Orchids and Moonbeams

Transcription

"Hey Joe, I was wondering if you could ask a video about why the moon orbits the Earth instead of the sun?" [MUSIC] The moon and the sun are about the same size in the sky, which is why we get cool things like this. But that’s just a coincidence, thanks to the fact that the sun is about 400 times farther away as the moon and its diameter is about 400 times bigger. Get a little farther away, and the view is different… still cool, though. The sun is big. We could line up 109 Earths across its face, and it’s 330,000 times as massive. In fact the sun holds 99.8% of all the mass in the solar system. But here’s something weird. If we plug the Earth, moon, and sun into the formula for Newton’s law of gravitation, we find out that the sun exerts twice the gravitational force on the moon as the Earth does. So does the moon really orbit the Earth? Well, of course it does. We know this is true because we’ve measured the moon and sun moving through the sky for hundreds of years, and we’ve also been up there. The fact that the sun exerts more gravitational force on the moon than Earth does just doesn’t matter here. Around everything in space–planets, moons, stars– is a volume where the gravity of the the thing in the middle beats out the gravity from something farther away, even if it is more massive. It’s called the Hill sphere. The Hill sphere around the Earth has a radius of about one and a half million kilometers, which is more than enough to fit the moon’s orbit. Move the moon farther away, or move us both closer to the sun, and we’d lose the moon, but that would be the least of our problems. The important thing is that inside the Hill sphere, the Earth’s gravity dominates, and the sun pulls on Earth and the moon together. So really, the moon does orbit the sun, it just orbits the Earth more. But what does that orbit look like? If I asked you to sketch out the path the moon takes as it travels with Earth around the sun, you might imagine something like this. But you’d be wrong. Imagine two cars racing around a circular track. One of the cars speeds up to pass the other, which is moving at a constant speed, then moves left and gets overtaken. It may seem like one’s driving spirals around the other, but trace the paths and you get this. But the distance to the moon isn’t much compared to the space between the Earth to the sun, so during our gravitational dance around the sun, those bumps smooth out… to a very familiar shape indeed. Stay curious. What did the Earth say to the sun when the moon was acting all full of itself? It’s just a phase! To find out how all these orbits combine to make lunar shapes from crescent to full to new, check out this video from our friend Phil Plait over at Crash Course Astronomy.