The Last Eclipse ... Ever?

I was talking about eclipses with someone the other day, and the wonderful coincidence we have here on Earth that the moon and sun both span almost the same angle in our sky – about half a degree – and so when they line up, the moon covers the sun almost exactly, and you get the view you see in those wonderful eclipse photos, with prominences and the corona streaming out from the edge of the moon’s silhouette.

And of course, it doesn’t always happen. If the moon’s near apogee, its farthest point from earth, it won’t quite cover the sun. That’s called an annular eclipse.

But wait a minute – isn’t the moon moving away from us, due to tidal friction? Will there come a day when the moon moves far enough away that all eclipses are annular? I wanted to find out.

For my starting numbers, I used The Nine Planets (nineplanets.org) and Rukl’s Atlas of the Moon, which gives a nice table of moon data early in the book. (I’d been using Rukl’s Atlas regularly for more than a year before I noticed that there’s a lot of really good info there besides just the maps. Check it out!) I calculated the moon’s angular size as 29.38” (that’s arc minutes, not inches) at apogee and 33.53” at perigee, versus sun sizes of 31.3” at perihelion and 32.6” at aphelion (those sun numbers vary depending on the exact solar radius you use). Then I did a little googling to understand how fast the moon is actually receding. The surprise I found is that most articles on the moon’s recession are on web sites debating evolution vs. creationism. What can tidal friction possibly have to do with that?

Well, it turns out that some young-earth creationists in the past have argued that the earth-moon system can’t possibly be 4.5 billion years old (the age pointed to by geologic evidence, both on earth and in rocks from the moon and meteorites recovered on earth). The argument is that at the speed it’s receding from us now, if you “run the movie in reverse” the moon would touch the earth long before that. Of course, this argument ignores a lot of research arguing that the rate hasn’t always been the same.

Anyway, I could see that I had quite a project ahead of me ... probably lots of biased and conflicting pages, none of them written by astronomers. The first link I clicked on was from the Talk.Origins Archive, an article called “The Recession of the Moon and the Age of the Earth-Moon System.” And then I saw the author – and stopped worrying. The author was Tim Thompson, a NASA physicist/astronomer who has spoken at the SJAA several times.

Tim’s article summarizes all the major research on the complicated gravitational interactions of the earth-moon system. It’s fascinating reading if you’ve ever been curious about the details of how tides slow earth’s rotation while they drive the moon into ever-higher orbits, and it offers a detailed bibliography if you want to track down the details. More to the current point, it also gives the figure for the moon’s current rate of recession from us as measured by the laser rangefinders planted on the moon by Apollo. Its orbit is increasing by 3.82 cm (±0.07) per year.

So how long before the moon recedes to the point where even at perigee it can’t cover the sun’s 31.3” size with earth at aphelion? Let’s make some simplifying assumptions: that the rate of recession stays constant (it won’t), that the sun’s diameter also won’t change (it eventually will), and that the moon’s orbital eccentricity stays the same (I don’t know but I wouldn’t bet on it). Let’s just assume that the moon’s perigee distance is going to increase at a steady 3.82 cm/year. Then the last total solar eclipse will happen in about 664 million years. (There’s a NASA eclipse FAQ page online – and a Space.com page that’s an exact copy of it – that calculates 1 billion years, but they’re using a figure of 1 cm for the moon’s recession, which doesn’t match the Apollo measurements. Go figure! Literally!) Anyway, it was a fun project, and it looks like eclipse chasers don’t have to worry about running out of eclipses for a while.

Meanwhile, what’s up in the sky right now? In the early evening, it’s Venus and Jupiter, though Jupiter sinks ever lower as the month progresses. On Dec 1, the moon, Venus and Jupiter make an especially close group. Try looking for them in the daytime: since the moon is easy to find, it should easily point you to the two planets. Late in the month, Mercury joins the fun in the early evening, but it doesn’t get very far from the sun.

Saturn rises around midnight, with its rings very close to edge-on – they’re less than a degree off of edge-on by the end of the year.

The rings’ angle to us will remain quite small throughout next year, never bigger than 8° around the middle of the year before finally closing to zero in September.

Uranus, a degree and a half northeast of Phi Aquarii, is up for most of the early evening, setting a little before midnight. At magnitude 5.9 (barely within reach of the naked eye at a dark site), it sits right next to a 5.6 magnitude star: they’re separated by a hair under nine minutes of arc, making an interesting small-scope “double star” target a little closer than Mizar and Alcor.

Neptune runs a couple of hours ahead of Uranus, so it’s much more borderline this month: try soon after the sky gets fully dark if you want to find it. Mars and Pluto are lost in the sun’s glare.