SJAA Ephemeris January 2012 | SJAA Home | Contents | Previous | Next

The Shallow Sky

Analemma dilemma

Akkana Peck

The equation of time, showing the contributions of earth’s orbital eccentricity and the obliquity, or tilt, of its axis. Plotted using code posted on Wikimedia Commons by Thomas Steiner.


Jupiter remains a force to be reckoned with in our early January evening skies, still high at sunset and visible until it sets, a bit after midnight.

Tuesday night, Jan 3, sees a double shadow transit a bit before midnight; then the following Tuesday night, Jan 10, sees another multiple-moon event, starting around 10 p.m. with Ganymede and Europa, then following up with the same two moons’ shadows starting around 1:15 am.

Venus remains in our dusk skies. It makes a fairly close pass (a bit over a degree) with Neptune on the 13th – can you find the dim blue orb in the twilight sky so close to bright Venus? Uranus, too, is visible in early evening, though it’s much higher in the sky, in Pisces.

Mercury is visible in the dawn sky through most of the month, disappearing in the last week of January. Saturn, too, is in the morning sky, showing a ring tilt of about 14 degrees, which won’t change much until October.

Mars rises in late evening, so late-night observers can start getting their “Mars eyes” on for this year’s opposition. True “Mars season” won’t start until the opposition, on March 3, but it always takes practice to remind your eyes and brain how to see details on that small, red disk, so it doesn’t hurt to start early. Right now it’s only about 10 arcseconds – but it’ll only reach 13” at opposition, so 10” now isn’t so bad.

Last month saw the successful launch of the new, much larger, Mars rover, “Curiosity”, more formally called the Mars Science Laboratory.

Curiosity is a lot bigger than the two rovers that are on Mars now, at about the size of a Mini Cooper (the new upsized version, not the classic sixties classic) and only weighs a bit less than the car.

It’s not as fast as a Mini Cooper, though, with a top speed of around 90 m (300 feet) per hour. On the other hand, Minis don’t have radioisotope power sources that last for 14 years without a visit to a gas station, and they can’t drive themselves around another planet taking chemical analyses of rocks and soil.

Last month also saw news from one of the older rovers.

Opportunity, still rolling along just fine, detected some gypsum – considered a definite sign of water. I know, water on Mars, yawn.

We’re used to new water-on-Mars news every month or so now. But really, when you look at it, that’s one of the amazing successes of the rover program, isn’t it?

I’m writing this on a dark, cold December evening. We’re still a few weeks away from the winter solstice, the shortest day of the year.

But there’s hope – last week, December 6th, was the earliest sunset, and from now on the sun will set later, even as we move into winter.

That’s always a hard thing for me to wrap my head around – why is the date of the latest sunset happen more than two weeks before the shortest day?

It has to do with the famous “Equation of Time”. And that’s tied up with the analemma, that odd figure eight that makers of world globes like to draw in the middle of the Pacific Ocean. Usually it’s just there, without any explanation for what it means or why. And it’s too bad, because it’s pretty interesting for astronomers.

If you take an accurate clock, and every day you go out exactly when the clock says noon, take a compass and measure the sun’s position, you’d expect it to be due south, right? But you’ll find that it hardly ever is. No, you didn’t mess up and forget about daylight savings time: the problem is that the sun appears to move at different rates across our sky, sometimes faster than the clock, sometimes slower.

That’s also why sundials seldom show the right time.

The rate changes for two reasons. First is the eccentricity of our orbit. Because earth’s orbit is elliptical and not circular, earth changes speed as it orbits the sun. So depending on whether we’re in a fast- or slow-moving part of earth’s orbit, the sun will appear to race ahead or lag behind the meridian even when our clocks say it should be noon.

Second, because our axis is tilted, the changing angle of the ecliptic at different times of year adds a second complication.

The “Equation of Time” combines these two effects to compute how many minutes ahead the sun’s position (“apparent solar time”) will be compared to our smoothly-running clock (“mean solar time”). Each effect is a simple sine wave, so adding them gives us the equation you’d need to keep your sundial adjusted.

Of course, in real life there are other influences too, including the gravitational effects of other planets like Jupiter. Calculating all those effects is a lot harder, but those effects are small and normally you can ignore them, unless you’re trying to guide a spaceship or analyze Large Hadron Collider results.

So what about that figure eight in the Pacific Ocean?

The analemma has two components. Its horizontal component is the equation of time. Take that, then add a vertical component representing the sun’s declination – how far north or south is it? – and you get that familiar figure eight.

The neatest thing about the analemma is that it describes the path the sun really takes in the sky. You can photograph it! Set up a fixed camera with a wide-angle lens in your backyard, pointing south, and take a photo every day (or once a week) at exactly the same time. (Subtract an hour during daylight savings.) Combine all those frames (or make it a multiple exposure), and you’ll end up with a beautiful figure-eight analemma.

So why do they put the analemma on globes? And why in the Pacific Ocean?

Well, ship navigators who tracked their location by sighting with a sextant (in the days before GPS) needed that information, so they could compare their sightings to what their clocks said.

But it would seem easier to use a table listing values for the equation of time, and I doubt many ships were navigating using small consumer globes. In truth, I can’t figure out why they put it on globes, except for the nice old tradition linking maps and celestial navigation.

The second question is easier to answer: if you’re going to stick an analemma on your globe, put it in the Pacific because that’s the biggest place where there’s no land to get in the way.

I guess an analemma is more useful than a warning like “Here there be dragons”.

One last thing about analemmas: because they’re due to the shape of a planet’s orbit and how much its axis is tilted, not all planets have similar analemmas. Quite a few planets have figure-eight shaped analemmas like ours, but Mars’ analemma is teardrop shaped, not a figure-eight – it never crosses itself. And Saturn’s is a figure eight with a tiny top loop, so it doesn’t look like an eight at all.

So watch the sun, pay attention to those sunrise and sunset times, and think about analemmas over the next few months as you’re waiting for the warm spring weather!


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