Expert: Tom Whiting - 12/15/2004

Question
Thanks Tom.  I have to read your answer over again and ponder it for a bit.

What I meant by the moon's orbit around the Earth being "skewed" is that it is "tilted" with respect to the Earth's axis, which was my first mistake.  I had considered the 5 deg. tilt of the moon's orbit with respect to the axis of the Earth, not the ecliptic.  I can see now that I misunderstood the definition of the moon's tilted orbit when I looked it up in Guy Ottewell's Astronomical Calendar.  I had considered the orbit of the moon with respect to the spin axis of the Earth.

Your reply brought several other thoughts to mind:

> In any case, even IF the moon was exactly on the ecliptic,
> that would be reason enough for the moonrise point on
> the horizon to change positions slightly, daily, and by 23.5 degrees (North and South)
> over the full lunar month.  In fact, the moonrise spot on the eastern horizon is
> dependent on 2 things, the changing angle of the ecliptic (because the moon is always
> on, or near, the ecliptic)  with the horizon (which changes slightly every day) and
> where the moon is at on its 5 degree orbital tilt with respect to the ecliptic.  Sometimes
> it's riding "high"...north of the ecliptic by a maximum of 5 degrees, and sometimes it's
> riding "low" south of the ecliptic by a maximum of 5 degrees.

I believe I understand your point above:  If there were no tilt in the moon's orbit WRT to the ecliptic, you would still see the swing of 23.5 deg. due to the fairly large angle of the Earth's spin axis.

The angle of the moon's orbital tilt appears to be completely independent of the tilt of the Earth's spin axis.

Back to the observational method: it would appear that we would fairly easily be able to measure the north/south swing of the moon through the range of 23.5 degrees, while the 5 degree tilt might be more difficult to account for.   And fudging a couple of daylight readings with software should be excusable, after all this is a 7th grade project.  I think we will take that approach and only attempt to account for the 23.5 degrees of the Earth's axis WRT to the ecliptic by watching and measuring the moon rising over the horizon when darkness permits.

I've had a fairly hard time explaining the concept of the ecliptic to my daughter.  I know I'm going to have to try harder.

Thanks again,
Marc      

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Followup To
Question -
Hi Tom,
You helped my son with a project involving light pollution last year for which he won first place at his jr. high school in D.C.  Thanks again for that expert assistance.

My daughter is now working on a project that I thought would be rather straight forward, but I wanted to check with you on our method.  We investigated the moon's orbit and discovered that it is skewed relative to the Earth.  We wanted to demonstrate that fact by measuring, in degrees with a compass, the location on the horizon of the moon rise every night or day.

Our assumption was that if the moon's orbit was NOT skewed, it would rise at the same location every night or day in its 29 day cycle.  If it IS skewed, it would rise at a slightly different location every night (or day)and that location would cycle back and forth through the 29 day period.

The problem we are having is measuring the moon rise during the day light hours against the horizon.  We have not had any luck attempting this and were wondering if you had any ideas?  I thought it might be easier to measure moon sets during day light hours, however I'm not sure how we would correlate moon sets with moon rises.

Any ideas?  Are we going about this in the right way?

Thanks in advance,

Marc and Lena Pfeiffer
Washington, DC
Answer -
Hi Marc...

Glad to help in the past and congratulations on his 1st place
results.

Well, I'm not familar with the astronomical term "skewed".....
do you mean "orbital precession" (which it does----one full cycle over 6585.3 days, or the Saros cycle) or do you
mean the standard 5 degree tilt of the moon's orbit relative
to the ecliptic (which it is)?

In any case, even IF the moon was exactly on the ecliptic,
that would be reason enough for the moonrise point on
the horizon to change positions slightly, daily, and by 23.5 degrees (North and South) over the full lunar month.  In fact, the moonrise spot on the eastern horizon is dependent on 2 things, the changing angle of the ecliptic (because the moon is always on, or near, the ecliptic)  with the horizon (which changes slightly every day) and where the moon is at on its 5 degree orbital tilt with respect to the ecliptic.  Sometimes it's
riding "high"...north of the ecliptic by a maximum of 5 degrees, and sometimes it's riding "low" south of the ecliptic by a maximum of 5 degrees.

Probably your best solution is to "fudge in" daylight moonrise times and positions with a computer program like
"Skyglobe" or an equivalent, rather than by direct observation, as like you said, its very difficult to see a
daytime crescent moon rising in the east.  You would only
have to fill in.....read that "computer-cheat" just a few days
every month....PLUS, the computer program could also
help you fill in those cloudy days/nights.

Since the moon visits all parts of the ecliptic during its
29 day period, your results will vary the horizon
rising spot by at least 23.5 degrees.  In December, the rising
point will be low in the SE when the moon is near the sun,
(since it's where the sun is)...against the backdrop of the
southern ecliptic down in the Scorpius/Sagittarius region
of the sky.  And the opposite for at, or near full moon, as the full moon is on the northern part of the ecliptic in
Taurus/Gemini/Cancer region of the ecliptic.
And of course, its the exact opposite in the June summer
time frame.  (That's why we have a low full moon in June,
and a very high full moon in December.....the full moon is
always 6 months opposite where the sun was, or will be. )

But back to your problem....depending on your accuracy,
if you were to be super-accurate, you would find that the
exact same spot both on the horizon (and in the sky) would
not exactly repeat for 6585.3 days, the Saros cycle of
18 years, 10 days, and 8 hours (that's why eclipses repeat
at that interval, {displaced 120 degrees westward due to the 8 hours of Earth's rotation}  which was even known to the ancients).
Because the Saros cycle is defined as the moon returning
to exactly its same spot in our sky as it was previously,
6585 days prior.

But if you are not being super-accurate, then your results
will repeat yearly,  relative to the moon's phase, not by
date.....(but not perfectly exact, because the orbit of the moon precesses by about 19 degrees per year, which will change
the rising point very slightly, of the same phase, next year).

So no, your basic assumption that  IF the moon's orbit
is not skewed (whatever that means) then it would rise at the
same spot on the horizon phase to phase and month to
month,.... is NOT true.   From phase to phase and month to
month, since the ecliptic tilt of 23.5 degrees is involved,
that is the primary reason for month to month and phase
to phase, horizon changing points.

I'd personally use a computer program to see the big
picture, and use it to "fill in" the dates where you can't
get any visual data.

Hope all this helps,
Clear Skies,
Tom Whiting
Erie, PA  

Answer
Hi Marc,
Well, easiest way to explain the ecliptic (which as you know
is the center of sun-center of Earth plane) is to first
picture the Earth's axis exactly perpendicular...straight up
and down.  Now take two hula hoops right over the
Earth's equator, surrounding the Earth, one representing the
ecliptic and the other one the celestial equator.  
With the perpendicular Earth, they are co-incident...the same.
Now tilt the Earth about 23 degrees, and allow one hula hoop
to tilt with it,.... while the ecliptic hoop remains flat, the
other hula hoop tilts and that is the celestial equator, which
is always right over the Earth's equator.  (Now tilted at 23
degrees)!
Now the moon's orbit can be represented with a flat dish
saucer, following along the ecliptic, but tilted slightly (5 degrees) to that ecliptic hula hoop.  But the dish itself is
wobbly, and it makes its own rotation once every
6585.3 days (the Saros cycle).

That's the easiest way to explain it to her.
Clear Skies,
Tom Whiting
bwhiting@velocity. net
if you need more discussion on the subject, if you wish.