I'm going to point out the obvious here. If you have an exception to the rule that in your mind reinforces a rule, then there really isn't a hard rule...
Obvious enough to know the exception demonstrates why the rule IS a rule and not just a "tendency." Thermodynamics, for example, works the way it does because energy tends to move from an area of high concentration to an area of low concentration. There are all kinds of interactions that can locally break these rules, but OVERALL, the rule still holds.
If the opposing starship is in an inertial orbit and unable to match the maneuver then it already is at a disadvantage. Riker wouldn't need to hide at all
That all depends on why he was hiding in the first place. To go back to our airplane example, Su-37s only perform a cobra maneuver in a close turning fight to try and throw off their opponents. The same maneuver from a distance of 25 miles results in you having a missile shoved up your ass, UNLESS you perform the maneuver close to a mountain or something where your sudden lack of movement causes you to blend in with the terrain around you and the other pilot looses his radar lock.
Really? Raptor hover? What's that?
A bad imitation of a Cobra maneuver performed with the intention of preventing Robert Gates from pulling the funding.
Yes, the same artistic license must have happened with poor Excelsior when she lost power and drifted to a stop when attempting to pursue the Enterprise in The Search for Spock.
"Drifted to a stop" relative to
what? If "relative to Earth" then Spacedock would have raced over the horizon at orbital velocities while Excelsior settled on a final position over a point on Earth's surface. If "relative to spacedock" then you have to come up with another as-yet unexplained mechanism for how the ship managed to instantly return to Space Dock's orbital velocity irrespective of conservation of momentum.
In point of fact, the only thing you can say is "relative to the camera," which is
indeed a matter of artistic license.
Well then the TOS-R version is obviously employing The Voyage Home effect then, since they can drop it and it stays in place.
Otherwise known as "bad science."
We could say that antigrav keeps it afloat, and momentum compensators (or thrusters, or whatever) worked.
Or we could say that Q farted on the satellites and changed the local laws of physics so they behaved the way they did. Anything is plausible if you're willing to pull solutions completely out of your ass.
A Geosynchronous orbit happens to be over the equator of the earth.
No, a geoSTATIONARY orbit is over the equator. A geosynchronous orbit only CROSSES the equator at a particular point every 24 hours.
A Synchronous orbit could easily mean stationary above a designated point
Yes, just as "starship" could easily mean "banana" but, we have no reason to pretend it does.
I think the bigger question is whether Star Trek as seen can be shoe-horned into real world physics.
Absolutely it can. "Synchronous orbit over [x] city" literally means the Enterprise repeatedly passes over that city at a regular predictable interval. Since stationary orbits ARE NOT POSSIBLE for targets that are not on the equator, we simply assume that a synchronous orbit is sufficient for most landing party operations and even (in the case of "Mirror Mirror") most planetary bombardment scenarios.
I don't think so since the series already allows artificial gravity, anti-gravity, transporters, warp drives, impulse engines, phasers, and a whole bunch of other technologies a free pass as they just work in Star Trek.
None of which are inconsistent with real-world physics. Real world TECHNOLOGY, yes, but nobody's suggesting the Enterprise is powered by hydrazine and and a panel.
Now, if you want to suggest that the existence of that technology renders Star Trek incompatible with the real-world laws of physics, that's fine too. I'd be more comfortable if you would just SAY that so I can know where you're coming from, because in my opinion every Trek device probably operates on real-world principles and inconsistencies are the result of their not-being adequately depicted (heavy use of stock footage, etc) or not adequately described (even real astronauts frequently confuse "fuel" and "propellant" in casual conversation).