3
$\begingroup$

Orbital paths of satellites around the Earth are usually shown as conic sections, as are paths of planets around the Sun. In truth, of course, the Earth's satellites are also orbiting the Sun, and the Sun (and its planets, and their satellites) are additionally orbiting the Milky Way. This video thumbnail captures the path that I'm talking about quite well:

earth seen moving in a 3d spiral around the sun

And for completeness, here is an example of the simplified view:

earth moving in a 2d circle around the sun

Is there a commonly accepted name for these different views?

The purpose is to use it as the label of a setting in a simulator that I'm building, so that the checkbox needn't have the above explanation as its label. One title I'm thinking of is 'true path', but there is probably a better term for it given how common such visualizations are.

$\endgroup$
2
  • 2
    $\begingroup$ I guess you're looking for the term "reference frame". In the first case it's the Milky Way, in the second the Sun. You can chose this frame arbitrarily: the Earth (like they did in the Middle Ages), the Moon, the Local Group, the CMB... $\endgroup$
    – asdfex
    May 28 at 16:10
  • $\begingroup$ @asdfex That sounds like an answer to me! Care to post it as one? $\endgroup$
    – Luc
    May 28 at 16:57
3
$\begingroup$

I would like to post a comment, but as I do not have enough "reputation" score to do so, here is my complement to @asdflex's comment.


As you probably know, motion is always defined relative to a reference (the point you define as fix in YOUR convention, plus the 3 orthogonal Cartesian axis in 3D space of YOUR CHOOSING). By definition then, your description of motion would be meaningless if you leave ambiguous your conventions.

Now, to address your question specifically:

It looks like your video is made with the type of reference called Celestial Reference Frame. There is an internationally agreed one called the ICRF. As an introduction to this concept you can look at this paper: The Next Generation Celestial Reference Frame by M. Johnson et al. Below is an extract of the intro:

It is only by using this inertial reference frame that we are able to disentangle our observations of the motions of celestial objects from our own complex path around our star, and its path through the galaxy, [...]

Your next drawing seems to designate the Sun as the center of the reference frame. Note that you still have to specify the 3 axis to have a fully-defined reference and here you have the choice between many possibilities (cf this link).

Note that people also use ECI (Earth-Centered Inertial) and ECEF (Earth-Centered-Earth-Fixed) references. Let's use these to illustrate the difference that the selection of the reference can make to the description of motions. When we say that a satellite is in geostationary orbit, implicitly we refer to the ECEF. The said satellite appears at rest compared to an observer on Earth, who feels that he is at rest also, because he is moving together with the rotating reference. Now, if we use instead the direction of a star to tie the X-axis with (this is the only difference between ECI and ECEF), then the motion of our geostationary satellite is a closed circle, not a fix point.

The bottom line is that, people choose a reference frame to describe a motion, in the way that is most convenient to them. There is nothing absolute, there is nothing we "neglect" in a given selection. As long as two reference systems are fully defined, a trajectory in one can be mathematically translated into the other. In other words, we don't loose the power of prediction of a motion when choosing a reference frame.

$\endgroup$
1
  • $\begingroup$ @Luc, There is another aspect of your question that I may have overlooked. What is the background of the users of your animation? Indeed, sometime using a scientifically adopted naming can add confusion. For ex., the name ECEF refers to rotating axis (the X and Y axis rotate at the same speed as Earth spins), "fixed" being understood as: as rotating reference frame so that this reference appear as FIX for an (any) observer on the surface. If your definition of "good name" is to avoid misinterpretations by people not too much math-inclined, then good answers may differ from above. $\endgroup$
    – Ng Ph
    May 29 at 7:55
2
$\begingroup$

You have to be careful because of the way gravity works. Everything attracts everything, there are no pure Keplerian orbits.

But if we ignore that and pretend say that the Sun is fixed, the Earth rotates around it, and the Moon rotates around the Sun, then if we draw the 2nd image we would call that perhaps a "top-down view of the inertial frame.

If we pin the Earth down so that they Sun-Earth line is fixed but the Moon keeps spinning around it, we can call that a "rotating frame" or a "synodic frame".

The first image could be from an inertial frame, but with the center of the Galaxy as the center.

So both can be inertial, but you have to explicitly say inertial with respect to what?

Here is a really beautiful video

One of my favorites, grab headphones too if you can. From What do the green lines represent in this Lagrange Point animation?

At about 00:35 you can see that the Moon's orbit around the Earth is a circle but appears like a flat spiral in this particular view at the same time

Don't let that fool you though, per this answer to Why is there no concavity in the orbit of the moon around the Sun? the Moon's motion is always concave with respect to the Sun. In this funky view with old fashioned vanishing-point perspective it's hard to get a clear understanding of the motion.

Also see this answer to Does the earth spiral around the sun's movement/motion path?

Lagrange points animation by 3D4U

Animation showing the Earth/Moon system and it's Lagrange points. It's not precise but it shows how these points revolve around Earth while staying fixed relative to The Moon and this was the overall goal here. Specifically, it clearly shows how the L2 point can never be seen from Earth even though it's constantly orbiting our planet - a source of confusion for many. From our perspective here on Earth the L2 point will always be behind The Moon and I hope this small animation illustrates that in a way that can be understood.

Georgia State University: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/lagpt.html

The "camera" always keeps the Earth in front of it, so it is rotating with the Earth. Thus it is in a "rotating frame" with respect to the Sun and and an "inertial frame" with respect to the Earth at the same time.

$\endgroup$
3
  • $\begingroup$ I am not sure that this answers the question, or perhaps I don't understand the answer. In the two examples given in the question, one taking into account the solar system's orbit around the galaxy and the other ignoring that for simplicity, would the latter be considered to have a 'rotating frame' and the former an 'inertial frame'? The motion doesn't seem like merely rotating the camera to me, perhaps that's where I am getting confused. $\endgroup$
    – Luc
    May 28 at 16:36
  • $\begingroup$ @Luc If RobertC5's answer works best for you then by definition it's the answer you should accept. But I left some comments there and you may get some pushback if you try to talk about "absolute" motion. All frames are relative to something and it's just what you choose it to be relative to. There is no absolute origin or x, y, z = (0, 0, 0) point in space; each case defines their own. In astrodynamics there are "inertial" and "rotating" frames. The quotes are because neither are perfect concepts. $\endgroup$
    – uhoh
    May 29 at 0:23
  • $\begingroup$ @Luc So questions about reference frames, while easy to ask, don't have simple one-liner answers that are also correct so being the kind of person that likes to try to write correct stuff, I can't give you a simple one-liner. You're welcome to ignore the video, but the purpose is to show how each of those motions is relative to something else, and that's really what people do when plotting trajectories. OK I can give you a one-liner that is also correct: Everything is relative. $\endgroup$
    – uhoh
    May 29 at 0:27
1
$\begingroup$

As your simulator has an absolute reference frame, I think you're looking for the words relative vs absolute path.
For a relative path you also need to indicate the reference point of course.

$\endgroup$
3
  • $\begingroup$ Thanks, I must say I'm having a bit of a hard time understanding the other answers even if they are interesting so I appreciate the direct answering of the question! Unless someone proves it inaccurate, I'll probably end up using this wording :) $\endgroup$
    – Luc
    May 28 at 23:02
  • $\begingroup$ As the author of one of the potentially hard to understand answers I agree! +1 nicely done! $\endgroup$
    – uhoh
    May 29 at 0:06
  • 3
    $\begingroup$ But I'll argue that there is absolutely no such thing as "absolute" in space, which was sort-of the whole point of Einstein's theories being about "relativity". $\endgroup$
    – uhoh
    May 29 at 0:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.