I need help figuring some things out about the moon with some data I have gathered. I have observed the moon throughout the course of the past month, and have gotten a good 8-9 measurements on its phase and approximate position in the sky from night to night. I measured its position relative to several bright stars, then used star charts to estimate the moon's approximate declination. How can I calculate the deviation of the moon from the ecliptic at the time of each observation? I'm a little confused as to how I figure that out. Also, where is the moon in its orbit when it crosses the ecliptic plane, and where it is in its orbit when it reaches its farthest above and below the ecliptic plane?
Hi Lindsey, If you are really interested in where the moon is located in the night sky from night to night (and this just isn't another 'homework' question)...get yourself a copy of Guy Ottewell's Astronomical Calendar 2009...although since it's near the end of the year, I'd wait and get the 2010 calendar since they cost around $30. But you get the entire sky every night and what's going on from a daily basis, of everything, not just the moon. (Thus the high cost for that particular calendar). Order through www.universalworkshop.com or Sky and Telescope magazine.
The moon's motion in the sky is the most complicated of all the heavenly bodies from a mathematical standpoint...even our navigator aboard my KC-135, circa 1969, never used the moon in celestial navigation, preferring bright stars and the sun for celestial fixes in the sextant...he didn't even use the bright planets as it involved too many calculations to pre-comp. (In the old days before GPS, navigators would pre-compute [pre-comp] their celestial sightings before the flight occurs to get most of their heavy work already completed).
As you probably already know, the moon's orbit is tilted 5 degrees to the ecliptic, and it precesses, so the ecliptic crossings are always moving backward during the complete Saros Cycle of 18.61 years, so none of those dates and positions you request are fixed on a monthly basis. One question is easy...as we know on eclipse dates the moon has to be crossing the ecliptic. These Greenwich dates for 2009 were (are) Feb 9, July 7, August 6, and December 31. Notice the backward precession dates of 9, 7, 6, and 31....so every month is different as the nodes (where the moon's orbit intercepts and crosses the ecliptic)...are different. And as a general rule, 7 days before eclipse and 7 days after, the moon was (is) at it's maximum deviation from the ecliptic, and these dates will migrate monthly too...about one day every 1.64 months. (How did I get this? 18.6 years is 223.2 months, and that number divided into a complete 365 days of travel = 1.64 days of travel around the ecliptic, per calendar month... on average.) And even this is not a constant number as the moon's orbit is elliptical, not circular. So see, the mathematics, even for the easy stuff, can become very cumbersome and bewiltering.
Actually from an observational astronomy standpoint, we astronomers don't even care about all this...since we hate the moon because when it's up it ruins our dark night sky, all we care about is when the moon is bright and visible in the night sky, because we don't go out observing the deep sky objects when it's up and bright. So basically from just after first quarter until last quarter, all deep sky telescopes (including the 10 meter Keck's on Hawaii) are out of business for about 2 weeks per month. So to us, the more important time is the moon's setting time so it gets out of the way from our observing schedule. And we can just look that time up on our computer star chart programs.
But to your question, rather than go through reams and reams of calculations if you want the actual dates of maximum deviation for the moon, simply look it up in Guy Ottewell's Astronomical Calendar, and it will save you an awful lot of un-necessary work and time...time better spent on actually observing the night sky, rather than sitting at a desk doing all those calculations. We are observational astronomers, not mathematicians. Plus, computers have already done all those calculations for us...there is no need for all that manual type work today. Hope this helps, Clear Skies, Tom Whiting Erie, PA