Happy Aphelion Day!

I ran out of time yesterday, and had to fix a computer issue before I went to work, so this post is way late.

Today the earth is at its furthest from the sun, an event that always happens in early July, which throws some people off because they have the mistaken belief we’re hotter because we’re closer. Nope: we’re hotter because the earth’s axis is tilted in respect to its orbit, and right now the Northern Hemisphere, where we live, is facing the sun at less of an angle. We see this as the sun being higher in the sky than in the winter. In the Southern Hemisphere, the axis is pointed away right now, which is why they’re in the middle of winter. Come the first week in January, the situation will be reversed: The axis in the Northern Hemisphere will be pointed away from the sun, and the one in the Southern Hemisphere toward it. That will put us in the middle of winter, while it will be summer in the Southern Hemisphere.

In any event, the difference between our distance at aphelion and at perihelion, when we’re closest, isn’t that much different. The earth, like all the planets, orbits in an ellipse about the sun, with the sun at one of the focal points on the major axis. Astronomers and mathematicians often use eccentricity, a measure of how “off” a class of curves called conic sections are from being a circle. Eccentric means off-center, so a type of wheel with the axis off-center is called an eccentric, just as we might call a person who’s a tad off-center (Rule of thumb: If someone’s off-center and rich, they’re eccentric; if someone’s off-center and broke, they’re nuts).

Ahem. Anyway, a circle has an eccentricity of 0, since the axis is at the center. Orbits can have eccentricities on up to 1. At that point they make a once-around and head back into space, so they don’t orbit a particular body. Earth has an eccentricity of about 0.017, which means it’s pretty close to a circle. Pluto has one of about 0.249, which means its orbit is more elongated. Halley’s Comet has an eccentricity of 0.967, so its orbit is very elongated.

It’s actually a misnomer to say that the earth is such-and-such distance from the sun at aphelion and perihelion. We’re actually that far from the barycenter, the point where we orbit around the sun. No, we don’t orbit around the exact center. Think of the barycenter like the center-of-gravity of a stick with a little weight on one end and a big weight on the other. The larger the difference in mass, the more it shifts to the larger weight.

Unless I’ve messed up the calculations, the earth-sun barycenter is about 449 km from the center of the sun, and I think about 457 km from the center of the sun at aphelion (I’m not an astronomer), but either way it’s well beneath the surface of the sun. This means, to be pedantic, that today we’re about 1.521 x 108 km – (sun radius – 457 km + earth radius) from the sun’s surface, which is 1.521 x 108 km – (348,000 km – 457 km + 3,186 km) = 1.521 x 108 km – 350,729 km = 1.517 x 108 km. So think of orbital distances like the distance between small towns: usually measured from the center of town and not the city limits.

One consequence of the barycenter is that both bodies twirl around that same point. If the solar system were only made up of the sun and the earth, the sun would orbit around that tiny barycenter just like the earth does. Even with objects the size of our earth – moon system, the barycenter can be well below the surface of the larger body. However, it can be outside of both bodies.

Here’s one of the early New Horizons videos of Pluto and its moon Charon, at https://www.nasa.gov/mission_pages/newhorizons/images/index.html?id=356701 . Click to watch.

The large sphere is Pluto and the little one Charon. Notice how they both revolve around a point beyond the surface of Pluto. That’s the barycenter.

Is that cool, or what?