Crashing into the Last Quarter Moon

It’s still getting colder.  Back on December 21 passed the winter solstice – accompanied, this year, by the Great Conjunction of Jupiter and Saturn – and then on December 31 the lamentable moment when once-Great Britain dropped out of a greater family, the European Union.

And on January 4 comes one of the moments that can be thought of as the depth of winter: the latest sunrise (at latitude 40° north).  The explanation of that, and why it differs with latitude and is different from the shortest day, is in my page about “Latest and earliest sunrise and sunset.”

And now the Moon is bright in the morning sky, approaching its Last Quarter moment of January 6.  So moonlight spoils the first of the year’s notable meteor showers, the Quadrantids. Their peak was early today, but you might see a few late Quadrantids as their radiant climbs into view after midnight.

See the end note about enlarging illustrations.

As for the Last Quarter Moon, the time to look out at it on January 6 is sunrise – that very late sunrise time of about 7:20.

To quote the “Moon as Signpost” section of our Astronomical Companion: “You are now looking forward along Earth’s orbit.  You will be there – out in space at that point where the Moon is now – in about 3{1/2} hours.”

In this diagram, the Moon is shown at intervals of a day.  Earth and Moon are exaggerated 5 times in size.

The golden arrow is the future path of Earth, divided into hours.  It looks like a straight line, but, believe it or not, is a curve.  But the left end of it dips so slightly – a quarter of a millimeter in the scale I’m using – as to be indistinguishable from straightness, unless you somehow hold it to a straightedge, such as the top edge of your screen.  For the Earth orbit is immense: about 400 times wider than the Moon orbit.

As the small arrow shows, Earth’s rotation from midnight around to sunrise brings you to Earth’s front – our planet’s nose, prow, bow, as we are tempted to call it.  And if you could stay there – if the Earth could stop rotating while continuing to fly along – and if the Moon could halt at that Last Quarter point in space, then you would crash into the Moon.

But slightly left of its center.  By a distance that I haven’t attempted to calculate.  Slightly into the sunlit hemisphere, anyway, if that’s any consolation.

Both orbits are simplified as circles, since this picture is generalized, not for a specific date.  So the diagrammed position of the Moon at Last Quarter is exact only if for a date when the Moon is at its average distance.  And your crash-landing would be north or south of the Moon’s center, unless the date were also at the ascending or descending node of the Moon’s orbit.

The instant of our Last Quarter on Jan. 6 happens to be 9:37 by Universal Time, which is 5 or more hours earlier by American clocks, thus before sunrise.  So you’ll hit the dark side of the Moon.  But do you care?  It won’t be a comfortable crash-landing, with the mass of Earth at your back.

I devised this diagram at the request of Deborah Byrd, who will use it in her far fuller post about Last Quarter in her celebrated EarthSky website.

I made heavy weather of the task, because at first I thought I could produce it as an application of my “sphere” family of programs, by which I make all kinds of space diagrams; until I realized it was impossible, because those assume that the picture is either heliocentric or geocentric – based on a stationary Sun or Earth – not both at the same time.  And this has to be both: the Moon moving geocentrically and the Earth heliocentrically.  In a heliocentric plot with Earth moving along, the Moon would be going along with it, just making a sinuous curve right and left of Earth.  Last Quarters would merely appear as the succession of points where this smooth line crosses inward over the Earth’s smooth line, like a thread in a rope.

(A paradox, mentioned in the “Moon’s Orbit” section of the Astronomical Companion, is that the Moon’s heliocentric orbit “is everywhere concave toward the Sun!”)

So I had to take another day and write a new little Moon-phase program, of only 180 lines.

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ILLUSTRATIONS in these posts are made with precision but have to be inserted in another format.  You may be able to enlarge them on your monitor.  One way: right-click, and choose “View image”, then enlarge.  Or choose “Copy image”, then put it on your desktop, then open it.  On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers).  Other methods have been suggested, such as dragging the image to the desktop and opening it in other ways.

Sometimes I make improvements or corrections to a post after piblishing  it.  If you click on the title, rather than on ‘Read more’, I think you are sure to see the latest version.

This weblog maintains its right to be about astronomy or anything under the sun.