The space station in "The Ultimate Computer", reamstered

[Christopher]

I quite agree that the Enterprise isn't orbiting the station. The very idea shows a complete ignorance of physics. The station hasn't nearly enough mass for anything to orbit it.

That's not actually true. Any two masses, no matter how small, are gravitationally attracted to each other. If there are no other, stronger gravity sources nearby to swamp that, then they certainly can orbit each other. Put two dust motes together in empty space and they'll go into orbit of each other, provided they aren't moving past each other at greater than escape velocity.

If K-7 and the Enterprise are the only two sizeable masses in the vicinity, and if they're at relative rest to start with, then their mutual gravity will draw them together, very slowly but inexorably. Eventually they'd collide with each other -- unless there were a bit of lateral motion so that they'd orbit each other instead.

Let's do the math. The usual figure given for the Enterprise's mass is 190,000 metric tons, though that's disputed. But let's go with it for convenience. K-7 has been alleged to mass 451,000 mt. Using those figures and the 2 km separation in your graphic above, this orbit calculator gives an orbital period of 31.4470 days, or 754.729 hours. With a circumference of 4*pi kilometers, I get a orbital velocity of 0.01665 kilometers per hour, or 0.0046 meters per second. So yeah, the ship would have to move very, very slowly to orbit the station, but an orbit is absolutely a physical possibility. And that month-long orbit is consistent with what we see in Lurry's office with the ship hanging motionless outside the window.

 

[CorporalCaptain]

I quite agree that the Enterprise isn't orbiting the station. The very idea shows a complete ignorance of physics. The station hasn't nearly enough mass for anything to orbit it.

That's not actually true. Any two masses, no matter how small, are gravitationally attracted to each other. If there are no other, stronger gravity sources nearby to swamp that, then they certainly can orbit each other. Put two dust motes together in empty space and they'll go into orbit of each other, provided they aren't moving past each other at greater than escape velocity.

If K-7 and the Enterprise are the only two sizeable masses in the vicinity, and if they're at relative rest to start with, then their mutual gravity will draw them together, very slowly but inexorably. Eventually they'd collide with each other -- unless there were a bit of lateral motion so that they'd orbit each other instead.

Let's do the math. The usual figure given for the Enterprise's mass is 190,000 metric tons, though that's disputed. But let's go with it for convenience. K-7 has been alleged to mass 451,000 mt. Using those figures and the 2 km separation in your graphic above, this orbit calculator gives an orbital period of 31.4470 days, or 754.729 hours. With a circumference of 4*pi kilometers, I get a orbital velocity of 0.01665 kilometers per hour, or 0.0046 meters per second. So yeah, the ship would have to move very, very slowly to orbit the station, but an orbit is absolutely a physical possibility. And that month-long orbit is consistent with what we see in Lurry's office with the ship hanging motionless outside the window.

Besides, these are both objects that generate artificial gravity, at least the Enterprise has a tractor beam, thrusters, and an impulse drive, and it wouldn't be unreasonable for the space station to have at least some of those too. "Orbiting" admits a lot of possibilities, from passive attraction to active attraction and even active circling on the part of the Enterprise. Perhaps the station itself conveniently generates a mild gravitational well artificially just for visitors so that their crafts can, well, conveniently orbit the station while they visit.

 

[Wingsley]

It is rather silly that starships, while visiting a space station on the frontier, would have to pursue some powered or otherwise artificially induced circular traffic pattern around a relatively "stationary" space station. This imaginary "orbit" doesn't serve any practical purpose. It would make far more sense for visiting starships to either dock with the station or rest relatively motionless in a simple parking position where it would be easier for ship-to-station transporter beams to lock on or for shuttles/travel pods to ferry personnel or cargo back and forth.

If we assume that K-7 is just a stationary port located strategically in deep space, then it would make sense for K-7 and any visiting spacecraft to "park" near each other unless a docking procedure is required. If we assume K-7 is itself orbiting a close-by planet, asteroid or star (which we never see), then it would make far more sense for the visiting space vessels to match K-7 with a parallel orbit, no?

The notion of the Enterprise circling K-7 always seemed cute to me. Even as a kid back in the '70s, I understood it seemed to be done strictly for appearance on TV, as if the visiting Enterprise were treating K-7 like any planet the ship would routinely visit. But let's say there's some valid technical or security reason that ships don't get too close to K-7 when they visit. Let's assume that K-7 is like a T.A.R.D.I.S. or a Romulan Warbird, with a singularity at its core for a power source, mandating that visiting ships keep their distance for some safety limit or "no wake zone" or somesuch. Unless this core is somehow creating a powerful gravitational force that requires visiting starships to apply a powered orbit at a prescribed distance or be sucked in, there's really no reason for the ships to circle K-7, is there? (And if there is such a powerful gravity force at work, wouldn't all the personnel and all the cargo aboard K-7 be crushed by it?)

The only reason I could fathom would be if K-7 were spinning on a central axis and the visiting starships were gently circling the station so their appearance in the station's "sky" would match that spin. I have zero idea why the station would unceasingly spin, as it seems clear the station does not require rotation to artificially induce gravity. (The station doesn't seem to be built like the donut-like station in 2001: A SPACE ODYSSEY, which seemed to rely on rotation.) Further, there is no canon evidence of K-7 rotating, either.

 

[CorporalCaptain]

Meh. The artificial gravity that's running all the time must consume enormous amounts of power. If they can run that constantly, they can do a lot of things. For all we know, it might even consume less power just to have ships orbit the station, because of all the magic artificial gravity fields in use, than not to.

If you want realism, you should really not allow artificial gravity, tractor beams, deflector shields, warp drive, transporters, et cetera. It's pretty silly to allow all that and then draw the line here at orbiting K-7.

 

[Albertese]

Meh. The artificial gravity that's running all the time must consume enormous amounts of power. If they can run that constantly, ...

Are we so sure of this? Seems like the AG is always the VERY last thing to go out, even when all other power is out. This suggests to me that generating and maintaining the gravity simulation is trivially easy to do with Trek technology. Whatever it is doing the work, must be cheap and reliable to be so commonplace and, well, universally present. And efficient/affordable to operate.

--Alex

 

[CorporalCaptain]

Meh. The artificial gravity that's running all the time must consume enormous amounts of power. If they can run that constantly, ...

Are we so sure of this? Seems like the AG is always the VERY last thing to go out, even when all other power is out. This suggests to me that generating and maintaining the gravity simulation is trivially easy to do with Trek technology. Whatever it is doing the work, must be cheap and reliable to be so commonplace and, well, universally present. And efficient/affordable to operate.

--Alex

In that case, the power that it would take to drive a low-level artificial gravitational field for a ship to leisurely orbit K-7 might also be equally minimal. We're talking less than a tractor beam for sure (well, most likely), because there would be nothing to hold the ship should it ramp up to escape velocity.

As to why it would be that way, I haven't a clue, of course. The only reason it's even on the table at all is because the notion that the ship is traveling in something like a circular path around the station seems reasonable, well to at least one of us, based on the (admittedly few) original VFX shots.

The station is also clearly shown as rotating. Perhaps the ship is orbiting in a field that is simply a by-product of the station's artificial gravity under the rotation of the station.

Further, there is no canon evidence of K-7 rotating, either.

I must disagree. The station is clearly shown as slowly rotating in the original VFX. Gerrold also mentions this in footnote 4 to the script in his book The Trouble with Tribbles (page 177, first paperback edition). He also scripted the Enterprise to be hanging motionless nearby the station, but clearly that was changed, as in the original VFX the ship is traveling forward in the direction it faces. The ship is traveling in the same direction that the station is rotating, which is another visual cue that the ship is orbiting the station. Perhaps someone intended the ship to be relatively motionless in Lurry's window, although the stars in the window seem awfully still too.

 

[Metryq]

As Alex already pointed out, the artificial gravity seems to be perpetual, even in cases like the Constellation. Having a movie budget to actually show freefall, as in THE UNDISCOVERED COUNTRY, makes all the difference.

But written sci-fi can drop the ball on this one, too—although whether that ball falls to the floor or flies off on a tangent will depend on the situation. I think it was Lester del Rey's STEP TO THE STARS where a crew building a space station decide on some unusual procedures to speed up construction in order to meet deadline. Rather than haul all materials in through the central airlock at the hub, they set the station rotating, allowing the crew to work under "gravity." Meanwhile, a small space truck hovers along side and passes materials in... This tactic is wrong for several reasons: spinning up the station before it is balanced would be disastrous (Kubrick did this in 2001, too, but at least the areas under construction were symmetrical), and the space truck would have to constantly expend fuel to hold relative position.

 

[CorporalCaptain]

Well, I'm pretty flexible when it comes to interpreting visuals. As has already been mentioned here and elsewhere, proportions and distances are often gotten wrong in Trek visuals in all of the series.

I can even separate the question of whether the original VFX were intended to show the ship orbiting the station from the question of whether the ship really was orbiting the station in-universe. I believe the answer to the former question is unreservedly 'yes.' The latter question I'm much more flexible on, if for no other reason than the fact that Trek visuals clearly often can't be taken literally. Consider the things I've said to explain the literal appearance as simply suggestions, because I'm prepared to take the visuals with a salt shaker.

 

[Christopher]

It is rather silly that starships, while visiting a space station on the frontier, would have to pursue some powered or otherwise artificially induced circular traffic pattern around a relatively "stationary" space station. This imaginary "orbit" doesn't serve any practical purpose. It would make far more sense for visiting starships to either dock with the station or rest relatively motionless in a simple parking position where it would be easier for ship-to-station transporter beams to lock on or for shuttles/travel pods to ferry personnel or cargo back and forth.

Yeah, but see my calculations above. If the ship actually were in orbit of the station, it'd be moving at mere millimeters per second. That's barely distinguishable from holding station, and it has the advantage of letting you maintain a constant separation from the station. If you were totally stationary... again, let's do the math. The force of gravity between the ship and station will be the universal gravitational constant G times the masses of the two objects divided by the square of the distance between them. If I've done the unit conversions right, that comes out to a mutual attractive force of 1.43 newtons. Force = mass x acceleration, so to get the acceleration acting on the ship, I divide that by 190,000 mt (190 million kg), getting 8 x 10^-9 meters per second. Since d = (1/2)at^2, at that acceleration and distance it would take 729,304 seconds or 8.44 days for the ship and the station to collide.

Sure, if you're only planning to be there for a few days, it'd be simple enough to keep station and use slight puffs on the maneuvering thrusters to cancel out the tiny gravitational attraction -- but why bother, when you can just go into orbit? Just apply enough thrust to move half a centimeter per second laterally to the station, and you can maintain your separation from it indefinitely without needing further thrust. It's a slight difference, but there's no reason not to do it. If two objects in space want to maintain a constant separation, going into orbit is the simplest, most natural way to do it, unless there's some specific reason to maintain a constant orientation relative to some outside reference point.

If we assume K-7 is itself orbiting a close-by planet, asteroid or star (which we never see), then it would make far more sense for the visiting space vessels to match K-7 with a parallel orbit, no?

Even two bodies sharing an orbit around a larger mass (like, say, the Earth and the Moon) are still going to have each other's gravity to contend with, so it really doesn't make much difference. Even if they are in parallel orbits of the primary, they're still going to be orbiting each other around a common center of mass.

Indeed, the whole point of orbit is that it's a free-fall trajectory. The inward pull of the primary is cancelled out by the orbital velocity. So the math that applies to the attraction of two objects sharing the same orbit is basically the same as the math that applies to two objects "standing still" in empty space.

But let's say there's some valid technical or security reason that ships don't get too close to K-7 when they visit. Let's assume that K-7 is like a T.A.R.D.I.S. or a Romulan Warbird, with a singularity at its core for a power source, mandating that visiting ships keep their distance for some safety limit or "no wake zone" or somesuch.

If anything, I'd say it's the other way around. A starship has powerful space-warping engines and an antimatter reactor. That makes it a major potential hazard. Keeping it at a distance from the station is probably about protecting the station's personnel. Remember, the reason Matt Jefferies put the engine nacelles way out on pylons was because he assumed they were emitting dangerous radiation or heat.

 

[Poltargyst]

I'm going to suggest that the Enterprise wouldn't want to be docked with the station once the Klingons show up.

 

[Wingsley]

All the more reason that starships would stay in a parking position, anywhere form 1 to 100 km away from the station.

 

[MGagen]

First, the month-odd long orbit, while just conceptually possible, is still preposterous.
The above mentioned occasional puffs from attitude jets, or anti-grav thrusters, or whatever the E uses to maneuver, would be far more reasonable.

Second, as my animation shows, motion is sometimes not what it appears to be. The exterior shots showing an (apparently) rotating station and an (apparently) orbiting Enterprise are only reconcilable with an (obviously) static ship and starfield outside Lurry's office window if we accept that the apparent movement was due to a traveling "camera."

All other explanations multiply absurdities. Occam's razor says bet on the simpler explanation.

 

[CorporalCaptain]

Second, as my animation shows, motion is sometimes not what it appears to be. The exterior shots showing an (apparently) rotating station and an (apparently) orbiting Enterprise are only reconcilable with an (obviously) static ship and starfield outside Lurry's office window if we accept that the apparent movement was due to a traveling "camera."

If it were the case that the camera itself were traveling in the exterior shots as the cause of the apparent motion, then in the exterior shots the star field would have to be rotating with the space station—which it isn't. The lack of rotation in the star field in the exterior shots is impossible to reconcile with the static star field in the interior shots. There is therefore evidently no single explanation that consistently accounts for all of the visual evidence. This episode, like all others, is an artistic expression created under constraints of time, available technique, and budget. The VFX were never perfect to begin with.

 

[CrazyMatt]

Let's keep in mind we're talking 1967 sfx on a limited budget scale as well. I don't really think they spend much time pondering these topics!

 

[CorporalCaptain]

Let's keep in mind we're talking 1967 sfx on a limited budget scale as well. I don't really think they spend much time pondering these topics!

Yes, I think we put all aspects of the show under such a microscope that the creators never would have imagined people doing!

 

[Christopher]

First, the month-odd long orbit, while just conceptually possible, is still preposterous.
The above mentioned occasional puffs from attitude jets, or anti-grav thrusters, or whatever the E uses to maneuver, would be far more reasonable.

I don't know why you think it's preposterous. It's a perfectly natural way for two objects in space to interact. There are plenty of asteroids that orbit other asteroids, some of them as low in mass as the Enterprise and K-7 are alleged to be.

And why is it less reasonable than using maneuvering thrusters? In that case, you'd have to keep firing thrusters over and over to cancel out the gravitational attraction between ship and station. In the orbital case, you'd only need to fire thrusters briefly to establish the orbit, and then you could stay in orbit indefinitely without needing further thrust. It's more efficient and wastes less fuel, so what in the world makes it unreasonable?

No matter what, the ship and the station are going to affect each other gravitationally. That's a fundamental fact of physics. So why not use that to your advantage, by going into orbit, rather than fighting against it by trying to maintain some arbitrarily static relationship with constant thrust?

Second, as my animation shows, motion is sometimes not what it appears to be. The exterior shots showing an (apparently) rotating station and an (apparently) orbiting Enterprise are only reconcilable with an (obviously) static ship and starfield outside Lurry's office window if we accept that the apparent movement was due to a traveling "camera."

I never take special-effects shots literally, since there are so many obvious impossibilities and absurdities in them. Ships being brightly lit in interstellar space; starscapes being clearly visible in the same exposure as those brightly lit ships; the Enterprise visibly turning as it orbits a planet even though its orbital path would appear as a perfectly straight line on that scale; ships being right next to each other when the dialogue explicitly puts them hundreds of thousands of kilometers apart, or crawling past each other when dialogue says they're moving at very high velocities; energy beams being visible in vacuum; explosions in vacuum consisting of roiling fireballs that are only possible in atmosphere; etc. I take special-effects shots as symbolic representations, dramatized for clarity and aesthetics.

Plus, of course, the whole episode was fictional anyway. I'm just talking about what would be physically reasonable in an equivalent real-life situation. You spoke of a ship orbiting a station as if it fundamentally made no sense in any context, when the fact is that it's actually the more reasonable, easier approach for keeping a spacecraft at a constant separation from another spaceborne object, even an object as small as a space station.

 

[Metryq]

There are plenty of asteroids that orbit other asteroids, some of them as low in mass as the Enterprise and K-7 are alleged to be.

http://www.johnstonsarchive.net/astro/asteroidmoons.html

 

[LMFAOschwarz]

I never take special-effects shots literally, since there are so many obvious impossibilities and absurdities in them. Ships being brightly lit in interstellar space; starscapes being clearly visible in the same exposure as those brightly lit ships...etc...

True. In reality, that's tricky to do. I've had enough experience photographing planetary conjunctions with the moon to know that to expose enough light to properly show the much-dimmer planet, you'll get an over-exposed moon in the picture. And of course, get a nice exposure on the moon, you get a way-too-dim planet. I imagine the same would hold true trying to photograph a bright starship and the stars behind.

I give Star Trek a pass on their nebula shots though...maybe a nebula seen from a much, much closer distance would show more color and structure than naked eye earth observing would. Who knows what that stuff looks like up close?

I've criticized the remastered episodes, but one set of shots (which you made me think of here) which I really enjoyed were the ones of the Enterprise inside the zone of darkness in The Immunity Syndrome. I can imagine that's what the ship might realistically look like in deep space.

 

[Warped9]

As I understand it real nebulae are not very colourful (if at all) to the naked eye. From what I understand all those pictures of beautifully coloured nebulae are actually composites of the same nebula taken at different wavelengths and with colours assigned to them to produce those gorgeous images. To the naked eye a nebula would look pretty much like a black dust cloud.

So TOS showing mostly black space was by chance more realistic than the later shows with vivdly colourful nebulae.

 

[Christopher]

As I understand it real nebulae are not very colourful (if at all) to the naked eye. From what I understand all those pictures of beautifully coloured nebulae are actually composites of the same nebula taken at different wavelengths and with colours assigned to them to produce those gorgeous images. To the naked eye a nebula would look pretty much like a black dust cloud.

Sometimes it's a false-color image like that, but sometimes it's just a really long exposure, brightening something that would be much dimmer to the naked eye.

Also, nebulae are very diffuse, nothing like the dense fogbanks portrayed in The Wrath of Khan and elsewhere. They're actually much thinner than Earth's atmosphere. From within, they'd be essentially invisible. Well, they might obscure the starscape somewhat, but they wouldn't affect your ability to see another ship inside the nebula with you. But if you were at an intermediate distance, and if your eyes were sufficiently night-adapted, you could see a certain amount of color.

Also, nebulae in Trek and other fiction are fairly tiny, when the real things are larger than star systems, sometimes light-years across. In my Trek novel The Buried Age, I postulated that these are actually "micronebulae," really dense, small pockets of interstellar gas in the process of collapsing into rogue planets, analogously to how larger nebulae collapse into star systems. It seems reasonable to me that such things could exist (since we know rogue planets exist) and are just too small and dim for us to have discovered them yet. If we ever do discover them, I hope somebody remembers that I thought of them first.