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Let's say a spacecraft is in an orbit like this one:

If the red arrows point to prograde and retrograde, and the blue arrows point to normal and antinormal, what do the green arrows point to?

In other words, what does one call the orientations that are perpendicular to both the orbit prograde and the orbit normal?

Note that it's not necessarily correct to say "towards the planet" or "away from the planet." In highly eccentric orbits like the one pictured above, both orientations can point "away."

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5 Answers

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I'm not sure there's any generally agreed on convention, but spaceships are often regarded as, well, ships, so similar terms will be often used. E.g. for the red arrows that you describe as prograde and retrograde orientation vectors, from a spaceship's point of view and relative to its movement, also ram-facing and wake-facing is often used to describe sides, but could be also forward and aft, or even bow and stern. For the blue orientation vectors, these could then be port for left and starboard for right, relative to the vehicle's movement, facing forward. The green ones are most commonly called the nadir and zenith facing sides, but as the terminology varies depending on who's referring to it, I'd guess there's all kinds of other terms used too, from obvious down, downward, and up, upward, to deck and overhead, or even towards and away from something, in our case the body it orbits around. So for orientation relative to the ship's movement we have:

  • ram-facing, forward, bow,...
  • wake-facing, aft, stern,...
  • starboard, right,...
  • port, left,...
  • nadir, deck, down, downward, towards sth,...
  • zenith, overhead, up, upward, away from sth,...

For example, from Reference guide to the International Space Station, Assembly complete edition, NASA 2010 (PDF), four of these sides are described in the definitions section as:

  • nadir: Direction directly below (opposite zenith)
  • port: Direction to the left side (opposite starboard)
  • starboard: Direction to the right side (opposite port)
  • zenith: Directly above, opposite nadir

And the remaining two sides mentioned in text as:

ram (forward) or wake (aft) pointing

Alternatively, movement relative to these three axes could be described using aviation terms roll, pitch and yaw to describe attitude of a satellite, but these don't really denote the sides, merely rotation of the body with respect to the x, y, z (in your case red, blue, green) axes in Cartesian coordinate system, respectively.

There might be other terms I didn't think of though, but as always, it will depend on who's using them and if they're referring to the sides from the perspective of the vessel and relative to its movement, or relative to some wider frame of reference, for example with respect to the body it orbits, in which case, alas, I fail to think of other ways these orientation sides could be named, short of describing them with respect to orbital elements in any of the various coordinate systems used, such as Keplerian, Cartesian,... like you did with prograde and retrograde, which are essentially broadly describing orbital inclination with respect to the body's plane of reference.

With specific spacecraft, often its sides are also named by its components or modules, which works irrespective of spacecraft's own movement relative to another object.

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I'd be surprised if ship terms like port and starboard were used much on spaceships. Because a spaceship does not have a constant attitude relative to its motion vector, "port" can refer to the forward direction one moment, and the nadir direction the next. –  Hobbes Feb 10 at 17:17
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Port and starboard are used extensively on the International Space Station, but then, the ISS generally holds a fixed attitude relative to its velocity vector. –  Tristan Feb 11 at 16:23
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There are 3 directions in any orbit. The typical convention is:

  • Nadir- This is the direction towards the center of the planet, straight down. Oposite to NADIR is the Zenith.
  • Velocity Vector- Direction of movement, Prograde/retrograde are a common, Prograde is the direction of orbit, retrograde opposite
  • Normal direction to plane of orbit. This is often referred to as the angular momentum vector.

See also this PDF.

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The zenith and nadir always go straight in and out of the planet's center, right? So they're not necessarily perpendicular to the velocity vector? –  Maxpm Feb 7 at 14:42
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I'm pretty sure that the velocity vector is perpendicular to the planet's center in any case, at least for relatively uniform gravity objects, like all planets and most large moons. –  PearsonArtPhoto Feb 7 at 14:45
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I don't think so. In the question diagram above, the green arrows miss the planet's center. If the planet were smaller, they would miss it entirely. The velocity vector (represented by the red arrows) is only tangential to the planet's surface if the orbit is perfectly circular or the spacecraft is at its periapsis or apoapsis. –  Maxpm Feb 7 at 14:56
    
For most orbital mechanics calculations, the green arrows will be aligned with the R-bar direction, i.e., pointing directly at the planet's center. This does lead to a convention where the three axes are not mutually orthogonal, but the vector pointing to the planet center is more meaningful than an inward- or outward-pointing vector normal to the velocity vector. –  Tristan Feb 11 at 16:26
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@Nickolai, the radius and velocity vectors will only be orthogonal in a circular orbit. –  Tristan Feb 11 at 21:33
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The mathematical names for those directions are tangent (the red arrows), normal (the green arrows, and binormal (the blue arrows). Geometers have made extensive use of these, so much so that these directions are a key part of the Fundamental Theorem of Curves. For example, see http://en.wikipedia.org/wiki/Frenet-Serret_formulas, http://mathworld.wolfram.com/FundamentalTheoremofSpaceCurves.html, and http://math.rice.edu/~hardt/401F03/ftc.pdf.

This theorem isn't of much use in orbital mechanics because torsion involves a third derivative of position with respect to time. Orbital mechanics is a study of second derivatives: F=ma.

The directions along the red arrows (v-bar) are useful in orbital mechanics because these are the directions along which you want to thrust to minimize gravity losses. The blue arrows are useful because angular velocity points in this direction. The green arrows? They're useful for geometers and for describing vehicles flying through an atmosphere. They're not so useful in orbital mechanics, which is perhaps why there isn't a standard orbital mechanics name for this direction.

Addendum

When looking at the uncertainties in where a spacecraft is, those directions are oftentimes called along track (the red arrows), cross track (the blue arrows), and radial (the green arrows). One can look at "radial" as being either a bit of a misnomer or as being spot on correct. It's a misnomer in the sense that "radial" only points "radially" (toward / away from the planet in the case of a circular orbit. It's spot on in the sense that "radial" always points toward / away from the instantaneous center of curvature.

A related set of directions is the local vertical / local horizontal system, or LVLH for short. In this system, +Z points to the center of the Earth, +Y points opposite the orbital angular velocity, and +X completes the right hand coordinate system (i.e., $\hat x = \hat y \times \hat z$). This means that $\hat x$ points along the velocity vector in the case of a circular orbit. This labeling a bit arbitrary. The Clohessy-Wilshire equations use +X as pointing away from the Earth, +Z as pointing along the angular momentum vector, and +Y completing the right hand coordinate system. Either the LVLH frame or CW frame used to describe the orbital mechanics of a spacecraft rendezvousing with the ISS.

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Yes, these 3 unit vectors were missing from answers, but how do you use them to name the 6 orientations or sides of an object in orbit? The same problem is with using radius vectors. How would one say, for example, "please meet me at the [?] of the spacecraft"? Surely, saying "... [negative normal facing side] ..." sounds awkward? –  TildalWave Feb 28 at 1:16
    
For now, "I'll meet you in Zvezda" (or the Cupola, or Kibo, etc.) works just fine on the space station. The names of the modules don't change with orientation. There's no need to say "I'll meet you at X" in the Soyuz because there's no room in the Soyuz to get displaced. –  David Hammen Feb 28 at 8:01
    
My query was about using these three vector names to name the six orientations along them. I'm familiar with the names of the ISS modules, thanks. –  TildalWave Feb 28 at 8:07
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Green arrows are the "radius" vectors, the inner one points to the center of the planet. Red arrows are velocity vectors. One of them will point in the direction of motion of the satellite, the other one, of course, in the opposite direction. Blue arrows point in the direction of angular momentum, a quantity often labelled as "h".

The radius vector is often called the R-bar and the velocity vector the V-bar. You see this often in discussing about vehicles docking with the International Space Station. When they say a vehicle is making an R-bar approach, it is essentially "climbing up" the green arrow from below (so the ship is between the Earth and the station). V-bar approaches, if I'm not mistaken, typically take place from behind.

Source: AAE 532 at Purdue University, graduate level course in orbital mechanics.

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The green arrows do not necessarily point to the center of the planet. See my comments on PearsonArtPhoto's answer. –  Maxpm Feb 10 at 18:22
    
I'm assuming that the coordinate system is orthogonal and in the orbital plane, therefore if the red vector is pointing in the direction of velocity, the green vector must point to the center of the planet. If it's not orthogonal or not in the orbital plane, then it's just a random set of vectors that don't do anyone any good. Unless it's part of some weird scavenger hunt. –  Nickolai Feb 11 at 19:14
    
Eccentric orbits are ellipses with the planet's center at one of the foci. At any given point on an ellipse, the line perpendicular to the tangent does not necessarily pass through either foci. Your statement would be true for a perfectly circular orbit, but not the one pictured. –  Maxpm Feb 12 at 4:07
    
You're right, radius and velocity vectors are not perpendicular for an elliptical orbit, they're separated by the flight path angle gamma, which is computed using the "local horizon" which is an imaginary line that is perpendicular to the radius vector. Wow, I'm rustier than I thought! –  Nickolai Feb 14 at 16:28
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During the Apollo moon landings, the astronauts referred to 'forward' and 'down' for the red and green vectors.
In the Gemini 12 voice comms transcript (page 29 of a 500-page PDF), a maneuver is referred to as 'Posigrade up south' (in @Maxpm's diagram these directions refer to red, green, blue in that order).
The spacecraft attitude is described as 'yaw 1 right, pitch 4 up', and they refer to the 'thrusters aft'.

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