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As explained in various sources (such as that answer), a planet in an s-type orbit orbits one of the stars of a binary star system, whereas a planet in a p-type orbit orbits both stars. A synonym for a p-type orbit (at least in binary star systems, not sure about N-ary systems in general) is "circumbinary", which is a self-explanatory term.

However, what do "s-type" and "p-type" mean, respectively?

Are "S" and "P" acronyms of anything?

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    $\begingroup$ p= planetary type s= satellite type commons.wikimedia.org/wiki/… $\endgroup$ – M. Farooq Sep 5 at 22:14
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    $\begingroup$ That seems to answer the question. Please copy it to the answer box. $\endgroup$ – James K Sep 5 at 22:19
  • $\begingroup$ @JamesK: While it does, and I would eventually accept it if no more comprehensive answer turns up, some background information and references on this terminology are appreciated ... as I find it slightly confusing. So planets can be on planetary or non-planetary orbits, and satellites (which, I think, planets that orbit something are a type of) can be on satellite and non-satellite orbits? Curious. $\endgroup$ – O. R. Mapper Sep 5 at 23:06
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"Satellite type" and "Planet type".

The terms seem to have been coined by Rudolf Dvorak in 1982 paper "Planetenbahnen in Doppelsternsystemen"

Due to the fact that quasiperiodic orbits exist around stable orbits 3 different types of possible planetary orbits are found: S-types (satellite type orbit around one primary), P-types (orbits around both primaries), and L-types (librating orbits in the vicinity of L4 or L5).

It's not immediatly clear from this whether "P-type" means "planetary type" or "primary type" (and the full paper would be in German and doesn't seem have been digitised). However in an English paper from 1986 Critical orbits in the elliptic restricted three-body problem. Dvorak is explict:

There are three types of stable motion for a third massless body that are interesting as regards this problem: the P-type (planet type) surrounding both primary bodies, the S type (satellite type) orbiting one of the primaries and L-type (Librator type) librating around the Langrangian equilibrium points ...

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