The Moon Does Not Orbit the Earth
Michael James Scharen

michaelsbookcorner.com
September 17, 2021

This article is in response to a question in Quora to the affect that why does the Sun’s gravity keep Pluto in orbit, but has no affect on the Moon? Scientists and other educators are quite often guilty of using shorthand explanations which deserve bit more rigor for the sake of the uninitiated.

To bring this discussion more Down-to-Earth in the beginning, let’s have a brief reminder about center-of-mass. This center-of-mass concept is something we all have an intuitive feel for and in space the definition is no different. Take the case of an overloaded truck with the load stacked too high or even an SUV taking a turn too sharp for handling the vehicle. These, we all know, are a problem based on the position of the center-of-mass for the vehicle-load system. Two objects in space follow the same definition.


Fig.1 - Illustration of the center-of-mass concept. For masses closer to each other in quantity, the center-of-mass lies in a point in space between both of them.

The Moon is affected by the Sun’s gravity but the gravity of Earth affects its local motion. There is a sort of hierarchy at work with all melding into it. It is a common misunderstanding based upon how science is taught to say that one body orbits around another. This is a shorthand which makes discussion easier but is not entirely accurate. In reality, two bodies of any mass orbit around their common center-of-mass. In the case of the Earth and any man-made satellite we put into orbit, that center-of-mass is so close to the Earth’s center of mass that, indeed, we say that the satellite orbits around the Earth or the Earth’s center-of-mass. This is also the case for the Earth and the Sun. However, if we take two bodies of equal mass, then their center-of-mass would lie on a line half way between them and outside of both of them. They both would orbit about that point in space. Pluto’s moon Charon has a mass much greater compared to Pluto than does the Moon to Earth. For that system, it is more apparent that they are co-orbiting a point in space between them, though even that point, as shown, is much closer to Pluto than Charon.


Fig.2 - The Pluto-Charon system illustrating that Charon does not orbit around Pluto but both bodies orbit about their common center-of-mass. The green cross is the point both bodies are orbiting about.

We’ve all heard of binary star systems in which a solar system has two stars rather than one. More than half of the solar systems studied follow this model, in fact. In those systems the center-of-mass could be at a point much farther away from the center of either star if the stars’ masses are more or less equal. Luke Skywalker comes from Tatooine, a world with two stars. The two stars are orbiting about their mutual center-of-mass.


Fig.3 - Tatooine, from Star Wars, is located in a binary star system.

To get back to the question, we know that the Earth orbits about the Sun, or rather the center-of-mass between them. But, it is more accurate to say that the Earth-Moon System and its center-of-mass orbit around the center-of-mass for the Sun on one side and the Earth-Moon on the other. It seems a bit of an abstraction to say that some point in space such as a center-of-mass is what is, in fact, in orbit, but that is the most accurate way of stating it. So, this is a way of explaining that our moon is affected by the Sun as it co-orbits the Sun via this Earth-Moon system, but our conventions in discussing it are what is really off. All bodies of any mass are affected by all other bodies of any mass. For convenience, we do not take all of these effects into account in our discussion as some effects or distances become negligible for sake of that discussion.

Incidentally, I make mention of the co-orbiting concept briefly in two of my books, Sol is Not Lost and For the Ages. The main character hails from secret breakaway colonies located many light-years away on two co-orbiting Earth-like planets called Magellan and Bering. I’ve conveniently set up these imaginary worlds such that their masses are not too far apart and their orbits are such that the tidal forces of one do not adversely affect the sister planet. Both worlds have continents and oceans but the gravity on Magellan is 1.4 x the gravity of Earth and the gravity of Bering is about 0.8 g.

The center-of-mass concept is also used in searching for planets far from our solar system. In attempting to observe a distant star as a stationary object, often a wobble is noticed. This wobble is due to the fact that the star and some massive planet say the size of Jupiter or Saturn, is in orbit — or more accurately — a co-orbit. The wobble is that distant star’s orbit about their mutual center-of-mass. The motion is usually detected by the Doppler shift in light coming from that star, bluer coming closer and redder moving away. By timing and other means of estimation, the mass of the unseen body can be determined.