I have often wondered what a "standard Orbit" is considered to be. The term is tossed around a lot but are there any consistent agreement as to what a standard orbit is ? And - Would it be SOP for a ship to maintain orbit in the general vicinity of a landing party / away team ? To me, this would make the most sense in order to respond quickly in the event of an emergency but the actual dialogue seems all over the place with this.
The Star Fleet Technical Manual established this in 1975. It may or may not have appeared as a background graphic in the early Trek movies.
Actually , in looking at this it would make sense that a specific set of distances might not be viable. Given differences in atmosphere, solar radiation output, gravitational fields etc a starships computer would set an optimal orbit for each planet that could be changed by manual control from the helm.
I assume one option the Enterprise would do is to be able to loiter above a spot over the planet to maintain communications and beaming contact. Fighting planetary gravity is easy-peasy for her impulse engines. Pick a planet surface spot of interest, then stay over it. Maybe this is standard orbit. This is supported by surface attacks by tractor beams, heat beams, finger pointing lightning bolts, etc.
Doing a little research, a geostationary orbit, often referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) above Earth's equator and following the direction of Earth's rotation. From Obsession, the maximum orbit is 30,000 km, which I assume is the maximum range of the transporter, so, a natural geostationary orbit is outside the range of the transporter. A conclusion is that the Enterprise is able to maintain lower geostationary orbits. In The Deadly Years, we get: SULU: Maintaining standard orbit, Captain. (Kirk enters.) KIRK: Increase orbit to twenty thousand perigee, Mister Sulu.Perigee is the closest orbital approach distance to the planet surface. This suggests: A. The orbit may be elliptical; and B. an orbit can be over 20,000 km. Elliptical orbits can extend the "dwell" time over one side of the planet. While in the dwell period, the orbit would be greater than the perigee distance and probably be outside the transporter range. I guess you can use the term "perigee" if the ship is hovering over one spot, too. We also see when the Enterprise turns off its impulse engines, she falls into the planet's atmosphere fairly quickly, usually within hours (The Naked Time, Court Martial), so, she must be station keeping in a very low orbit.
Should compute the drag coefficient of the 1701, but hours seems too quick unless you were a few hundreds KM in altitude.
Probably correct, a low orbit. The Naked Time, maybe not a good example because the planet was compacting mucking up gravity and magnetic fields. SPOCK: Captain. At our present rate of descent, we have less than twenty minutes before we enter planet atmosphere.Court Martial, the best example, which takes about 20 minutes or so once Kirk shuts down the impulse engines until his repairs: KIRK: Our impulse engines have been shut down. We'll maintain orbit by momentum. KRASNOVSKY: And when the orbit decays? KIRK: We hope to be finished long before that. (and later) KIRK [OC]: The damage he'd caused was considerable, but not irreparable. With luck, I would be able to effect repairs before our orbit decayed completely.
Using Earth as an example: R = 3,963 miles (6,378 kilometers) R' = 3,963 + (0.174*3963) = 4,652.562 H= Sensible Atmospheric Limit = 689.562 miles 689.562 miles seems like a sensible minimum. ________________________________________________________________________________ - Transition Zone of Space - - 117,408,136.48294' = 22,236.0 mi = 35,786.000 km = A circular geosynchronous orbit - 401,280.00000' = 76 mi = 122.310 km ~ 122 km = Space Shuttle uses Aircraft Control Surfaces instead of Steering Thrusters - 327,360.00000' = 62.1371 mi = (100)km = Kármán Line - 264,000.00000' = (50) mi = 80.467 km ~ 80 km = 1960's USAF Definition - ( 70,000.00000') = 13.257576 mi = 21.336 km ~ 21 km = is where the U2 operates, Pilots need Space Suits, Speed Margin between 1G Stall & Mach Buffett is 4 knots ________________________________________________________________________________
The ISS also experiences atmospheric drag and must occasionally be "re-boosted" to maintain its orbital height. Annually, about 8000 pounds of propellant are expended to do so. That being said, you are still talking many months (if not years) for it to de-orbit if there were no re-boosts. Certainly not hours or minutes. The space and astronomy centered site Heavens Above provides a nice Height of the ISS chart where one can see both the orbital decay and the re-boosts.
What value should I assume for the mass? I do not recall a canonical value. Use the scale for the 947' version?
Math is is a little tweeting bird chirping in a meadow and physics is a wreath of pretty flowers which smell bad. With that in mind, all I can offer is this line from, in “Mudd’s Women” where Scotty said, “Almost a million gross tons of vessel depending on a hunk of crystal the size of my fist.”
For comparison , here is the last year of decay of the Chinese Tiangong-1 space station which fell to the Pacific ocean in 2018, five years after it was last visited (didn't find any info on when it was last boosted.). And Skylab also took roughly five years to fall after its last boost, and it came down earlier than expected due to higher than normal solar activity.