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When it comes to orbital mechanics, are zenith and radial the same?

Or to put it another way, are nadir and anti-radial the same?

Coomie
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When it comes to orbital mechanics, are zenith and radial the same?

Or to put it another way, are nadir and anti-radial the same?

Sometimes yes and sometimes no!

Mostly this excellent answer to the question In “spacecraft talk” is nadir just a fancy word for “down”? explains the considerations necessary when talking about "up" and "down" for an oblate spheroid like the Earth. In this answer to the question How small a location is possible to identify when any visible star is at its zenith directly above? I link to the Wikipedia article Zenith and show the following diagram:

enter image description here

Source: Gravimetric Datum Orientation

So when reading texts that include terms like zenith, nadir, and radial, I would say you need to refer to previous paragraphs or chapters within that work to see if they have defined their usage and/or definitions for zenith and nadir. Radial however should mostly be unambiguous.

Radial: Direction pointing outward from the central body's center of mass, through the spacecraft's center of mass.

Zenith: Options:

  1. See Radial
  2. Direction of local gravitational potential gradient. Since Earth is oblate, this would tend to be angled slightly towards the nearest pole from the radial direction.
  3. Normal to the local reference surface/ellipsoid, sea-level, or even the local sub-satellite terrain. These is not so likely to be used for orbital mechanical purposes, but it might be used if you need to view the local terrain below you at normal incidence, or if you are standing on the ground and wondering "which way is up, exactly?"
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uhoh
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  • "through the spacecraft's center of mass." While a radial burn will have to be directed through the center of mass, I'm not sure that it is relevant when only referring to the direction... – Antzi Oct 31 '18 at 05:36
  • @Antzi It takes two points to draw a line. Without more details in the question, CM is the only point that all spacecraft have, and this is the only point which is going to be attitude-independent. – uhoh Oct 31 '18 at 06:01
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    I think the "Not sure" is the important keyword here. It seems to be confusing for NASA engineers too, since they had to write this note While OP did specify the orbital mechanics concept, maybe there is some clues to take from the words etymology – Antzi Oct 31 '18 at 06:22
  • My understanding was that radial was related to the direction the spacecraft is travelling in; while zenith is related to the center of mass of a different body; but don't quote me on this ! – Antzi Oct 31 '18 at 06:30
  • @Antzi As far as I know, for any conic Keplerian orbit $\mathbf{\hat{r}}$ and $\mathbf{\hat{\theta}}$ are the radial direction and it's perpendicular, and the direction of motion $\mathbf{\hat{v}}$ is the tangential direction. I don't know what its perpendicular would be called. I saw a recent Q&A about some confusion, which may have been related to $\mathbf{\hat{\theta}}$ and $\mathbf{\hat{v}}$ being the same for precisely circular orbits, but I can't find it right now. – uhoh Oct 31 '18 at 06:55
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    @uhoh - Cross track, orbital angular momentum direction, or binormal. – David Hammen Oct 31 '18 at 12:57
  • @DavidHammen I meant the other perpendicular to velocity, the one that's roughly in the $\mathbf{\hat{r}}$ direction. – uhoh Oct 31 '18 at 13:01
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    That would be the outward normal, designated $\boldsymbol N$ (or sometimes $\boldsymbol n$) in the Frenet frame. – David Hammen Oct 31 '18 at 13:02
  • @DavidHammen just fyi, a link to your other answer about Frenet frames. – uhoh Oct 31 '18 at 13:16