What is the frame of reference for orbital speed?

Don't treat this question lightly. It's a thing that's been biting me for a pretty long time, and while it's "intuitively obvious", if you get into finer details, it gets quite convoluted.

So, a satellite in orbit, means it moves at a speed defined by a bunch of equations, relative to... what exactly?

"Translationally" the frame of reference is bound to barycenter of the system considered. Usually happily approximated to the planet center, which won't be so simple with binary stars, but that's the lesser problem.

What about rotation of the frame of reference?

Obviously not surface, but then - what?

"Direction of equinox" is subject to precession of the planet.

"Distant stars" is a common approximation but distant stars belong to the galaxy and rotate with it too.

Distant galaxies? But clusters and even superclusters move reative to each other, never mind space expansion.

Cosmic background radiation? Would seem plausible, except... if our supercluster is spinning (or distorting in some other way), won't frame-dragging make it false? What about orbits in neighborhood of supermassive bodies where relativistic effects like local frame-dragging are non-negligible?

So what is the inertial frame of reference in which orbital motion happens bound to?

• I was certain there would be a duplicate question on Physics SE, but I wasn't able to find one that was particularly close. You have my upvote, though I wonder if you wouldn't get more qualified answerers there.
– Bear
Apr 27, 2017 at 12:25
• @Bear: You wouldn't. They absolutely LOATHE anything that even most remotely reminds "special frame of reference" It takes a LOT of effort in phrasing your question not to have it closed without reading as duplicate of something with an answer of "aether doesn't exist, there are no special frames of reference". This is what I asked, had to set a bounty to get an answer, and still needed to squeeze details out of the answerer.
– SF.
Apr 27, 2017 at 12:46
• It's a theoretical physics site, and things as mundane as our specific instance of the universe are not really their thing :) As I asked how enthalpy of fusion of water varies with pressure (a function or a table), I got the question closed as duplicate of "does enthaply of fusion vary with pressure", with an elaborate "yes" for an answer.
– SF.
Apr 27, 2017 at 12:50
• Hey! I'm a big fan of the physics.SE sister site. You just have to understand that physicists are fans of spherical cows, and all that that entails. Apr 27, 2017 at 16:56
• – SF.
Apr 27, 2017 at 17:50

So what is the inertial frame of reference in which orbital motion happens bound to?

TL;DR: Whatever you want. Conceptually, all frames of reference are equally valid. However, some frames are computationally better than others, depending on context. While you could do it, it would be ludicrous to describe the formation of a hurricane or the orbit of a satellite in low Earth orbit from the perspective of a Triton-centered, Triton-fixed frame.

But you could do it!

In fact, modeling the orbit of an object in low lunar orbit from the perspective of a Neptune-centered inertial frame is one of my favored tests of the orbital mechanics package I developed for the Johnson Space Center. The result is pure garbage after a few dozen orbits, but it does work initially. The object initially orbits the Moon, but numerical issues quickly arise.

What is this thing that you call an "inertial frame of reference"? As a supervisor said to me almost 40 years ago, name one. The so-called Earth-centered inertial frame obviously isn't inertial; the Earth is accelerating gravitationally toward the Sun, the Moon, the other planets, nearby and remote stars, other galaxies, etc. In addition, the axes of an ECI frame are almost certainly rotating with respect to those of a Newtonian inertial frame of reference.

There's one catch, good luck finding a Newtonian inertial frame of reference. Or as my supervisor said almost 40 years ago, name one. To make matters worse, this doesn't even take general relativity into account. Ultimately, the concept of a Newtonian inertial frame of reference is a fiction. That said, it is a very, very useful fiction because our solar system is very close to Newtonian in behavior. Even the motion of Mercury can be approximated extremely accurately as being due to Newtonian gravity plus some very small post-Newtonian accelerations.

There are two challenges with regard to defining a Newtonian frame of reference, the placement of the origin and the placement of the axes. It's important to keep in mind that all frames of reference are equally valid. Using a quasi-inertial solar system barycenter frame to describe the motion of a satellite in low Earth orbit doesn't make any sense. An Earth-centered inertial perspective is a much more sensible perspective.

As previously mentioned, an Earth-centered frame is an accelerating frame. This is easily addressed: Add fictitious accelerations due to the Earth's gravitational acceleration toward the Sun, the Moon, and perhaps the other planets. In the space exploration community, the term describing perturbations due to choosing a frame based on the center of some massive body is "third body effects" (or third body accelerations, or third body perturbations).

A rotating frame makes for a much messier situation. Up until the mid 20th century, the preference was to use a very slowly rotating frame based on the location of the vernal equinox. This resulted in apparent apsidal precessions of the orbits of the planets about the Sun. As is the case with third body effects, this is not necessarily problematic. The techniques that addressed this apparent precession were sufficient for the 19th century discovery that Mercury suffered a precession that could not be explained by Newtonian mechanics.

Three key things changed in this regard during the latter half of the 20th century. One was that humanity started putting things into space. Another was drastic improvements to astronomical observations. Both motivated the improvement of the concept of frames of reference.

The third key item was the discovery of quasars. Quasars are so remote that their proper motions are are extremely small and are unrelated to anything close by. (A galaxy even remotely connected to the Milky Way qualifies as "close by" compared to quasars. The current gold standard with regard to the orientation of a frame of reference is the International Celestial Reference Frame (ICRF). This is based on almost 300 quasars, with over 3000 other quasars used as a sanity check.

• So what is the frame of reference for orbital speed? You went into some depth here, but I don't see any answer to the actual question asked by the OP. Maybe it just needs highlighting, or a TL;DR?
– user
Apr 27, 2017 at 12:10
• @MichaelKjörling As I didn't read the entire answer, I second your tl:dr request ;) Apr 27, 2017 at 13:12
• As I understood, for practical purposes, it should be one local to the simplified system's barycenter, it won't be fully inertial, but with all "non-inertionalities" expressed as "third body effects" (fictitious forces), and its own position/movement can be described in ICRF, which is as close to inertial as practically applicable.
– SF.
Apr 27, 2017 at 14:58
• @uhoh -- Yes and no. There's a key underlying assumption in using quasars to define a non-rotating frame, which is that the universe as a whole is not rotating. This does not make sense from a Machian point of view. However, general relativity deviates from Mach's principle in a number of ways, and this is one of them. Whether the universe as a whole is rotating remains an open question. Apr 27, 2017 at 16:35
• @MichaelKjörling and others, I added a TL;DR at the start. Apr 27, 2017 at 16:53

David gave the only answer this question needs. A tl;dr would be this: There isn't an inertial reference frame. Orbital motion isn't bound by anything other than the forces that act on it, which includes every mass in the universe (and maybe some other stuff who really knows). Even if you did as you suggested, and used a reference frame that was centered using the masses of the universe (which would be ridiculous when you include relativistic effects), it wouldn't necessarily be "the inertial reference frame". Inertial isn't an absolute, it's relative.

• With regards to your opening statement, this should perhaps be a comment instead of an answer.
– wim
Apr 27, 2017 at 16:24
• @wim in this particular case, it's handy to have both answers as answers. I've already linked to this one because of it's tl;dr nature. Comments should be considered temporary, and this clarification or alternate wording is worth keeping as a permanent answer. (at)DavidHammon's answers are golden, but for some of us, an up front tl;dr is just the thing we need to see first.
– uhoh
Apr 27, 2017 at 16:38
• So perhaps an edit to the other answer, incorporating this? Apr 27, 2017 at 16:42
• @OrganicMarble plausible. There's a repeated sentence there, but the answer is so well structured in general that in this case I'd just leave it alone myself in this case.
– uhoh
Apr 27, 2017 at 16:49
• @uhoh -- Even though it happened almost 40 years ago, that supervisor's statement ("What do you mean by 'inertial frame'? Name one!") had a profound impact on me. That statement was worth repeating, so I did just that in my answer. Apr 27, 2017 at 17:31