Dance a Little Dance

Astronomy follows me everywhere. Yesterday I attended a wedding of a couple of very close friends, who asked my daughter to be the flowergirl. At the reception after the wedding, I was dancing with my daughter, who is three years old. She wanted me to spin her around, so I held on to her hands and we spun. I had to lean backwards a little to make sure we didn't topple over, and as I spun her in a big circle around me I made a little circle on the floor too.

Those circles (her big one and my little one) are very telling. She tips the scales at about 15 kilograms, and I mass about 75. Since I mass five times what she does, she made a much bigger circle than I did; not coincidentally, her circle would be five times as big.

What was happening to my daughter and me on a small scale as we danced happens on a much bigger scale when planets dance too. The Earth, for example, has a mass about 81 times that of the Moon. That's a lot, but the Moon still has quite a grasp on us. As it orbits us, the Moon makes a circle about 400,000 kilometers across. But since it has a substantial mass it tugs on the Earth too. The Earth makes a little circle while the Moon makes its big one, and the Earth's circle is about 5000 kilometers in radius, about 1/81 of the Moon's (the ratio of the masses). In a sense, the Moon and Earth are both orbiting a single point in space, called the barycenter, commonly called the center of mass. It is mathematically correct to say that it is the barycenter that orbits the Sun, while the Earth and Moon circle the barycenter. So really, we both make wiggly lines as we go around the Sun; it's the combination of our orbital path around the Sun plus our smaller path around the Earth/Moon barycenter.

The Earth is about 6400 kilometers in radius, so as it happens the circle we make around our barycenter is smaller than the Earth itself. But this isn't true for everyone. The Sun is about 1000 times the mass of Jupiter, which orbits the Sun at a distance of about 780 million kilometers. When you crank through the math, you find that the barycenter of the Sun/Jupiter pair is actually above the surface of the Sun! So if you were an observer sitting some distance from the Sun, you would see the Sun moving back and forth over the course of one Jupiter orbit (about 12 years). You'd have to measure it carefully, but the telltale signs of a planet are there.

This isn't just some theory. This is a good way to find planets around other stars! Right now, it's the only way. As the star gets tugged back and forth by a planet, the little circle it makes affects the light emitted by the star (this effect, regular readers know, is called the Doppler Shift). By measuring that shift, we can find out all sorts of things about the planet, like its orbital period and mass. That's how all the new extrasolar planets have been found!

So astronomy really does creep into everything in my life. What started as a dance at a wedding ties into the discovery of massive planets orbiting distant stars. But all my daughter really cares about is that she and Daddy got to dance. I'm glad. Sometimes I need something like that to get everything into perspective.