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Assume the approximation that the Earth is spherically symmetric — without higher order gravitational multipoles, and other effects that might be related to gravity from other bodies or the Earth's orbit around the Sun are ignored. Given a circular orbit, "down" would be a vector pointed towards the center of the Earth, and I think the "nadir" would be in exactly the same direction.

But in a realistic circular orbit, do "down" and "nadir" have any more nuanced meaning by convention or usage?

For example, there is a vector that is perpendicular to instantaneous velocity and orbital angular momentum, another that is the local gravity gradient, and yet another that points towards the Earth's center of mass.

All of these could be thought of as roughly "down" or in the direction of the "nadir", but are any of these (or something else) used preferentially or by convention?

note: This question is asking a lot more than just What are these orientations called in orbit?

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    $\begingroup$ Possible duplicate of What are these orientations called in orbit? $\endgroup$ – GdD Jan 9 '17 at 8:26
  • $\begingroup$ @GdD and other close-voters. Please take a moment to re-read my question fully and carefully and note the care I have taken ask this question. Although there is discussion of the word "nadir" and DavidHammen's answer addresses the other question well, this is in fact a related but different question, and there is not an answer to this question there. If you have specific questions or need further clarification, please take the time to ask. Thanks! $\endgroup$ – uhoh Jan 9 '17 at 10:36
  • $\begingroup$ @DavidHammen do you have any thoughts here? $\endgroup$ – uhoh Jan 9 '17 at 10:40
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    $\begingroup$ @uhoh I suggest you mention that related question in your question text and state why the current question is an extension/not a duplicate. $\endgroup$ – Jan Doggen Jan 9 '17 at 12:02
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    $\begingroup$ There are some subtleties here, which are what I think @uhoh is after. If that's the case, this is not a duplicate. $\endgroup$ – David Hammen Jan 9 '17 at 12:27
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There are some subtleties here. The fields where the concept of nadir are most important are nadir-pointing Earth observation satellites, satellites formation flying, and rendezvous and proximity operations. The latter two almost inevitably use some form of a local vertical / local horizontal frame (aka a Hill frame), in which vertical (i.e., nadir and zenith) points to / away from the center of the Earth. This is primarily because of the use of the linearized Clohessy-Wiltshire equations in these fields.

The first almost inevitably uses nadir as pointing toward the subsatellite point, which is usually taken to mean the geodetic subsatellite point rather than the geocentric subsatellite point. The geocentric subsatellite point is where the line connecting the center of the Earth with the satellite intersects the surface of the Earth. The geodetic subsatellite point is that point on the surface of the reference ellipsoid that is closest to the satellite. This is equivalent to the point on the ellipsoid where the satellite is at zenith ("straight up"). Using nadir as pointing to the center of the Earth will miss this geodetic subsatellite point by up to 21 km for a satellite in a sun synchronous orbit.

An even more subtle meaning is that nadir points in the direction of the point on the geoid that is closest to the satellite. This concept is important in satellite altimetry measurements of sea surface height. If this point is within the beam width of the radar altimeter, it is this point that will register as the satellite's altitude. Some other point will give an erroneous reading if this point is outside the altimeter's beam width. The distance between this point and the geodetic subsatellite point can be nearly a kilometer.

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  • $\begingroup$ Spectacular - another @davidHammen Teachable Moment. Every time i start writing $\ddot{\mathbf{r}} = -\mathbf{r} \ \mu/r^3$ I just reflexively reach for a handy solver (for me it's scipy because of my allergies to braces) in cartesian coordinates. There's a lot to be learned from studying more advance mathematical techniques, and I can imagine computation-intensive cases where they might come in handy. I have a 4 hour train ride in the morning, now I know what I will be reading about. $\endgroup$ – uhoh Jan 9 '17 at 16:38
  • $\begingroup$ I really appreciate these answers that build a complete framework of understand and related concepts - this answer and especially this answer for recent examples. Much appreciated! $\endgroup$ – uhoh Jan 9 '17 at 16:41
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In the ISS Operations community, "zenith" and "nadir" are commonly used to refer to the Z axis directions relative to the ISS, instead of specifically Earth-pointing directions. (Although they got these names because the ISS does normally fly in an attitude that points the so-called nadir direction at the earth).

Here's an example from a crew procedure where one of the Node docking ports is referred to as the Nadir port - "ISS coordinates assume MPLM on Node Nadir". Pitching the station 180 degrees wouldn't cause this name to change, of course.

enter image description here

Here's an image from a "ISS Location Coding" lesson showing the same concept.

enter image description here

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    $\begingroup$ Thanks for digging deeper on this. There's that "D" word again (deck). $\endgroup$ – uhoh Jan 9 '17 at 17:01

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