Both BLSSDWLF and Timo make great point for this episode. I look forward to your "math"; maybe NASA can step up to the plate and do this analysis as a training exercise on their super computer (hint, hint). Or you may need to use a Spirograph kit. My take on the orbit mechanics (no math): The asteroid was knocked out of its orbit toward the sun. It started making repeated passes by the planet. This happened three times since the harvest (I missed that line), it must be in a close and highly elliptical orbit for its entire orbit. If moving fast, and it must be to pass by the planet three times in a short period of time (less than one year or ~6 months), its closest approach to the sun must be very close, and its farthest point must be just past the planet. Also, I imagine that the asteroid orbit was changed each time it came near the planet. Maybe the previous close passes were in-bound, out-bound, in-bound, and the next would be out-bound directly into the planet? Or, the close approaches were all from one direction and most likely in the out-bound direction. Initially if the E wants to have the best chance to deflect the dense asteroid (it looked a little metallic and lumpy in the original special effect shot and almost the size of our moon), I would think E would try to intercept it at its farther away point from the sun were its speed is slowest and gravitational attraction force would be weakest. And maybe, they already missed the chance to do that; the rock is already past the planet in-bound to the sun for its final pass and then out again directly into the planet. Maybe then, E would want to get at it very close to the sun. I can see the E warping from one side of the sun where the planet happened to be, and zoom past the sun to get directly to the other side where the asteroid may have been at its closest point at the time. (Moving slow at warp speed!) The real reason that Spock would want to intercept the asteroid close to the sun because the internal stresses on the asteroid would be highest and gives E the best chance to fracture the rock into two pieces. Remember when comet Hale-Bopp broke up in Jupiter's gravity! My "eureka" moment. That was Spock's plan A. Spock did the math and concluded that the chance to affect its orbit with the ship's deflector beam was nil (or meteoroid beam in "The Cage", I wish they would have used that term...); this was only Spock's plan B. He calculated that fracturing the rock was his best chance, but it depended on too many unknown factors about the internal composition and stresses inside the irregular asteroid. Spock knew he could melt down the M/AM reactors in the ship's warp engines for this Plan A. He was committed to go all the way; which would break first: the rock or the ship? I love techno-drama.
Sequence of events and how they are observed from the planet and the Enterprise once it arrives: A moon-sized asteroid travels in-bound from an outer asteroid belt and has a near miss to the planet. First "sky darkens" event. Asteroid's orbit deflected by the planet to send it in a sun-grazing new orbit. It slings around the sun and shoots out-bound back at the planet. It encounters another near miss with planet. Second "sky darkens" event ~4 months from the first event. Deflected again by the planet, it turns back in-bound and boomerangs back at the planet and very near misses again. The third "sky darkens" event ~1 to 2 months after the second event. ELDER: Our skies have darkened three times since the harvest. The last time worst of all. ~2 months later, the Enterprise arrives. The asteroid is approaching its closest point to the sun. The E travels at warp 9 to get in front of the asteroid when it is at its closest approach to the sun. Fails and limps back to the planet for ~2 months on impulse (fighting the sun's gravity well) with just enough time to make orbit, grab Kirk and break orbit before the big collision. I assume Spock called Starfleet to send a tug to drag them back to Starbase for repairs immediately after Scott's repair report: SCOTT [OC]: Don't ask for anymore warp nine speeds, Mister Spock. Our star drive is completely burned out. The only thing we have left is impulse power. SPOCK: Estimated repair time? SCOTT: Hanging here in space? Forever. SCOTT [OC]: The only thing that'll fix these poor darlings is the nearest repair base. SPOCK: I've already surmised that. Thank you, Mister Scott. MCCOY: Well, Spock, you took your calculated risk in your calculated Vulcan way, and you lost. You lost for us, you lost for that planet, and you lost for Jim. SPOCK: I accept the responsibility, Doctor. MCCOY: And my responsibility is the health of this crew. You've been driving yourself too hard, and I want you to get some rest. SPOCK: Mister Chekov, resume heading eight eight three mark four one. MCCOY: Back to that planet? Without warp speed, it'll take months, Spock. SPOCK: Exactly fifty nine point two two three days, Doctor, and that asteroid will be four hours behind us all the way. MCCOY: Well then what's the use? We might not be able to save the captain even if he still is alive. We might not be able to save anything, including this ship! You haven't heard a word I've said. All you've been doing is staring at that blasted obelisk. SPOCK: Another calculated Vulcan risk, Doctor. The asteroid shoots back to the sun, slings around the sun and shoots back out-bound for the final time with a bullseye on the planet. As it gets near impact, the "sky darkens" for the final time. Enterprise crew beams down. The planet asteroid deflector system is fixed by Spock and successfully deflects the asteroid into a safe orbit. The sun comes up tomorrow. A space tug arrives on Tuesday to haul the E to the nearest repair base.
Just to clarify, I suggest that "she was captured in the asteroid's gravity well and had to reserve fuel for escaping from the planet after they try one last time to rescue Kirk." This is consistent with the situations where the Enterprise has lost her star drive and was stuck with only impulse power. From "Where No Man Has Gone Before" after burning out their star drive they have just enough fuel to enter orbit but not enough to leave. SPOCK: Recommendation one. There's a planet a few light days away from here. Delta Vega. It has a lithium cracking station. We may be able to adapt some of its power packs to our engines. KIRK: And if we can't? We'll be trapped in orbit there. We haven't enough power to blast back out. From "Mudd's Women" after burning out their star drive (crystals) they have just enough fuel to enter orbit but not enough to leave. Captain's log-- Stardate 1330.1. Position, fourteen hours out of Rigel 12. We're on auxiliary impulse engines. Fuel low, barely sufficient to achieve orbit over the planet. Lithium replacements are now imperative. Now apply this to "The Paradise Syndrome"... if the Enterprise races away from the moon-sized asteroid (which they could) and achieve orbit of the planet they won't have enough fuel to leave the planet. But if they cruise with the asteroid they could they could then transfer from the asteroid to the planet's sphere of influence with minimum fuel usage so they can still get out of the planet's orbit. IMHO. SULU: Tracking report, sir. Sixty five minutes to end of safety margin. ... KIRK: Scotty, if the deflector isn't activated within twenty minutes, get out of orbit. Get the Enterprise out of the danger zone. The landing party is expendable. The Enterprise isn't. Kirk out. I disagree because the dialogue from Kirk clearly has him concerned about getting stuck in orbit (or falling out of orbit and crashing.) There definitely was a purpose to leaving orbit (or even just maintaining it) in those two instances. I believe that the nature of the Enterprise's impulse engines (versus say a shuttlecraft) is that they are meant to be used by itself in strict emergencies. But in emergencies the fuel is super limited, allowing just enough to blast off and coast to a single distant destination but not multiple visits to different far off locations. If they have a working m/am system then the impulse engines could operate significantly longer with a near infinite fuel source. The other three times I can remember emergency impulse-only fuel being an issue are "The Doomsday Machine", "The Immunity Syndrome" and "Elaan of Troyius". Actually from the dialogue it sounded like the Enterprise didn't leave the vicinity of the asteroid at all because darkened skies, gravitational effects, etc were impacting the planet when they beamed down. Not more than a few minutes after finding Kirk that we hear that they only had 65 minutes of safety margin presumably calculating for when the asteroid will strike and how much of a head start they needed on full impulse to escape the danger zone. To me it sounded like they stayed true to Spock's statement of staying only 4 hours ahead of the asteroid.
I see no reason the Phoenix has to be limited to one warp jump. I think they jumped again back to Earth orbit and used the unused upper stage engine to land intact upright like SpaceX is doing these days.
Were I Cochrane, I certainly wouldn't tempt Fate a second time. There'd be no point to this, not when space travel as such seemed effortless. And Cochrane's design was multistage to begin with, perhaps suggesting the limitations of the state of the art (as available to him, that is). Certainly the crew capsule seemed eminently separable. Why not separate, and fall down on idiotproof parafoils? While trying a second warp jump would mean risking it all, so would trying to land the warp engine. Better leave it safe and sound in space rather than subject it to any further strain or risk. Alas. It is quite objectionable for the starship to be so incapable of sublight travel when her shuttlecraft are not, after all. Many a plot would be solved by sending the shuttles ahead, and this is only covered by us assuming that the shuttles are inferior to the mothership at both warp and impulse. Uh, what purpose? Remaining in orbit above Rigel XII or Delta Vega would leave the heroes in the very same jam as if they limped out of these star systems - incapable of reaching home or further safety. If anything, any further deteriorating of their situation would best be covered by remaining close to planetside safe haven and prepared for evacuation, be it by beaming down, shuttling down or parachuting down. Maintaining shouldn't be an issue, really. While most orbits in Trek could be tight figure-eights above the landing party or the starbase, in both of these cases the helmsman would know better than to establish a non-freefall orbit. If the ship is incapable of doing the hovering for extended periods of time, then we're at loss to explain any of the "power lost, ship falls" events - why was the ship hovering in the first place, if she was close to incapable of doing so by design? Yet how would this be a fuel-saving maneuver? Staying ahead either consumes power or then does not. If it does not, then it should be trivial to consume a bit of power and get ahead, adding to the margin. In any case, we have to account for the fact that Spock implicitly refused to send any shuttlecraft ahead to search for Kirk. Since he did that, his refusal to make the ship go to the planet is a natural part of said command decision and doesn't require a further celestial mechanics explanation (although it doesn't preclude one if we wish to go there). Timo Saloniemi
These are two separate issues: 1. In the specific case of "The Paradise Syndrome" where they've lost their stardrive and the ability to regenerate power then they must conserve their fuel. The Enterprise is completely capable of sublight travel since we know at the end of the episode where they are rescuing Kirk they were going to use the Enterprise to escape the danger zone. I'm simply pointing out that with limited fuel they have to pick when to use that capability. 2. As you said, Spock implicitly decided not to send shuttles ahead. He also implicitly decided not to leave behind a search party with supplies before leaving to deflect the asteroid. So there are causes that we just don't have line of sight to. We do know from "The Menagerie" that shuttles are inferior to the Enterprise in regards to range but does reasonably well in top speed. Purposes? Here you go: "WNMHGB": Stay in orbit over Delta Vega and they'll get swatted down or worse by the god-like Mitchell. The two reasons why they diverted away from the nearest starbase and over to Delta Vega were to 1) find a way to repair the stardrive and 2) drop off Mitchell before his powers grew so much that they would have to self-destruct the ship. "Mudd's Women": Rigel XII they had only enough power to enter into a temporary orbit. The extra power use drained her batteries much quicker than estimated so yeah, I'd say not crashing by staying in orbit is a purpose. SULU: Power curve still dropping, Captain. FARRELL: We'll make orbit, sir. A temporary one. KIRK: Lay in. Computer? SPOCK: We can sustain this orbit for three days, seven hours. The dialogue neatly spells out that due to a lack of available power they could not enter into a stable orbit. Okay, lets see: Staying ahead consumes power = they run out of fuel before reaching the planet and is then pulled into the asteroid Staying ahead consumes no power = they cruise with the asteroid until they reach the planet's sphere of influence where the planet's gravity is stronger and then the Enterprise uses power to enter orbit with a little of the planet's help. They retain fuel to leave planet. Staying ahead consumes no power but we'll consume power to get ahead to reach the planet sooner = Enterprise expends fuel to get ahead plus expends fuel to enter orbit could leave them without enough fuel to leave orbit. Well, thinking about your shuttle argument then it would seem consistent to not send shuttles in similar stardrive-deprived situations where they could have been useful. Shuttles were not sent in "WNMHGB" to drop off Mitchell or fetch repair equipment. Shuttles were not sent in "Mudd's Women" to fetch the crystals. The impulse fuel limitation is also consistent in stardrive-deprived situations so IMHO it adds a nice layer of consistent detail to the episode. As always, YMMV and you could just go your way and assume there was a good (and consistent) reason for the shuttles to not be employed
Fuel for the Impulse units is the common hydrogen isotope Deuterium for the fusion reactors. Its not going to be too hard for USS Enterprise to refuel.
In any case, gravity and starships cannot be evenly matched adversaries. If starships really struggled with defeating one gee, they could never engage in sublight combat, or cross star systems the way they do in "Elaan of Troyius" or "Doomsday Machine"; they'd run out of oomph not in seven hours, but in seven seconds or thereabouts... We really need workarounds for every perceived case of a starship being inconvenienced by one gee. Extreme damage is one way to go. But if the ship in "Paradise Syndrome" suffered from such, then Spock ought to be spending all of his allotted two months trying to struggle free of the rock with what little he had available, rather than risking it all on one final burst that might fail. Timo Saloniemi
BINGO. The M/AM engines were not working. Also, maybe impulse power reserves were used heavily with phasers in the attempt to stop the asteroid. Spock kept firing the phasers after main power failed. How long does impulse power last? The follow impulse power uses with main power out were observed on-screen: "WNMHGB" Note: go from energy barrier to planet in several days, maybe weeks, make orbit "Mudd's Women Note: partial main power for some of the trip in 2 days, barely make planet orbit "The Apple" Note: full power resisting tractor beam for 16 hours, big thrust, phasers use "The Doomsday Machine" Note: full power for up to 7 hours trying to out-race the DM, shield use, phaser use "The Immunity Syndrome" Note: energy sucking zone, full power for 2 hours for engines, shield use, big thrust "Elaan of Troyius" Note: slow planet to planet trip in several days. Full power for shields, 3 hits drained power "This Side of Paradise" Note: phaser use, conserving power back to planet for 2 months, make and break orbit "The Savage Curtain" Note: on battery power only, no problems with battery power in orbit for at least 4 hours... Impulse power just gobbles up its energy reserves (no evidence that it uses deuterium in TOS, we get terms "power cells" and "battery power", the only time fusion is mentioned was in DM when they exploded the Constellation's impulse engines). You can push the Enterprise on full impulse power for hours. Using her conservatively, you can get to a nearby solar system in a few months and make orbit at a planet. I hate to admit it, but the old girl's kind of a dog on impulse without main power.
I propose that shuttles are charged up by the same power and fuel from the ship's reserves. Shuttle use would be stealing valuable power resources from the ship that is in conservation mode. TOS makes no references about collection of space gas or deuterium, but lets assume it uses this technology. I propose that the "Bussard collectors" go down without the M/AM main power, so, no refueling from space gas. The gases collected are primarily for use in the M/AM reaction. Only a small percent of space gas is deuterium which is probably separated and stored. According to many episode dialog we get the following impulse power scheme, the impulse engines generate the power for the ship and for propulsion. If deuterium is used, it is used directly in the impulse engines. No separate fusion reactors without engines. The rest of the power system is power cells and batteries. One reference to "Reactor #3" put us in main engineering, so, I assume it is a 3rd M/AM reactor in the engineering hull. Usually, all reference about reactors are in conjunction with the M/AM reaction.
I tried running some tests on Spaceflight Simulator. It's really difficult to get three passes with a highly elliptical orbit within a >1 year time frame. I haven't been able to do it yet. But I admit to being a novice. Certainly there isn't absolute evidence given in the movie, so a wide variety of theories are possible. The reasons why I didn't use this idea in my chart is because a return warp jump toward earth would be risky. On a first warp flight I wouldn't want to risk smacking into earth or overshooting by too far, etc. As far as landing the upper stage I don't know if there is enough fuel for the upper stage engine to deorbit and land the Phoenix. There just isn't much there to indicate a fuel tank for this engine. But more importantly, why would Cochrane want to land this section in the first place? Whether you believe that Vulcanians brought FTL travel with them to first contact, or not; Zefram Cochrane would have been planning for the April 5th flight to be the first of many test flights. With launch vehicles in short supply it would be a huge waste of effort to relaunch the entire Phoenix for another flight. In my opinion it would take significantly less effort to re launch a refurbished cockpit, with fuel, then dock with the warp platform in orbit. I haven't run any calculations so I could be wrong though. But those are the ideas that I put into my chart. But the movie is vague enough it leaves lots of room for interpretation. Here's a thought. What if shuttle craft doen't have matter-antimatter reactor. What if instead, they are charged with warp plasma into a "fuel tank." Then they use this limited fuel supply to achieve their speeds. That would mean that if the ship's Matter-antimatter reactors when down, the shuttle craft couldn't be fueled and therefore would be useless. It would also explain why the shuttle bay is located just aft of the nacelle pylons.
But Shuttles do have M/AM reactors, it's been stated on screen several times. They've shown Warp Plasma containers to be quite bulky, not space efficient compared to carrying Deuterium & Anti-Deuterium in two separate tanks
...hence my NASA supercomputer comment. We could make this simple on ourselves. Like Hale-Bopp breaking up into a string of 30 or so objects, maybe a very large asteroid broke up into a string of 4 moon-sized asteroids (it did look lumpy), over a long period of time, strung out in ~4 month spacings, maybe irregular spacings and were on a near approach to the planet. The first 3 missed (the 3rd was the worst = closest) but the 4th one won't miss. No orbital calculations. Easy peasy. Agreed, a M/AM reactor must be onboard, but if the Enterprise's M/AM reactors are burned out, then I propose that it can't produce antimatter for the Shuttles, neither. So, why wouldn't you charge up the shuttles prior to burning out the warp drive? Most likely, they were out of Shuttles at the moment. Two were coming on Tuesday.
I'd keep fuel and propellant well separate in Trek spacecraft propulsion. The latter, the stuff that gets kicked out for Newtonian thrust, might be a triviality that never runs out; the former, the source of power, might take half a dozen forms even aboard a simple shuttlecraft. Shuttle accidents are supposed to demonstrate "antimatter residue" as per "Metamorphosis", but that doesn't yet mean there'd be a M/AM reactor or a warp core aboard. Shuttles also run on "ion power" as per "The Menagerie" - perhaps the polaric ion power that's banned from being applied in larger scale in "Time and Again", out of fear of kabooms, but mastered by aliens in "Spock's Brain". A shuttle that appears to have warp coils may lack a warp core as in "The Sound of Her Voice" - or have one that can easily be yanked out if need be. Phaser pistol batteries may stand in for power-producing fuel and move the craft even when liquid fuel or propellant is gone in "The Galileo Seven". And so forth. The times when Kirk's ship underperforms at sublight might be related to a shortage of power where plenty of propellant remains. If said propellant is deuterium, then it does double duty as fuel, but perhaps using it for fusion is a pitifully inadequate substitute for annihilation power and just eats up the fluid at double rate to little return. That is, assuming that there is any propellant or Newtonian rocketry involved to begin with. Impulse drives might be purely "field" drives, the only role for exhaust being to carry away unwanted wastes and heat (the "tailpipe" comparison from TUC). In the end, I only want to steer clear of the scenario where a functioning starship has trouble fighting the gravity of a planet. Lack of the required performance reserves ought to be a malfunction rather than a feature there. But the whole range of poor performance can probably be covered by saying that sublight flight is sadly Newtonian and ineffective unless well-working main power is used to reduce the ship's rest mass. And that aspect of the sublight drive might be closely related to warp drive, and down when warp is down. Timo Saloniemi
Ok. I did some searching and I haven't found any direct evidence of a M/AM reactor on shuttle craft. What I did find is circumstantial evidence. Shuttles leave antimatter residue and they have reactors. So a case for M/AM reactors on shuttle craft could be well made. Though we still have the problem with what sort of conversion Scotty would be making to convert an M/AM reactor from taking in Matter and antimatter as fuel, to taking in phaser energy as fuel. I also don't recall any instances of them showing warp plasma containers. We know that magnetic bottles for antimatter are spherical, but we're never shown whether these are standard size or a smaller size compared to what is used to store anti-matter in the nacelles. I would imagine that if you could store warp plasma, it would have to be stored in a magnetic bottle similar to antimatter. That one is much easier. The first three were near misses, but the last one was going hit. It does kind of take the fun out of the looming asteroid though. Well regardless of the fuel supply shuttles use. It makes the most sense to me that volatile fuel, be it warp plasma or anti-matter, would be transferred to the shuttles just prior to launching. There's no point in having a bunch of anti-matter bombs waiting to go off inside your hull. But with regards to your question, it's not like they PLAN on burning out the warp drive.
The TOS shuttlecraft appears to have a dual propulsion system: First, two small M/AM warp engines (hanging on the sides of the shuttle) that uses a limited supply of M/AM fuel stored in the nacelles (no regenerative dilithium system). For long trips, then the warp drive is used for planet to planet, or to ferry out past the edge of a solar system and back. There's enough warp M/AM fuel to go out and come back. Trips are less than a day since we see no sleeping quarters. Second, a small impulse drive (see vents across rear and square pad under nose) that uses a limited supply of stored energy in plasma-fuel cells and batteries. The impulse drive is primarily used for planetary jaunts down and up to a planet and orbital scans. Based on "The Galileo Seven", the Columbus shuttle searched from orbit for several hours on impulse before it had to return for refueling. Again, trips are less than a day since we see no sleeping quarters.
That makes a lot of sense, I just have this scene in my head of Cochrane talking to a potential buyer (his original plan). Buyer: A faster than light ship huh, That's quite a claim, can I see it? Cochrane: The Engine section is in orbit, you can look at it through a telescope if you want. I know he has telemetry, and all his calculations as proof, but still.
The scenario plays out in my head more like this: Buyer: A faster than light ship huh, That's quite a claim, can I see it? Cochrane: Sure. I'll take you for a test drive. *They climb aboard a capsule, launch into orbit. Dock with the Phoenix, refuel the antimatter and other fuels. And they're ready for a second go* Rather than: Buyer: A faster than light ship huh, That's quite a claim, can I see it? Cochrane: Yeah, it's right here in this launch silo. But you can't take it for a test drive because we're fresh out of Titan II missiles. I see the point you're trying to make. But in my mind it just goes against the basics of launching things to space. Once it's up there you don't want to bring it back down until its usable life is over. Repeatedly landing and launching would be wasted energy. In my head canon, the Pheonix make a few more test runs and then gets discarded in orbit. For several decades its just another piece of space junk. Then some enterprising individuals were able to de orbit it and bring it safely to the ground, so it could be re-attached to its cockpit module and refurbished.