TOS Enterprise Question...
- Thread starter MadMan1701A
- Start date
At that level, where there are no physical differences whatsoever? Yes, I do. Even identical twins are generally distinguishable on some level, and they are genetically identical (and usually share common nurture as well as common nature).
Furthermore, the odds drop to the infinitesimal once you start saying "two identical people on one ship, within just a couple of years' time" and then another identical person on a ship with the same name, a number of decades later.
To claim that such a thing is plausible is just... wrong. No, we have to accept that what we're looking at would never happen in a "real-universe" version of Star Trek. The people might be "somewhat similar" but not identical.
You can also argue that it's odd that Zephram Cochran changes appearance utterly, and ends up looking like a number of alien characters who showed up on the 1701-D at various times. Or how Spock's dad was such a dead ringer for a Romulan naval commander, or so on and so forth.
We either abandon all pretense of "willful suspension of disbelief" and never watch it again without viewing it ONLY as an exercise in TV-show production (without regard to the story being told), or we excuse the "wrong" bits in some fashion in our minds' eyes and "rewrite" the objectionable bits... but only rewrite as much as is necessary in order to have it make sense to us.
Some of us... those who, like me, tend to get very deep into the technical side of things... tend to overwrite the technical bits a bit more extensively than others do. And I think MOST Of us in this forum are like me in that regard.
I wholeheartedly agree.. "the universe" (the TREK in-story universe) does not require Diana Muldaur to play each part, or Mark Lenard to play each part. The "real" people would likely bear less overall resemblence than the "recreated, acted" versions do.
See, that's how I watch the show. ALL of the shows. I view them as "historical recreations" for entertainment purposes. "Holodeck programs" so to speak.. based upon what information is available, but occasionally abandoning "real universe" bits in the name of "storytelling." And some storytellers... like whoever was tasked with telling the story of the alien race who used Spock's brain to drive their planet-wide computer network... got retold in, shall we say, less successful ways than other stories got retold.
Well, this is either "bad storytelling" (something similar, but not identical, "really" happened?) or it's "incomplete storytelling" (meaning that there should be some science-fiction explanation for how somehow, a space-time event occurred which caused multiple near-identical copies of Earth to be created, which our crew occasionally come across?).Something more challenging would be in TOS what the odds of two or more planets developing exactly like Earth, with one even having the same Declaration of IndependenceIf anything, the odds are "out of whack" in TOS
But in the end, I prefer the first option. I can accept that whole episode, if the EXACT WORDING of the US historical documents is removed, and if the people are no longer southern-Californians, and if the "parable" nature of the story is a bit less bluntly in-our-face.
These stories aren't always bad. "A Private Little War," for example ,was a much better parable, and that's in large part because it was less blatantly preachy.
Its only when we say that there is no "personal interpretation" possible, or when there is "official reinterpretation" which CONTRADICTS elements seen on-screen, that we have problems.
SO... back on topic...
We don't know what the panels really are "in universe," and if you want them to be sensor system windows, more power to you... unless you get onto a production team and try to "formally redefine" this to say that EVERYONE must accept your personal interpretation. Then, and only then, will people have the right to argue with your position.
And that brings me back to my very earliest point - all we REALLY know is that they are made in the exact same manner, and have the exact same appearance, as the "windows" on the 11-foot model, and thus I am convinced that they are intended to represent windows on the real ship. And because they face upwards, and because human psychology would be best served by having a few open spaces with "sky" overhead, I am convinced that they are for that purpose. But nobody else has to agree with me. Even if I know I"m right and you're all wrong!
On the way of interpreting visual shots, I have some points.
Let's take some of the stock footage of the TOS Enterprise orbiting a planet. You all are aware, aren't you, were such a scene photographed in real life, that the ship would not appear to travel in a curved path, right? What I mean by this is that the ship often looks like it's a model a few feet long that's circling a beach ball a few feet in diameter that's sitting only a few feet away from it. I regard this as a trope intended to help the viewer realize that the ship is circling the planet.
But in real life, the planets would be many, many thousands of times larger than the ship and hundreds or thousands of miles away. As the ship is cruising through its orbit, over the period of several seconds it would appear to be going in a straight line, and not in a curved path.
This is one example when what we see in the visual FX is all wrong.
TNG was guilty of another sin many times. Ships are said to be hundreds or thousands of kilometers apart; then we switch to exterior visuals and they couldn't be separated by more than a few hundred meters.
Come on, you all know what I'm talking about right?
The visuals, as a general rule, can only be sketchy at best in Star Trek. In most cases, attempting to interpret the visuals literally and concoct in-universe explanations based on precisely what is seen is looking at it all wrong IMO. The intent was never to dissect things that accurately, but rather only in general terms. For example: the two ships are in proximity and facing each other, close enough to do damage if they start shooting, nothing more specific. Or, the ship is orbiting the planet, nothing more specific.
Of course, some particular cases do seem more realistically composed than others. But the fact that some of these exist doesn't mean that every FX shot was constructed with the same attention to scale and realism.
Let's take some of the stock footage of the TOS Enterprise orbiting a planet. You all are aware, aren't you, were such a scene photographed in real life, that the ship would not appear to travel in a curved path, right? What I mean by this is that the ship often looks like it's a model a few feet long that's circling a beach ball a few feet in diameter that's sitting only a few feet away from it. I regard this as a trope intended to help the viewer realize that the ship is circling the planet.
But in real life, the planets would be many, many thousands of times larger than the ship and hundreds or thousands of miles away. As the ship is cruising through its orbit, over the period of several seconds it would appear to be going in a straight line, and not in a curved path.
This is one example when what we see in the visual FX is all wrong.
TNG was guilty of another sin many times. Ships are said to be hundreds or thousands of kilometers apart; then we switch to exterior visuals and they couldn't be separated by more than a few hundred meters.
Come on, you all know what I'm talking about right?
The visuals, as a general rule, can only be sketchy at best in Star Trek. In most cases, attempting to interpret the visuals literally and concoct in-universe explanations based on precisely what is seen is looking at it all wrong IMO. The intent was never to dissect things that accurately, but rather only in general terms. For example: the two ships are in proximity and facing each other, close enough to do damage if they start shooting, nothing more specific. Or, the ship is orbiting the planet, nothing more specific.
Of course, some particular cases do seem more realistically composed than others. But the fact that some of these exist doesn't mean that every FX shot was constructed with the same attention to scale and realism.
Then can you show that the characters have no physical differences whatsoever? Are we shown both naked and from all angles?
We both can't, so how can you even "scientifically" make a counter-claim without evidence to show the two characters are both identical in-universe?
Actually, I don't for Zephram. The differences between the TOS Zephram and the TNG-Movie/Enterprise Zephram are enough to waive into alternate universe/timeline territory and as *early* as "The Alternative Factor" Star Trek introduces the existence of alternate universes. You don't have to buy into it, but that "in-universe" explanation works pretty well, IMHO. Spock's dad and the Romulan commander can look facially a "dead ringer". The idea that everyone must look "unique" doesn't even hold true in the "Real World" when there is a whole industry of celebrity "look-alikes".
It's not that black and white. Not everyone will have the same level of "rewrite" to have it make sense. Heck, some folks might not even care and no re-writing is necessary.
Well, this is either "bad storytelling" (something similar, but not identical, "really" happened?) or it's "incomplete storytelling" (meaning that there should be some science-fiction explanation for how somehow, a space-time event occurred which caused multiple near-identical copies of Earth to be created, which our crew occasionally come across?).Something more challenging would be in TOS what the odds of two or more planets developing exactly like Earth, with one even having the same Declaration of Independence
But in the end, I prefer the first option. I can accept that whole episode, if the EXACT WORDING of the US historical documents is removed, and if the people are no longer southern-Californians, and if the "parable" nature of the story is a bit less bluntly in-our-face.
These stories aren't always bad. "A Private Little War," for example ,was a much better parable, and that's in large part because it was less blatantly preachy.
Its only when we say that there is no "personal interpretation" possible, or when there is "official reinterpretation" which CONTRADICTS elements seen on-screen, that we have problems.
Or when different people have different interpretations. You, me, Carboncopy, etc all are approaching the same things we all watch and filtering it with our own set of experiences and beliefs. The main thing to me is laying the facts out so we all know how it's being filtered and not just saying, "Warp can only go forward or backward" or "It's impossible that so many people should look alike" (even though it's only 2 in TOS and an older version in TNG) when we only can study their faces.
Actually, I think all items should be on the table since we don't know either way. I've stated I think it's a sensor thing as my own opinion. My specific objection was CarbonCopy's statement of how he thought the TOS Enterprise warp/impulse worked that would limit the sensor direction.
Recently, I gave in and started watching Voyager on Netflix... it was the only series I never fully watched (having seen just a few episodes on rare occasions, and never really liking any of the characters except Tuvok and, on occasion, the Dr.)
One thing that hits me, every single episode, is the title sequence, as the Voyager flies over a planetary ring, and you can see the reflection of the ship in the ring.
This means that this entire planet, including its rings, is just tiny. Seriously... you would be able to HIKE the entire circumference of that ring in just a day or two!
I can't even watch that sequence without wincing...
How about this, which TOS shot are you talking about and we can try and re-create it (with the power of computers!
)There's a wonderful catalog of every TOS FX shot seen available here:
http://www.trekplace.com/tosfxcatalog.html
That way, we can see what the ship appears to be doing at that moment before just saying it should look like any one of these orbits (or if it's just powering in place because it can.)
@DrBashir - check out some of the catalogued FX shots - there might be a few where we can see the top of the saucer clearly.
How about this, which TOS shot are you talking about and we can try and re-create it (with the power of computers!
There's a wonderful catalog of every TOS FX shot seen available here:
http://www.trekplace.com/tosfxcatalog.html
That way, we can see what the ship appears to be doing at that moment before just saying it should look like any one of these orbits (or if it's just powering in place because it can.)
Very nice catalogs; thanks for spoon-feeding me both of these pages.
What I said applies to any of these, which includes the iconic planet orbit shots:
- WNM Orbit Towards (Where No Man Has Gone Before - The Enemy Within) [4]
- Orbit Away (Mudd's Women - Turnabout Intruder) [98]
- Orbit Towards (Mudd's Women - Turnabout Intruder) [113]
The Tressaurian Intersection Exeter fan film has some wonderfully modernized orbit shots that have much better perspective; yet they still seem to be perfectly in the style of TOS. I really suggest checking it out. I have confidence the last part of TTI will be done eventually.
On the other hand, this would be an accurate portrayal of the ship flying a figure-eight orbit above the spot of interest on the planet down below.
And the ship would probably be quite interested in doing that very thing, as its phasers and transporters both seem to suffer from limitations in operating beyond the planet's horizon. Transporters struggle to penetrate even a couple of kilometers of rock; phasers are even worse.
A powered orbit in figure eight shape would also nicely explain why ships that lose engine power are often in danger of falling down to the planet below.
(Then again, in "Mirror, Mirror" the evil starship is interested in intimidating a local center of political power on the planet down below - yet is established to be on an orbit that takes her away from the optimal firing position from time to time! This would certainly be a good time to do a powered orbit above the region of interest.)
A more interesting thing about those "orbiting" scenes IMHO is that most ships maintain an attitude of portside-to-planet, in fact carefully avoiding the pointing of "dorsal" or "ventral" or "bow" sensors towards the most interesting target in the vicinity. ST3:TSfS offers some rare shots of the ships flying with their bellies towards the planet, while DS9 and ENT did a lot of shots where the ship's dorsal side points to the planet (which in turn is located on the upper part of the screen, so the ship is still "the right side up" but the setup carries an impression of defying gravity).
If the topside of the saucer of the TOS Enterprise is part of a sensor system with four orifices, it should worry us a bit that the topside is never pointed at anything interesting when the camera dwells on the ship. Never. Of course, it may be that the sensor is actually omnidirectional (or downward-oriented), and the four glowy things aren't orifices for incoming information but merely exhausts for glowing emissions associated with the functioning of the instrument. Still, the fact that only three of them glow properly is somewhat counterindicative of a single four-element instrument...
Who knows? Some of the windows on the ship are established to be shuttered normally ("Mark of Gideon"); if all the shutters were opened, perhaps the ship would be a veritable Christmas ornament of nearly unbroken lit surfaces, some of which would be windows while others would be sensor orifices for instruments more refined than our eyes.
It's just a bit curious that all the portholes we do see open and glowing are always the same ones. If there are others, seamlessly closed (much like the torpedo tube muzzles, supposedly!), why are they always closed?
Timo Saloniemi
While I think the idea of a figure eight orbit, or other powered orbit, maintaining an overhead relation to a landing party makes sense, I'm unaware that this is what was intended. We hear about "standard orbits", which really implies something elliptical. But we don't really hear any details about how the ship maneuvers in orbit, beyond the hand-wavy (and far-fetched) need to maintain power lest the ship spiral down to the planet in a matter of minutes.
Timo your idea makes sense, but based on the evidence it would be a flat out retcon, I believe. Any descent into the atmosphere can be avoided by a powered ascent to a circular orbit which should remain stable for days, weeks, months, or longer, depending on the altitude. If the orbit is decaying rapidly due to atmospheric drag, then the ship would be heating up and the hull ablating. That never happened. If it's decaying rapidly due to a lot of moons in the area, then I really doubt that system would be stable enough to last very long, and at least one of the moons should be disintegrating into a ring system, and the ship shouldn't be in low orbit anyway. And so forth.
The determining factors have always favored something that on the surface sounds plausible enough (to stay in genre), but which doesn't have any scientific depth (sparing the viewers from science lectures), and otherwise whose attributes serve the drama (because milking things for dramatic effect is what keeps viewers tuning in).
Timo your idea makes sense, but based on the evidence it would be a flat out retcon, I believe. Any descent into the atmosphere can be avoided by a powered ascent to a circular orbit which should remain stable for days, weeks, months, or longer, depending on the altitude. If the orbit is decaying rapidly due to atmospheric drag, then the ship would be heating up and the hull ablating. That never happened. If it's decaying rapidly due to a lot of moons in the area, then I really doubt that system would be stable enough to last very long, and at least one of the moons should be disintegrating into a ring system, and the ship shouldn't be in low orbit anyway. And so forth.
The determining factors have always favored something that on the surface sounds plausible enough (to stay in genre), but which doesn't have any scientific depth (sparing the viewers from science lectures), and otherwise whose attributes serve the drama (because milking things for dramatic effect is what keeps viewers tuning in).
Well, here is the first look at Where No Man Orbit Towards.
TOS Enterprise is moving relative to the camera at 357 ft/s. Altitude approx 6,600 miles.
Time of visual shot is ~4 seconds.
So, the questions are:
What kind of orbit could it be? The TOS Enterprise is not going fast enough to be in a natural orbit. Timo's idea of a deliberate powered orbit makes sense. A "standard orbit" might just put the ship over a specific hemisphere of the planet. Loss of power would mean the ship falls out of orbit because she's not going fast enough naturally to have any stable orbit. This jibes with "Return of the Archons", "The Apple" and even "Court Martial" given loss of power equals a very fast drop out of the sky.
It might be a very strange elliptical orbit but we don't have enough visual time to give a good orbital track.
As Timo points out, rarely (if never) is the top of the saucer facing the planet. If they were sensors, it doesn't look like they were meant for planetary survey. If they were skylights, the folks looking through are never treated to a view of the planet they are visiting
TOS Enterprise is moving relative to the camera at 357 ft/s. Altitude approx 6,600 miles.
Time of visual shot is ~4 seconds.
So, the questions are:
What kind of orbit could it be? The TOS Enterprise is not going fast enough to be in a natural orbit. Timo's idea of a deliberate powered orbit makes sense. A "standard orbit" might just put the ship over a specific hemisphere of the planet. Loss of power would mean the ship falls out of orbit because she's not going fast enough naturally to have any stable orbit. This jibes with "Return of the Archons", "The Apple" and even "Court Martial" given loss of power equals a very fast drop out of the sky.
It might be a very strange elliptical orbit but we don't have enough visual time to give a good orbital track.
As Timo points out, rarely (if never) is the top of the saucer facing the planet. If they were sensors, it doesn't look like they were meant for planetary survey. If they were skylights, the folks looking through are never treated to a view of the planet they are visiting
- How can you make this determination?
- What is the frame of reference of the camera (can't it be in orbit too, albiet a slightly different one)?
- Are you taking into account the apparent rotation of the planet and the length of its day?
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Answer to #2: There does not appear to be a shift in camera position relative to the planet or the background stars. (You can compare the two screenshots at Trekplace as they are approx 4s apart.) If the camera is moving it is not in a detectable means as my virtual version works with the camera stationary. Do you have any suggestion to how it might move so I can try it out?
Even though these were eyeballed by FX guys, they make sense in context to what we know of the majority of Enterprise's orbits. Lose power, fall from the sky.
Even though these were eyeballed by FX guys, they make sense in context to what we know of the majority of Enterprise's orbits. Lose power, fall from the sky.
Well, if it's an extreme range sensor array then you'd never point it at anything less than many AU's distant. And I imagine it'd be more like a large radio telescope array (like the Very Large Array) and therefore would be used to observe objects on the scale of light-years distant. The ship has plenty of other sensors which would be quite adequate to the task of observing the planet. So, whether it's ever pointed at a planet in the show is immaterial as that's not what it's for. And if it ever was pointed at something of interest, it would much too far away to see with the unaided eye and would thusly not be included in any shot of the ship in operation.
As to why three are lit and one isn't.... Really? The obvious intention is that we are meant to imagine the forth one is lit too. If we simply must insist that what was shown on screen is the unalterable gospel truth then I suppose we might speculate that you only need three to operate at any time or maybe the forth one has a certain specialty sensor which doesn't need be kept on standby like the others, or's it's shuttered beneath a white painted door because it's more delicate than the others, or any other sensible idea. And I'm pretty sure the TOS E in "Trials and Tribble-ations" and the TOS Defiant in "In a Mirror, Darkly" did have all four squares illuminated.
I just woke up so maybe I'm not thinking straight, but can you explain to me how point number three is relevant at all? How would the the speed of a planet's rotation effect it's gravity well? I don't see how that's relevant to an orbit? Maybe you mean to somehow extrapolate the planet's size from that? I'm not sure we have enough information from the show to do that in any case. The landing party didn't seem effected by unusually heavy or weaker gravity so I suppose it's more-or-less 1G and therefore essentially Earth-sized. Maybe I'm missing the point, help me out here...
--Alex
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FWIW, "Miri" shows our heroes doing the "standard" approach to the planet that proves to be a Second Earth. That is, their ship is seen from behind as she approaches the planet, just like in the opening credits, and then the ship curves to the right, seemingly to orbit the planet counterclockwise, or counterrotationwise, or whatever you want to call it when you go towards the sunrise. Kirk then calls for "fixed orbit". And the very next thing we see on the viewscreen is the continents floating past, from left to right, as the ship travels from east to west!
Certainly suggests that starships don't respect freefall orbits much.
And even a badly hurt starship whose crew is unconscious can manage this easily enough, as in "Tomorrow is Yesterday". Yet a starship that suffers a loss of power due to human sabotage or alien influence cannot. Which is probably because the malevolents specifically hurt the ship in a manner that makes the use of propulsion of any sort impossible. In which case any powered orbit quickly becomes fatal enough.
The hull tolerates atmospheric flight easily enough, it seems. And speeds would be fairly low if the ship merely fell straight down towards the planet when her hovering power failed - the first hour could well be spent just drifting down through vacuum, from the apparent height of several thousand kilometers.
True enough. It wouldn't do anything plot-relevant, then, but might conduct scientific research despite the ship being engaged in the plot of the week.
It sounds a bit unlikely for this seemingly "lean and mean" ship to carry such gear, but by no means impossible. Perhaps this is the technology that was used for taking the star photographs in "Corbomite Maneuver"? Although plotwise, we have never heard of a sensor that would be pointed by pointing the ship; when the planet below or the ship ahead is scanned, this takes place at fairly odd orientations (typically planet to lower port, ship of interest to upper starboard bows), and the viewscreen shows angles unrelated to the orientation of the hero ship, too.
Timo Saloniemi
Certainly suggests that starships don't respect freefall orbits much.
And even a badly hurt starship whose crew is unconscious can manage this easily enough, as in "Tomorrow is Yesterday". Yet a starship that suffers a loss of power due to human sabotage or alien influence cannot. Which is probably because the malevolents specifically hurt the ship in a manner that makes the use of propulsion of any sort impossible. In which case any powered orbit quickly becomes fatal enough.
The hull tolerates atmospheric flight easily enough, it seems. And speeds would be fairly low if the ship merely fell straight down towards the planet when her hovering power failed - the first hour could well be spent just drifting down through vacuum, from the apparent height of several thousand kilometers.
True enough. It wouldn't do anything plot-relevant, then, but might conduct scientific research despite the ship being engaged in the plot of the week.
It sounds a bit unlikely for this seemingly "lean and mean" ship to carry such gear, but by no means impossible. Perhaps this is the technology that was used for taking the star photographs in "Corbomite Maneuver"? Although plotwise, we have never heard of a sensor that would be pointed by pointing the ship; when the planet below or the ship ahead is scanned, this takes place at fairly odd orientations (typically planet to lower port, ship of interest to upper starboard bows), and the viewscreen shows angles unrelated to the orientation of the hero ship, too.
Timo Saloniemi
Using the parameters suggested by blssdwlf, I have plotted a theoretically real orbit for the camera, according to Newtonian mechanics. This solution is offered "as is", but I'll explain my work, so that it can be checked. Note that other alternatives are possible; I am describing only one proposal.
The displayed units are SI, so distance is measured in meters. The planet's surface is red, the camera's orbit is green, and the Enterprise's orbit is blue. The center of the planet is market by a cross, and the point of closest approach between the camera and the Enterprise is marked by a circle on the left. Both the Enterprise and the camera orbit counterclockwise in the diagram. This diagram is to scale.
The planet is assumed to be a sphere that can function as a point mass. The radius of the planet is 6371000 meters and its mass is 5.9736*10^24 kilograms, both Earth values. The value of Netwon's gravitational constant G that I am using it is 6.67384*10^(-11) in SI units. The mass of the Enterprise is assumed to be zero (which is a reasonable assumption for otherwise if its mass were not vanishingly small relatively speaking, the Enterprise would disrupt every solar system it visited).
The Enterprise orbits at an altitude of 6600 miles in a circular orbit, as suggested by blssdwlf. There, it will orbit the planet in 6.122994278617534 hours. It travels at a constant speed of 4843.676699517414 meters per second in the Newtonian inertial frame.
The orbit of the camera that I am plotting is in the same plane as the orbit of the Enterprise. For simplicity, I have chosen the point of closest approach to be the apogee of the camera. At this point of closest approach, the camera, the Enterprise, and the center of the planet lie in the same line, and the camera is 417 feet further from the center of the planet than the Enterprise (which is one ship width, or about that depending on your source; this is done just so that the ship and camera do not collide). To completely determine the rest of the camera's orbit, we need only know its speed at the instant when it reaches apogee. For this value I choose 357 feet per second slower than the Enterprise, in accordance with what blssdwlf has suggested. Using the vis viva equation and slugging things out using the properties of the ellipse and elliptical orbits, we determine that the eccentricity of the camera's orbit is 0.04441833885412092, its perigee has an altitude of 5701.960117206670 miles, and its period is 5.736632021918684 hours. So, although the camera is moving slower than the Enterprise during the hypothetical stock footage in question, it will fall in towards the planet soon and outrun the Enterprise on the next lap around the planet. The camera will even survive that lap easily, in that it will come nowhere near burning up in the atmosphere.
Now for the part which may come as some surprise to some. Over the course of about 4 seconds, the trajectory of both the camera and the Enterprise may be very accurately approximated by constant speed straight line motion. I will leave it as an exercise for the reader to run calculations that will convince him- or herself that this is so in the case of the Enterprise; these calculations are straightforward since the Enterprise orbits the planet in a circular orbit at constant speed. Convincing oneself that this is so in the case of the camera is somewhat more involved which I will now partially describe, hopefully adequately enough to convince the reader.
The speed of the camera is controlled by Kepler's second law: it must sweep out equal areas of the ellipse in equal amounts of time. Although a closed form solution for the motion of the camera does exist, and is within the ability of a very advanced student of first semester integral calculus to grasp, presenting that solution and mathematically proving the point will not really be helpful in this forum. Therefore, I will simply present the following observation: if the motion of the camera is approximately at a constant speed and in a straight line over the four seconds of the shot, then the area swept out by the triangle accumulated along that line of motion between the center of the planet will be equal to the fraction of the area of the whole ellipse that is four seconds divided by the period of the orbit. This is so to 16 digits of accuracy, if one takes the line of motion and speed to be the values the camera has at apogee.
Furthermore, over this four second interval, if the camera is pointed in a fixed direction and not rotating according to the Newtonian inertial frame, then the celestial sphere (on which the stars lie) will appear to turn at most .06532751490506261 degrees, which is hardly at all. However, by tweaking the camera zoom setting, I suppose some apparent stellar motion could perhaps be seen. I say these things only to indicate how rapidly the stars might appear to move; naturally, the camera is free to pivot and point in any direction during the shot, in order to frame the ship in a cinematic manner.
So, therefore and in other words, straight line motion, against a nearly fixed stellar background, is what the camera will appear to see, over the four seconds of the shot.
ETA: The lower bound for how much the celestial sphere will appear to turn in four seconds is .06385944919511107 degrees. The actual amount is in between this value, and the upper bound value given above, but it is almost exactly equal to this lower bound given here.
The lower bound is the value assuming that the camera orbits (hypothetically and non-gravitationally) at its tangent velocity at its apogee. The upper bound is taken according to the orbital velocity of the Enterprise itself, which at all times during the four seconds of the shot is moving faster than the camera. As you can see, these values are very close to each other; the lower bound is .0224723948566697 percent less than the upper bound.
The displayed units are SI, so distance is measured in meters. The planet's surface is red, the camera's orbit is green, and the Enterprise's orbit is blue. The center of the planet is market by a cross, and the point of closest approach between the camera and the Enterprise is marked by a circle on the left. Both the Enterprise and the camera orbit counterclockwise in the diagram. This diagram is to scale.
The planet is assumed to be a sphere that can function as a point mass. The radius of the planet is 6371000 meters and its mass is 5.9736*10^24 kilograms, both Earth values. The value of Netwon's gravitational constant G that I am using it is 6.67384*10^(-11) in SI units. The mass of the Enterprise is assumed to be zero (which is a reasonable assumption for otherwise if its mass were not vanishingly small relatively speaking, the Enterprise would disrupt every solar system it visited).
The Enterprise orbits at an altitude of 6600 miles in a circular orbit, as suggested by blssdwlf. There, it will orbit the planet in 6.122994278617534 hours. It travels at a constant speed of 4843.676699517414 meters per second in the Newtonian inertial frame.
The orbit of the camera that I am plotting is in the same plane as the orbit of the Enterprise. For simplicity, I have chosen the point of closest approach to be the apogee of the camera. At this point of closest approach, the camera, the Enterprise, and the center of the planet lie in the same line, and the camera is 417 feet further from the center of the planet than the Enterprise (which is one ship width, or about that depending on your source; this is done just so that the ship and camera do not collide). To completely determine the rest of the camera's orbit, we need only know its speed at the instant when it reaches apogee. For this value I choose 357 feet per second slower than the Enterprise, in accordance with what blssdwlf has suggested. Using the vis viva equation and slugging things out using the properties of the ellipse and elliptical orbits, we determine that the eccentricity of the camera's orbit is 0.04441833885412092, its perigee has an altitude of 5701.960117206670 miles, and its period is 5.736632021918684 hours. So, although the camera is moving slower than the Enterprise during the hypothetical stock footage in question, it will fall in towards the planet soon and outrun the Enterprise on the next lap around the planet. The camera will even survive that lap easily, in that it will come nowhere near burning up in the atmosphere.
Now for the part which may come as some surprise to some. Over the course of about 4 seconds, the trajectory of both the camera and the Enterprise may be very accurately approximated by constant speed straight line motion. I will leave it as an exercise for the reader to run calculations that will convince him- or herself that this is so in the case of the Enterprise; these calculations are straightforward since the Enterprise orbits the planet in a circular orbit at constant speed. Convincing oneself that this is so in the case of the camera is somewhat more involved which I will now partially describe, hopefully adequately enough to convince the reader.
The speed of the camera is controlled by Kepler's second law: it must sweep out equal areas of the ellipse in equal amounts of time. Although a closed form solution for the motion of the camera does exist, and is within the ability of a very advanced student of first semester integral calculus to grasp, presenting that solution and mathematically proving the point will not really be helpful in this forum. Therefore, I will simply present the following observation: if the motion of the camera is approximately at a constant speed and in a straight line over the four seconds of the shot, then the area swept out by the triangle accumulated along that line of motion between the center of the planet will be equal to the fraction of the area of the whole ellipse that is four seconds divided by the period of the orbit. This is so to 16 digits of accuracy, if one takes the line of motion and speed to be the values the camera has at apogee.
Furthermore, over this four second interval, if the camera is pointed in a fixed direction and not rotating according to the Newtonian inertial frame, then the celestial sphere (on which the stars lie) will appear to turn at most .06532751490506261 degrees, which is hardly at all. However, by tweaking the camera zoom setting, I suppose some apparent stellar motion could perhaps be seen. I say these things only to indicate how rapidly the stars might appear to move; naturally, the camera is free to pivot and point in any direction during the shot, in order to frame the ship in a cinematic manner.
So, therefore and in other words, straight line motion, against a nearly fixed stellar background, is what the camera will appear to see, over the four seconds of the shot.
ETA: The lower bound for how much the celestial sphere will appear to turn in four seconds is .06385944919511107 degrees. The actual amount is in between this value, and the upper bound value given above, but it is almost exactly equal to this lower bound given here.
The lower bound is the value assuming that the camera orbits (hypothetically and non-gravitationally) at its tangent velocity at its apogee. The upper bound is taken according to the orbital velocity of the Enterprise itself, which at all times during the four seconds of the shot is moving faster than the camera. As you can see, these values are very close to each other; the lower bound is .0224723948566697 percent less than the upper bound.
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Determining the apparent rate of rotation of the planet is only for gauging how long it is taking the ship to make one lap around the planet; knowing the length of the planet's day let's you know when to say you've made one whole lap, relative to the surface of the planet. The rate of rotation of the planet doesn't determine the gravity well. Does that help?
@CarbonCopy - that's a fascinating analysis. I'll put a little movement in the camera and confirm but I don't see any reason why it doesn't sound correct. Interestingly, the Enterprise in that orbiting configuration would not be orbiting "nose first" in its travel direction but pointing about 45 degrees away from the planet most of the time
If I may, I'll add one further set of comments.
In a free fall orbit, which I've modeled, no power is necessary to maintain altitude. Now eventually, in reality, due to perturbations from various sources, the orbit could decay; the planet is not really a point mass, there are other gravitating bodies in the system, etc.
Even though this is so, for even extended periods, measured in hours, days, or more, the ship is free to reorient in any direction.
At such an altitude as this, it would only need to correct its orbit every now and then. For these corrections, the ship should fix its orientation in preparation to fire the impulse drive, and then fire the impulse engines and make the correction, after which it may freely reorient arbitrarily.
In a free fall orbit, which I've modeled, no power is necessary to maintain altitude. Now eventually, in reality, due to perturbations from various sources, the orbit could decay; the planet is not really a point mass, there are other gravitating bodies in the system, etc.
Even though this is so, for even extended periods, measured in hours, days, or more, the ship is free to reorient in any direction.
At such an altitude as this, it would only need to correct its orbit every now and then. For these corrections, the ship should fix its orientation in preparation to fire the impulse drive, and then fire the impulse engines and make the correction, after which it may freely reorient arbitrarily.
