NavList:

Russell Sampson, you wrote:
"Four things come to mind regarding the apparent slowness of the moon; 1) apogee/perigee and Kepler’s laws (apogee on February 4), 2) parallax due to the spinning Earth angular rotation rate vs angular orbital rate of moon (15:1) which is at maximum when moon is at meridian, 3) measurement uncertainty of visual observations possibly due to the gibbous phase and 4) moon near a node so moon is approaching Mars at an angle to the ecliptic and thus its component of motion along ecliptic is at a minimum (ascending node January 28).  

Such a fun and complex problem. "

First, glad you like it! Yes, it's tricky. Your #4 here could be combined with any off-dead-center motion of the Moon across the sky. For example, if we measured the angle from the Moon to Betelgeuse that same night, we would find some impact there since Betelgeuse is some degrees off the ecliptic. In this case, though, for Mars, I would say it's not a major factor.

As for your #3 here, I cheated and double-checked in Stellarium before writing about this. I did measure the angles manually using one of my handy-dandy pocket "paper sextants" (don't leave home without one!), but I made sure the numbers were legitimate in Stellarium. And #1, apogee versus perigee had only a minimal impact on the date in question which we can verify by looking at the actual geocentric rate which was quite close to 0.5° in one hour.

Finally, yes, you're right: it's parallax :). Not too long ago we discussed the apparent slowing of the Moon's motion caused by changing parallax. Contrary to first impressions, this does not imply that the determination of GMT by lunars is reduced in accuracy. We correct for that. Changing parallax can reduce the apparent motion of the Moon by 50%. In a somewhat simplified model, the rate of change of the Moon's apparent angular distance from another celestial body (aligned more or less directly with the Moon's apparent velocity vector on the celestial sphere) changes at an hourly rate given by:
   v = ƒ·0.5° - (HP/57')·0.24°·sin(Alt_mer),
where ƒ is a factor near one representing any change in the Moon's normal geocentric rate of change of distance (due to orbital speed near perigee/apogee e.g.) and 0.5° is an assumed value for the average rate. The value of HP is compared here to a value close to the mean value of the Moon's HP. And Alt_mer is the altitude of the Moon at meridian passage. This is not a complete picture of all the variability and represents an imaginary case where the Moon's orbit runs right along the celestial equator, but it gets the main details. When the meridian altitude of the Moon is relatively high and as long as ƒ is not unusually high and HP is not on the low side, then the rate of change is reduced to around 0.25° per hour, give or take. That's just about half the expected geocentric rate. The Moon is crossing the sky, relative to the other stars, at "half speed" when it's relatively high in the sky. To confuse things a bit, that actually means it's travelling faster across the sky in diurnal motion terms. Normally, from a geocentric point of view, the Moon "falls behind" the stars at a rate of just about half a degree every hour. But in observer-based, topocentric terms, the Moon is "falling behind" at a slower rate of about a quarter of a degree per hour.

Frank Reed