There are some serious problems with the OP's own answer, and so I think conjunction won't do for a satellite in Earth orbit, at least in LEO (where many/most of them are). While Archimedes could move the Earth with the proper fulcrum and a large lever, I'm not sure this can apply to the aforementioned "shoe-horn" as well.
There are two problems actually:
- In the context of artificial satellites, the term "conjunction" is frequently used for a three dimensional event; a very close approach of the variety that might result in collision. Satellite conjunction detection and conjunction reports have to do with scenarios where two spacecraft may collide resulting in "end of mission" and a whole lot of brand new space junk.
To read more about this, see what the letter "C" stands for in Celestrak's SOCRATES; Satellite Orbital Conjunction Reports Assessing Threatening Encounters in Space as well as the questions
- Parallax! for satellites that are not in absurdly large distances from Earth, their apparent solar conjunction wanders all over the place depending on the location of the observer. Even in 2D, for satellites in LEO (the ISS for example) there's a ~140° difference between apparent solar conjunction as seen from one side of the Earth compared to as seen from the other. With a significantly inclined orbit, formulating the way that a definition can be worded based on apparent solar conjunction becomes even more difficult, as does even trying to draw it correctly in 3D.
Here's a sketch of the 2D problem for a 400 km altitude circular orbit lying in the plane of the ecliptic, showing that the effects of parallax are huge!
