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Where on (or off) Earth Are We?

Week of March 22, 1999

Where are you right now?

Let me guess: in front of a computer. That was easy! But let's get more specific. Where on Earth are you?

There are many ways to answer that question. You could give a latitude or longitude if you want to be really specific, or you could have named a continent, country, or general area (``the Sahara Desert'', perhaps, if you have a long extension cord).

The same thing happens in astronomy. Where you are depends on what you're asking. You can be very general (``on Earth'', or ``150 million kilometers from the Sun''), or very specific. As it turns out, the details count!

As part of my daylife work, I was assigned the task to find out just where the Earth is at a given time. We need this because we are observing a target that pulses, and to time the pulses we need to know just where the Earth is in relation to the Sun. It's like timing the delay between a lightning flash and the thunder: the amount of time tells you how far away the bolt was. The farther you are, the longer the delay. We had a similar problem with the pulsar. As the Earth revolves around the Sun, the pulses take a longer or shorter time to reach us as we increase or decrease our distance to it. To understand the delay, we need a very good position for the Earth.

I quickly found out that to determine the position of the Earth any better than `right underneath me'', you need a fierce amount of math. First, the Earth orbits the Sun. That means its position changes, and you need to keep track of it. Worse, it orbits in an ellipse, so the distance from the Sun is constantly changing, sometimes closer, sometimes farther. Worse, the other planets tug on Earth, pulling it slightly off course in different directions. Worse yet, the Moon tugs on the Earth, changing its position. Still with me? There are other factors too. We are using Hubble, which orbits the Earth, so we need to know just where it was too. Luckily, we have software that calculates that for us!

And then, what do you mean by ``Earth's position at a given time''? What time? Universal time (which is Greenwich Mean Time), TAI (Temps Atomique International = International Atomic Time, a time based on the ticking of atomic clocks), Terrestrial Dynamic Time, which is based on TAI but is 32.184 seconds ahead, or just plain Julian Date, a calendar that is counted from the day January 1, 4713 B.C. (as I write this, today is JD 2451259).

So you can see why I started to get a bit stressed by this. I read a lot of books, did some research, and finally, after a few days, gave up. Instead of starting from square one, I went right to the source, the United States Naval Observatory. They are the official timekeepers of the U.S., and they also publish the Astronomical Almanac, a compendium of planetary positions and times. A helpful scientist there pointed me to some software that, for a given instant of TAI (and therefore TDT which I can get from UTC and JD), provides the position of the Earth with respect to the center of the Sun. The accuracy is about 1/100000 of the distance from the Earth to the Sun, or roughly 150,000 kilometers. That's pretty good!

If we need even better accuracy, I still have access to software that should get it better, as soon as I can figure it out. There are over 11,000 terms that go into those equations, so I'd better clear my calendar...



©2008 Phil Plait. All Rights Reserved.

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