Notably astronomers, both of the professional and garden variety amateur. But that topic has been explored elsewhere.

I'm talking about over the road truck drivers. I spent nearly three decades on the road. That translates to a lot of miles, mostly in the open spaces of the western US, many of them at night. Unlike the deep sky astronomer who curses the glare of the full Moon, truckers love it.  On moonlit nights you can see a horizon and you get a frame of reference.  On moonless nights your perspective is limited to the funnel of light down the road from your headlights.

So on any given day if you were to ask me at lunchtime, I could probably tell you what time the moon would be up that night, and which quarter it would be in. Could your stock broker tell you that?

So after years of living this way, I had a vague notion that the Moon was higher in the sky in the Winter than it was in the Summer. It seemed a little counterintuitive to me. If the Winter Sun crossed the sky so low, why wasn't the Moon also low in the sky at night?

I don't remember the time or place, but the contradiction bothered me until I did a little thought experiment. I was aware of the rudiments of the tilt of the Earth's axis and the seasonal changes. So I knew that the path followed by the Sun across the sky, the ecliptic, was low in the sky during the day. So at night the Earth rotates half a turn underneath the ecliptic plane and it appears high in the sky. I deduced that since the Moon also travels along the ecliptic, although not perfectly, it would be higher in the sky in the Winter, lower in the Summer.

Which is a convenient arrangement for the trucker. During the Summer months, we enjoy long hours of daylight and the significance of that bright full Moon at night becomes less important.

About five years ago I purchased a little telescope and rekindled my childhood interest in astronomy. Satisfied with my conclusions about the high flying Winter Moon, I didn't think much about it for a long time. Except of course to avoid the Moon while hunting Messiers and Herschels.

Then my December 2018 issue of Reflector (the quarterly publication of the Astronomical League) arrived in the mail. One of the cover articles caught my eye: "Orbital Tilts and High-Flying Moons" by Bill Romanishin. Subtitled "Understanding the geometry of Lunar and Solar declinations".

What a great article. Here was the confirmation of my unproven suspicions about the behavior of the Moon. And a lot more, like why there aren't two eclipses every month, a solar at new Moon and a lunar at full Moon. And how eclipses are predicted.

At this point I was already pretty familiar with the Astronomical League's observing programs. Having completed a couple of deep sky observing programs, I was beginning to shift my focus inward to the Solar System.

I was already interested in the Analemma program, so I looked through the list once again to see if there was a program related to observing lunar and solar and seasonal cycles. It was then that I came across the newly announced Astronomy Before the Telescope program and immediately decided to give it a try.

Inspired by the Reflector article, I have designed a voluntary optional activity to the ABT program:

"Lunar and Solar Declinations

Make monthly observations of solar and lunar elevations above the horizon. Make the lunar observation at meridian transit on the night of the full Moon. Make the solar observation at solar noon on the following day. Plot these elevations on a graph for a period of at least twelve months. What kind of lines are generated?  Is there a relationship between the two plots?"

Here is my graph and observational data (in progress):

 

Date of Full Moon
-  -  -
Observed Lunar Altitude
 at Meridian Transit
Observed Solar Altitude
 at Solar Noon
12/23/18 72o 27o
01/20/19 70o 30.5o
02/19/19 60o 40o
03/20/19 53o 52o
04/19/19 40o 62.5o
05/18/19 clouded out-40oStellarium clouded out-72.5oStellarium
06/16/19 30 74o
07/16/19 28o 72o
08/15/19 data missing-32o Stellarium data missing-64o Stellarium
09/13/19 39o 53o
10/13/19 55o 42o
11/12/19 clouded out-63o Stellarium 33o
12/11/19 71o clouded out-27o Stellarium
01/07/20 72o clouded out-28o Stellarium
02/08/20 68o 34o

These observations were made using the hand held quadrant described in section 8.  All observations made at Aurora, Colorado latitude 39.66o N.  Observations were made at lunar/solar transit as determined by Stellarium.  Time was determined by an analog dial wristwatch with second hand sweep synchronized to an atomic clock.

Field notes from August 2019 are currently missing, data will be entered when notes are recovered.

 

Comments May 27, 2017 - April 19 anomoly

The lunar transit reading for April 19 appears to be an anomoly.  It was late, it was dark, I probably messed up.  After giving this process a little further thought, I came to the conclusion that tying these readings to the full Moon is not really necessary, it just makes for a pretty graph with regular interval spacing.  The transit altitude of the Moon is independent of the phase, the transit just happens at a different time each day.  Full moon is pretty hard to miss, cloud cover permitting.  It's possible to get lunar transits any first quarter evening or third quarter morning.  It get's tougher to impossible around new moon.  The Solar transit is always right around noon and can be done on any day of the month.

I feel like I'm cheating a bit using Stellarium to time my transit observations.  I may not be using a telescope, but I'm using modern technology.  When I get my mural transit constructed (activity #8), I'll be able to measure the transits as they cross the meridian without looking up the time and using a timepiece.  The mural transit will also give me higher degrees of precision and accuracy than the hand held quadrant that I am using now.  I may also be inclined to make more frequent readings which will give me more data points and smoother curves on my graph.

Later that same day....

OK, the April 19 anomoly was really bothering me, so I did a little investigating.  As it turns out my assumption that "The transit altitude of the Moon is independent of the phase" was totally incorrect.  I did a little Stellarium exercise for the month of May 2019, recording the lunar transit time and altitude for a 28 day lunar cycle.  As it turns out, the transit altitude varies widely from day to day, reaching a maximum in the first quarter and a minimum in the third quarter.  The April 19 lunar transit measurment of 40o was not the anomoly, it corroesponds more closely to the Stellarium prediction of 39o.  The May 27 measurment is the anomoly.  While quite different from a full moon altitude reading, the 40.1o measurment is spot on to the Stellarium prediction of 40.1o,

 

Transit time seems to follow a pretty linear relationship:

I'll have to do a little thinking about a model that explains this data.

Once again, these data were generated artificially using Stellarium software.  These data could be confirmed by direct observation, the exception being transits on either side of the new moon when the moon is not observable at transit.

 

Comment added Oct 15, 2019:  Once I have completed a good mural transit, I would be very interested in recording daily observations of lunar transit altitudes and times.  This would of course be limited to phase limited visibility, probably first quarter through full moon to third quarter.  Observations closer to new moon would be impossible due to solar glare washing out the visibility of the moon.

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