When should one use something like "conducting experiments in orbit" vs. "conducting experiments on orbit"?
The phrase "in orbit" is the common English phrase to refer to things and locations that are orbiting; this is the phrase that everyone should be familiar with.
The phrase "on orbit" appears to be a phrase with an identical (or nearly identical) meaning, but is used by those in the actual space industry.
Here is an informational packet (PDF) from the NASA website called "On-Orbit Mission Operations". Aside from the evidence in the title, this sentence also appears:
The operational events occurring on orbit are grouped into two categories: daily operations and periodic operations.
Here is another informational packet (also PDF) called "History of On-Orbit Satellite Fragmentations", with the following excerpt:
As of November 21, 2000, this object had been on orbit 5 years and 121 days.
Here are the results of a Google search on the nasa.gov website that show numerous uses of "on orbit", which all seem to correspond to having a meaning identical to "in orbit".
One other bit of insight comes from this excerpt from "Orbit: A Novel" (which may or may not be accurate, but acknowledges the industry-specific use and possibly their original logic for doing so):
"Everyone keeps saying 'on' orbit instead of 'in' orbit. Is that a space thing?"
"Yep. Mainly started at NASA, but there's good scientific reason to call it that. In brief, we have to get on speed and altitude to be there, so we're on orbit, like being on a perch."
So, the answer for when to use one and the other depends on what you want to say and who your audience is. If you want to give the common meaning of "in orbit", then say "in orbit", but if you are speaking with an audience familiar with the jargon of the space industry, and you want to sound knowledgeable, use "on orbit".
It is my understanding that, within the aerospace industry, "on orbit" means "in the correct orbit" (such as "on target" or "on path"). I think "in orbit" is more generic. A spacecraft can be "in orbit", but not in the correct orbit. If it is "on orbit" it is both "in orbit" and in it's intended orbit.
"In orbit" specifies the location where the experiments take place.
"On orbit" (which should be "on orbits" to be grammatical), specifies the subject of the experiments.
"The astronauts conducted a number of interesting experiments (while) in orbit."
"Kepler performed many experiments on (the) orbits (of heavenly bodies)."*
*In both examples, the parenthetical words are not necessary to be grammatical, but help to make the meaning clear, and the sentences sound more natural.
I've thought about this question some more and decided that it's very interesting, so I've upvoted it!
First, I'd like to say that I completely concur with Res's answer. "In orbit" is such a well-used and well-understood phrase in its own right that "experiments in orbit" can only really mean "experiments that take place while circling the earth". Which means that if you want to talk about experiments concerning bodies' orbits, you have to use another word: "about" or "on".
However! Elsewhere, "to experiment in something" does NOT mean to experiment in a location. "Experiments in social marketing" is the same as "social marketing experiments". "Experiments in chemistry" sounds a bit more stilted than "chemistry experiments", but I think most people would agree it means the same thing. So I fully understand why someone might try to say "experiments in orbit", to mean "experiments in the field of orbits". But because it sounds so much like "experiments taking place in outer space", I think native English speakers would steer clear of such a phrasing.
"To experiment on", conversely, conventionally means that you are experimenting in order to see the resulting effects in the object of the experiment. "Experiment on animals" is probably the most common usage of this, sadly. To "experiment on an orbit" might mean to do various things to an orbiting body to see how its orbit changes from one test to the next.
I hope this has clarified things a little bit, and not just confused them further!
An orbit is a two-dimensional line. An object that is orbiting cannot be inside a 2D line, since of course, all objects are 3D. It can, however be ON the line. On orbit.