What are these orientations called in orbit?

Question

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."

Answer 1

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

NASA's Guide to the International Space Station Laboratory Racks Interactive however names direction towards nadir as deck and direction towards zenith overhead, and alternatively also the +/- axial values that follow the right-hand rule more commonly used by astronaut pilots during navigation or to describe station's attitude (such as during docking):

    

    ^{Image above: The International Space Station’s coordinate system. Credit: NASA}

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.

Answer 2

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.

Answer 3

In Kerbal Space Program, they are called Radial and Anti-Radial on the Nav-Ball.

Radial and anti-radial

These vectors are parallel to the orbital plane, and perpendicular to the prograde vector. The radial (or radial-in) vector points inside the orbit, towards the focus of the orbit, while the anti-radial (or radial-out) vector points outside the orbit, away from the body. Performing a radial burn will rotate the orbit around the craft like spinning a hula hoop with a stick. Radial burns are usually not an efficient way of adjusting one's path - it is generally more effective to use prograde and retrograde burns. The maximum change in angle is always less than 90°; beyond this point the orbit would pass through the center of mass of the orbited body and the ship would traverse a slow spiral in towards the orbited body.

- KSP Wiki - Maneuver Node Directions

Answer 4

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.

Answer 5

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.

Answer 6

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'.

Answer 7

There are specific body centered coordinate frames describing these directions. The two most commonly used are:

RIC (aka UVW, RTN): Radial, In-Track, Cross-Track

Radial: In the direction of the satellite position vector

In-Track: Radial x Cross-Track (where 'x' denotes the vector cross product)

Cross-Track: Position x Velocity (aka angular momentum vector)

TNW: Tangential, Normal, W (angular momentum)

Tangential: In the direction of the Velocity vector

Normal: Normal to the velocity vector & down - W x T

W: P x V