# Does the moon's argument of periapsis and right ascension of the ascending node vary uniformly?

I've heard that the moon's argument of periapsis changes as well as its longitude of ascending node (right ascension of the ascending node), both having periods of: $T_{\omega}=8.85$ years and $T_{\Omega}=18.6$ years. $T_{\omega}$ is the period at which the periapsis makes one full revolution and $T_{\Omega}$ is the period at which the ascending node makes a full revolution.

However, I found certain sources which say that for the moon that, $\omega=318.15^{\circ}$ and $\Omega=125.08^{\circ}$ without any significant differences between each source. These include Wolfram Alpha, and some research papers.

This seems rather contradictory, since the values seem to be static, rather than varying periodically.

I suppose that these values are relative to a certain time, perhaps J2000. If so, will the following give the current argument (15 October 2016) of periapsis and longitude of the ascending node?

Time from J2000 to current time: $t=5.306 \times 10^8 \space s$.

Because $\omega$ increases as $t$ increases & $\Omega$ decreases as $t$ increases (prograde orbit), $\omega=318.15+\frac{360t}{T_{\omega}}$ and $\Omega=125.08-\frac{360t}{T_{\Omega}}$.

If $T_{\omega}$ and $T_{\Omega}$ are converted into seconds, I obtain:

$\omega \approx 282.574^{\circ}$ and $\Omega \approx 159.431^{\circ}$.

Now, the questions.

1) Is my reasoning correct?

2) Do the parameters $\omega$ and $\Omega$ have uniform variation?

3) Are the values for $\omega$ and $\Omega$ correct for 15 October 2016 (current date)?

4) If not, how would I calculate these parameters?

These include Wolfram Alpha.

WA is great most of the time, but at times it spouts nonsense. This is one of the cases where the latter is the case.

From JPL's HORIZONS website, the Moon's argument of perigee at 12:00 1 Jan 2000 was 308.92 degrees from the perspective of an Ecliptic and Mean Equinox of Reference Epoch frame or 61.54 degrees from the perspective of an Earth Mean Equator and Mean Equinox of Reference Epoch frame.

Note well: HORIZONS provides osculating orbital elements. Your 318.15 degrees may well be some unspecified set of mean orbital elements. Who knows?

Also note that the frame of reference makes a big difference. It also makes a difference in the rate at which the argument of perigee precesses. From the perspective of an ecliptic based frame, the Moon's argument of perigee advances by 360 degrees ever 6.0 years. From the perspective of an Earth equator frame, it takes 8.85 years for the Moon's argument of perigee to advance by 360 degrees.

Does the moon's argument of periapsis and right ascension of the ascending node vary uniformly?

The answer depends on which set of orbital elements one uses (osculating orbital elements versus various mean orbital elements) and which frame of reference one uses. Due to perturbations from the Sun, Venus, Jupiter, and the Earth's non-spherical mass distribution, the osculating elements that would be nominally constant if the Moon's orbit was Keplerian are not constant. They instead exhibit periodic and secular variations.

The intent of mean orbital element sets are to smooth out those periodic variations, leaving just the secular effects. The variations in the Moon's argument of perigee and right ascension of ascending node can be made to appear to be nearly linear in time given an appropriately chosen set of mean orbital elements and an appropriately chosen frame of reference.

According to the Nasa website it is 318.15 degrees

https://ssd.jpl.nasa.gov/?sat_elem