Moon speed

We had very clear skies in the Chicago area last night, and I was able to see Mars just before the Moon passed in front of it. This happened somewhere between 8:00 and 8:30. A couple of hours before that, I tweeted

Mars is about two Moon diameters away from the Moon right now. Will go behind the Moon in a couple of hours. It’s a very clear night in the Chicago area; seeing this makes the cold that comes with cloudless skies worth it.

The prediction of when the occultation would occur was made with the help of GoSkyWatch, an app I’ve had since shortly after it was released in 2008. But with a little thought, I realized that I could have made the same rough prediction with no help at all.

As we learned in the Antikythera post, the Moon travels

360 +29.1067 =389.1067

in 29.5306 days or 708.734 hours. Therefore, the Moon moves at an average speed of

389.1067708.734=0.549deghr

against the background stars.

Because of the media’s recent obsession with supermoons, we know that the Moon’s apparent diameter varies, but on the average it’s about 31 arcminutes or

3160=0.516

Therfore, it moves roughly one diameter per hour. If it’s two diameters away from Mars at 6:15, it’ll start to occlude Mars at 8:15. More or less.

Do we need to account for the motion of Mars? Not at the level of precision we’re using. A Martian year is about 687 Earth days long, so its movement against the background stars is about 1/25 th that of the Moon. When considering its motion relative to the Moon over the course of a few hours, Mars is essentially as fixed as the background stars.