Why isn’t the Precession of the Lunar Nodes Uniform with Time?

-- | November 9, 2014

Question: I am an amateur naked eye astronomer. I teach astronomy to 6th graders, I read a lot on the subject, and I do a lot of experiments and observations to better understand the movements of the sun, moon, etc.

I have been looking at the precession/regression of the lunar nodes and I am a bit confused. I know the nodes are just imaginary lines where the titled orbit of the moon crosses the ecliptic and that they move westward, opposite the direction the earth spins and the moon orbits the earth and the earth orbits the sun and that this takes 18.6 years. I have found vague references to the fact that this is not a steady movement but just moves in that direction on the average to complete one rotation relative to the fixed stars in 18.6 years. I have made some simple models to test this with ephemeris listings of moon phases and when it is in the ascending or descending node, and if checked over long periods of time it does indeed seem to be working its way westward, but if checked over the short term, the position of the moon in the nodes seems to jump back and forth by quite a bit relative to the fixed stars. So, my question is (sorry for the long explanation) what is causing this? Is it just the complexities of the moon’s orbit that make it swing around a bit erratically each time around while adding up to a general westward precession, is it something to do with the elliptical shape of the orbit along the line of apsides between perigee and apogee that is also precessing (which I guess is a further deformation of the orbit since its orientation moves about in the opposite direction in a different amount of time: 8.85 years), or am I looking at this all wrong? I’ve tried my best to figure this out but I just can’t wrap my head around it. Please help! — Tyrel

Answer: This is a rather complicated problem as it involves some rather complex interactions amongst the Earth, Moon, and Sun. It involves the construction of a complete theory of lunar motion, which has been tackled by some of the most noteworthy physicists and mathematicians of all time, including Newton and Euler. After consulting Orbital Motion by A. E. Roy, I think that the major contributor to this oscillation of the Moon’s position in the nodes is due to the Sun’s gravitational pull and its affect on the parallactic inequality This effect produces a variation in the longitude of the Moon with amplitude (E-M)/(E+M)*(a/a1), where E and M are the masses of the Earth and Moon, respectively, and a and a1 are the mean geocentric distances of the Moon and Sun, respectively. The amplitude of this term is about 2 arcminutes and has an amplitude of one synodic month. There are other contributors to these motions that are very well described in Roy, Chapter 10.2, if you are interested in digging into this subject.

Jeff Mangum

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