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

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!

• Following this closely. – Muze Sep 30 '18 at 18:21
• IIRC there used to be some controversy over whether Pluto orbited Neptune. Might be worth looking up discussions of that -- whether an eccentric solar orbit is better described, or more correctly based, on one orbiting the other. – Carl Witthoft Oct 1 '18 at 18:07
• A useful metric might be total (potential + kinetic) energy: <0 for an elliptical orbit, >0 for a hyperbolic trajectory. – Mike G Oct 1 '18 at 18:27
• Things orbit each other. The physics is quite clear about that. No other point of view makes sense in terms of physical laws. Adopting a coordinate system where e.g. one body is always the origin only complicates the maths, but does not change the underlying physics of the system. – StephenG Oct 2 '18 at 0:45
• @StephenG If you are prepared to explain "the underlying physics" of Mars' orbit of the Earth and Moon (rather than the semantics of it) as mentioned in the question, let me know and I'll ask a new question to provide you the space to do so! – uhoh Oct 2 '18 at 2:05

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.

• I might agree with every single thing you've written (not sure yet, but it's likely once I read through slowly) but what I need something "established and systematic" and ideally "a link to point to in the future". This is your position, and I thank you for it, but what I need most is a verifiable source to what is generally agreed upon. – uhoh Sep 30 '18 at 19:31
• @uhoh I agree with James K that there's probably no official answer to this because there doesn't need to be. I'll give an answer with an example. – userLTK Oct 1 '18 at 13:07
• @userLTK I'm always amazed when people conclude that if they don't know the answer, nobody does, or there is none. In the last half-millennium quiet a substantial amount has been written about Astronomy. Just because one person feels a given paragraph needn't be written does not mean that nowhere has anyone ever written such a paragraph. – uhoh Oct 1 '18 at 14:37
• @uhoh It's not that nobody knows the answer. I'm saying it's like pornography. We know what it is, but there's no precise point where art ends and pornography begins. There are numerous examples, both in astronomy and outside of it, of unspecific boundaries. If the boundary is unspecific, then there's no precise dividing line and no need for the scientific community to create one. When a pluto like controversy arises, then perhaps the astronomical community will address this. You're assuming a definition exists but I can tell you even as a novice, that it almost certainly doesn't. – userLTK Oct 1 '18 at 22:55
• side note: Hayabusa-2's current "home position" is deep inside Ryugu's Hill sphere. I guess that if they have chosen to propulsively hover in the Sunward direction instead of orbit it's for photographic illumination, but an orbit is certainly possible. At 30 km away from the < 1km diameter, roughly 5E+11 kg body, the period would be two months, so the propulsive cost for "hovering" would in fact be costly for the craft in terms of propellants. – uhoh Oct 2 '18 at 1:21

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:

• I like this answer for several reasons; it offers a way to look at things systematically; the motion of Earth as seen from Mars would definitely lead martians to conclude they do not orbit the Earth, just as we do not believe we orbit around Venus, and it offers a link to a source that addresses this question head-on. Thanks! – uhoh Oct 4 '18 at 3:18
• I don't know if you'd like to add the link to your question, but the first minute of the video lagrange points animation offers a way to see the Moon's serpentine motion. (video discussed here) – uhoh Oct 4 '18 at 3:20

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.

• I might agree with every single thing you've written (not sure yet, but it's likely once I read through slowly) but what I need something "established and systematic" and ideally "a link to point to in the future". This is your position, and I thank you for it, but what I need most is a verifiable source to what is generally agreed upon. (identical to the comment I left here and for the identical reason) – uhoh Oct 1 '18 at 14:38
• Just saying "I don't think your question needs an answer, so I'm going to write an answer to a different question here" is the best way to proceed. You've written here mostly just an opinion, which is not a proper SE answer. – uhoh Oct 1 '18 at 14:40
• @uhoh It's rock solid fact that there's no clear dividing line between where a heavy Jupiter ends and where a brown dwarf star begins. That means that there's no precise dividing line between where a large planet/star system ends and a binary star system begins. Hence, orbiting two stars or two planets orbiting one star can't be precisely definable. LOGICAL DEDUCTION isn't the same thing as opinion. Now in reality, when we get better looks at other solar systems, nearly all will be one or the other, but there's no way to make a precise definition. – userLTK Oct 1 '18 at 23:06
• @uhoh I should have probably added that mine was really more of a comment that I thought relevant than an answer, but explaining circumbinarys would have been difficult in the limited space of the comment section. – userLTK Oct 1 '18 at 23:16
• If you could make this suggested edit I'd be tickled pink, and would be able to amend my voting as well. – uhoh Oct 2 '18 at 9:17

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.

• Interesting! I'll do a quick check but I'm pretty sure that by this test an object in a halo orbit associated with the Sun-Earth L1 or L2 will appear to be in a 6 month orbit around the Earth when in fact it's in a heliocentric orbit that happens to be in 1:1 resonance with the Earth. – uhoh Mar 26 '20 at 23:12

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.

• -1 This is not at all an answer to the question as asked. These are just random factoids about orbits. – uhoh Sep 30 '18 at 19:37
• @uhoh last paragraph answers it. I just wanted to share how in reality saying x orbits y is incorrect since they orbit a common center – User24373 Sep 30 '18 at 19:38
• The barycentre is simply the "center of mass of two or more bodies that orbit each other". You haven't answered the key issue of defining what an orbit is, except to reaffirm James K's answer that "orbit" is defined as a gravitationally curved trajectory. – Chappo Hasn't Forgotten Monica Sep 30 '18 at 23:56
• I think it's a relevant piece of information in relation to answering the question. Maybe not the best answer, but it explains the reality of the situation the OP is asking about, so it contributes to the discussion. – FJC Oct 1 '18 at 13:41
• @FJC I don't see any information here that would address how astronomers generally address someone saying that Mars orbits Earth. In what way would explaining barycenter do that? I haven't asked how orbits worked, my question is fairly narrow. – uhoh Oct 2 '18 at 9:22