Do astronomers have an established, systematic way for saying what does or doesn't orbit what? (e.g. "Mars orbits Earth")

Question

A recent comment

An object far enough away can certainly orbit the Moon and the Earth (and the Sun) -- Mars, for instance does this. An object in the Earth-Moon L2 is also orbiting both the Earth and the Moon.

A recent comment about that comment:

according to your way of thinking all solar system bodies orbit Mercury, except the Sun, which is just silly. Or does the Sun in fact orbit Mercury as well? I think your use of the word orbit is not workable, nor shared by almost anyone else.

So I'd like to ask if astronomers have an established, systematic way for saying what does or doesn't orbit what within the solar system, and if so, a link to point to in the future would be greatly appreciated!

Answer 1

It is possible that there is nothing "official", there is just the technical use of language. For example Phil Plait notes that He incorrectly used the word "orbit" for the motion of the Hayabusa probe, which does not orbit the asteroid Ryugu. But hovers over the surface.

So what does Phil mean when he talks about orbiting? I summarize the meaning thus: Object A is in orbit around object B if A moves around B (ie the True Anomaly of A increases from 0 to 360 degrees in fairly regular fashion) principally as a result of the gravitational field of B.

So although Mars does move around the Earth, its motion is not principally due to the gravitation field of the Earth, so it is not in orbit. However the moon's motion is principally due to the gravitational field of the Earth. It is in orbit around the Earth.

The moon is also in orbit around the sun: It moves around the sun and the reason for this motion is principally the graviational field of the sun.

A body at the Earth Sun L2 point is not in orbit around the Earth (it is fixed relative to the Earth) It is in orbit around the sun. A body in the Earth Moon L2 point (which is probably very unstable) is orbiting the Earth and orbiting the sun. Its motion relative to the Earth is primarily due to the Earth (and secondarily due to the moon). Its motion relative to the sun is due to the gravity of the sun.

Cruithne is in a 1:1 resonance with the Earth, but its postion is not primarily due to the gravity of the Earth. It is in orbit around the sun, not the Earth.

Hayabusa is not in orbit around an asteroid, it is maintaining position by thrusters. Similarly, A Jumbo jet is flying not orbiting, it's motion is not mainly due to gravity.

This idea can be sharpened by the notion of a Hill sphere. Inside the Hill sphere, a body will orbit. Outside it, the body will not orbit.

Answer 2

This is a neat question in that it made me think deeper about the word "orbit". The answer that mentions barycenters has a point, but in the end, it is a bit about references frames.

Let's take a relatively uncontroversial statement and make it controversial.

"The Moon orbits the Earth".

I would have never challenged this statement, except that once I plotted the path of the Moon and the Earth together relative to the SSB, I realized that the Moon is actually orbiting the sun (SSB) and is merely being heavily perturbed because it happens to be in close proximity to the Earth's gravitational influence.

If we zoom out we would next say that we are all merely orbiting the galactic core and simply because we are in proximity to the Sun, our galactic orbit is heavily perturbed by the Sun.

However, depending on the relative sizes of the influences we can make practical (sensible) inferences.

So, does "Mars orbit the Earth"?

No, because if we place a reference frame at Mars and try and explain the motion of the Earth and the Sun we get nonsensical results.

If we place a reference frame on the Sun, or at the SSB and then try to explain the motion of the Earth and Sun it becomes much clearer.

Does "the Moon orbit the Earth"?

Actually, yes, if we place a reference at the Earth we can explain the motion of the Moon pretty sensibly.

And so on.

Here is an article that is decently written about such frames of reference questions: https://www.wired.com/2012/12/does-the-moon-orbit-the-sun-or-the-earth/

Here is the video suggested by @uhoh:
https://www.youtube.com/watch?v=z52WWLE8bBo

Answer 3

Take binary star systems as an example.

Circumbinary, the planet orbits two stars, or, you could say it orbits their center of mass or barycenter.

We can also imagine a star with a brown dwarf/heavy jupiter orbiting it and a planet orbiting a bit further out. There's no precise point where the brown dwarf/heavy Jupiter stops being a binary system and becomes another planet orbiting the star. Because there's no precise place where the system changes, I'd be very surprised if there's a verifiable, official answer. I'd bet money that there isn't.

Astronomy is full of situations like this. Sometimes definitions can be set up, like the qualifications for being a planet. Sometimes it's harder to set up a precise definition, for example, what is the smallest size a moon can be?

There's no precise switching point where a planet orbiting two stars becomes two planets orbiting one star and there doesn't need to be. It's OK to say that a brown dwarf of low enough mass could be a heavy Jupiter.

It's easier to say that Mars orbits the Sun, but in a sense, Mars orbits the center of mass of the Sun + Venus + Earth & Moon (and all the small stuff in there too). Both statements have truth to them.

Venus and Earth together, when lined up, create a barycenter that's only about 70,000 km from the center of the Sun, or about 0.03% of the distance Mars is from the Sun (a bit less than 1 part in 3,000).

I believe (but can't do the math), that it's more accurate to say that Mars orbits the Venus/Earth/Sun barycenter more closely than it orbits the Sun. Both likely deviate from a perfect Kepler orbit to some degree. Mars' mass also plays a role in deviating from a pure Kepler orbit at least in terms of orbital velocity, and there's the perturbations from the outer planets, Jupiter and Saturn primarily and relativistic dilation has a tiny effect too (more noticeable with Mercury).

When NASA wants to land a craft on Mars, they need to take into account the gravitational influence from several planets, not just Mars orbiting the Sun, though I gather the early lunar landings, they were able to ignore relativitistic effects. With Mars, they likely need to factor in relativity.

It's also important to remember to convert to the metric system when needed, but, I digress.

Answer 4

One way would be to look at the phase of the radial motion of each object, i.e make a radial velocity curve for each object. Things in orbit with each other will have their motions in anti-phase with each. Thus as one object moves in one direction the other must move in the opposite direction as they orbit their center of mass. The amount of motion will depend on the relative masses but the sign of the motion must be opposite for each object.

If you followed the Earth's orbit relative to Mars's, sometimes they will move in opposite directions but sometimes they will move in the same direction. Thus they can not be in orbit with each other. The Earth/Moon case will be the same but you have to subtract the Earth/Sun effect first.

Answer 5

What if I told you that technically speaking, the Moon does not orbit the Earth, and the Earth doesn't orbit the Sun, and that the Sun orbits something that is nothing? Welcome to the world of barycenters, which seem to be skipped over in elementary school science, though for good reason. It would be a mouthful for the students to learn.

In the Earth-Moon system, the Earth does not orbit the Moon, and the Moon does not orbit the Earth. Rather, they orbit a common center of mass, referred to as the Earth-Moon Barycenter, or just barycenter if the situation is unambiguous (as you will see later, you can have multiple barycenters).

The Moon tugs on the Earth with the same force that the Earth tugs on the Moon. Therefore, the orbit looks more like this:

The Moon has roughly 1.2% the mass of the Earth. Therefore, the Moon should orbit roughly 83x further away (it's just $\frac{100}{1.2}$) from the barycenter than the Earth does. The Moon's semi major axis is 385000 km. Therefore, the Earth's semi major axis around the Earth-Moon barycenter (not the Sun) is roughly 4500 km. And that is the case, as shown below. The diamond symbol is what Space Engine uses for barycenter symbols.

If we zoom in we see the Earth's orbit around the barycenter:

Because the Moon has such a low mass compared to the Earth, the barycenter is actually located inside the Earth. As the Moon slowly travels away from the Earth in the next few hundred million years, the barycenter will slowly leave the Earth's surface.

Can the barycenter be located outside of the planet? It sure can. The Pluto-Charon system looks a bit like this:

In Space Engine it looks like this (brightness increased to you can actually see it):

What about the Sun-Earth system? Well the problem is that the Sun is also affected by all the other planets in the solar system. The sum of all these interactions is where the Solar Systemic Barycenter is located. It doesn't travel in a nice circle though, but it is mostly affected by Jupiter since Jupiter is the most massive planet in the Solar System. It looks like this:

How about binary stars? Well it's pretty much the same thing. Here's $\alpha$ Centauri.

Ok, last thing, how about systems with 3 or more stars? Well here's the thing. barycenters can orbit other barycenters. The Castor system is a sextuple (6) system. Here's what it looks like:

Those three points of light are actually two stars orbiting very closely together, so that they look like one star. So to answer you question, no they don't orbit anything really, but they instead orbit a common barycenter, and we determine what orbits what by seeing if it goes around that barycenter.