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Star Trek Problems with Distance, Time and Speed

MAGolding

Fleet Captain
Fleet Captain
This thread is for discussion of warp speed paraxoes in Star Trek, and the various solutions proposed for them.

Most of us have done math problems in school where we had to calculate how long a train will take to travel a specfied distance at a specifed speed, or if a train travels 150 miles in 2.5 hours what is its average speed, and so on.

And I suspect that most Star Trek writers, producers, and other creators hated doing those problems in school, because it seems like they never bothered with them ihen creating various productions, and the evidence about warp speeds is highly conradictory.

There have been separate "official' warp speed scales for TOS and for TNG era productions. And as early as TOS , few writers seemed to follow those "official" warp scales. According to the semi canon sources, the speed of a TOS Warp factor equalled c, the speed of light mulitiplied by the warp facctor cubed. So warp factor 1 ws the speed of light, warp factor 2 was eight times the speed of light, and so on. Warp factor 6, the fastest speed that was safe to use for long periods of time was 216 times the speed of light.

And it should be obvious that the significantly higher warp speeds should have been chosen due to the vast distanced traveled during the five year mission. For example, in about a year Mudd traveled from Rigel to Deneb and then to Mudd's planet.

Many TOS episodes involved travel much faster than the warp scale. It is possible that the most extreme example was in "That Which Survives" where the Etnerprise has to travel 990.7 light years very fast. They start at Warp 8 and soon are travelling a little faster.

RAHDA: We're holding warp eight point four, sir. If we can maintain it, our estimated time of arrival is eleven and one half solar hours.
SPOCK: Eleven point three three seven hours, Lieutenant. I wish you would be more precise.
.

Warp 8.4 should be 592.704 times the speed of light, so it should take them about 1.671492 years to get there. But the estimated travel time is 11.337 hours, which would require a speed of 766,029.46 times the speed of light. So they are travelling 1,292.4317 times as fast as they should according to the warp scale.

There are many other examples of interstellar travel much faster than the TOS warp scale.

But there are some examples of interstellar travel in TOS happening at speeds similar to the TOS warp scale.

In "This Side of Paradise", at Omicron Ceti, Kirk says:

KIRK: Another dream that failed. There's nothing sadder. It took these people a year to make the trip from Earth. They came all that way and died.

And obviously if the trip from Earth to Omicron Ceti took about 0.5 to 1.5 Earth years, the colonists' ship would travel at speeds consistent with the TOS warp scale.

In "By Any Other Name":

KIRK: What's the point of capturing my ship? Even at maximum warp, the Enterprise couldn't get to Andromeda galaxy for thousands of years.
ROJAN: Captain, we will modify its engines, in order to produce velocities far beyond the reach of your science. The journey between galaxies will take less than three hundred of your years.
Spock Fascinating. Intergalactic travel requiring only three hundred years. That is a leap far beyond anything man has yet accomplished.

The Andromeda Galaxy is about 2,500,000 light years from EArth, so travel there in about 250 to 300 years would take speeds of about 8333.33 to 10,000 times the speed o flight, which is much slower than the speed in "That Which Survives". But Kirk seemed to imply that it would take at least 10,000 years, which would require speeds slower than 250 times the speed of light - close to warp 6 at 216 times the speed of light.

In TNG era productions a different warp scale is used, and ships are supposed to be faster than in TOS (see VoY "Flashback"):

JANEWAY: It was a very different time, Mister Kim. Captain Sulu, Captain Kirk, Dr. McCoy. They all belonged to a different breed of Starfleet officer. Imagine the era they lived in. The Alpha Quadrant still largely unexplored. Humanity on verge of war with Klingons. Romulans hiding behind every nebula. Even the technology we take for granted was still in its early stages. No plasma weapons, no multiphasic shields. Their ships were half as fast.

But the entire plots of DS9 and VOY depend on TNG era ships, faster than TOS era ships, still taking many decades to travel 70,000 lgiht years, thus making their speeds average about 1,000 times the speed of light. Much slower than the fastest speeds in TOS and about twice the official TOS Warp scale, indicating that TOS ships shouldn't have been faster than the TOS warp scale..

And then there is Star Trek: The Motion Picture (1979), which had two science advistors, biochemist and science fiction writer Isaac Asimov, and NASA rocket expert Jesco von Puttkamer. In a thread: https://www.trekbbs.com/threads/distance-speeed-and-time-in-tmp.312160/#post-14252735 I calculated that the distances and times were consistent with V'Ger travelling at warp factor sevenof the TOS warp scale, with the Klingon's a had a base at Barnard's Star and if V'Ger came from the far side ofthe galaxy,and I think tht it is fairly proble that the science advisors also did the calculations.

And in that that thread I offered a possible explaination for the many contradictions in "galactography", the geography of outer space (a term coined by Asimov, I think) and problems with times, distances, and speeds of various voyages:

One solution to the warp speed paradoxes is to imagine that there some type of wormholes or other space time tunnels connecting different star systems. A space ship can enter the mouth of such a tunnel and emerge from the mouth of the tunnel in another star system in much less time than it would take to travel the entire distance between the two systems, even at top warp speed.

So some starship voyages actually cross the spaces between stars using warp speed, while others bypass those vast distances by using those interstellar short cuts.

And so my theory is that on a space map the Federation would look like a collection of disconnected bubbles floating in space, consisting of stars systems connected by those shortcuts surrounded by spherical zones of space claimed by the Federation. And in some places two or more neighboring star systems would both be part of the Federation and the Federation would claim a larger zone of space around those systems.

And if other star traveling societies have discovered those space shortcuts their territories would also tend to look like disconnected soap bubbles in space maps.

Including the Klingon Empire. So my theory is that in the era of TMP the Klingon Empire rules a star system only a few light years from the Solar System, and claims a volume of space of space several light years around that system.

Thus when the Klingons detected V'Ger heading toward that system on a line toward Earth they would have sent three warships to that system to get ahead of V'Ger and then turn back and head toward V'Ger like they were coming from Earth, and attack V'Ger to make V'Ger think Earth was hostile to V'Ger.

The Klingon high command no doubt figured that if three warships could defeat V'Ger no harm would be done, since V'Ger wouldn't have been powerful enough to defeat Earth's defense system anyway. And they probably also figured if the three warships couldn't defeat V'Ger, it might be powerful enough to defeat Earth's defenses, so sacrificing a mere three warhships to increase the probability that V'Ger would attack and destroy Earth would be worthwhile.

That is one theory to explain the many warp speed paradoxes in Star Trek.

Of course there are other theories which have been proposeed to explain warp speed paradoxes, and still other theories which are possible solutions which have not yet been proposed.

So I thought I would start a thread to list all of the known theories about solutions to the warp speed paradoxes.
 
I had posted this a while back as my own theory specifically for TOS Warp that space terrain affected base speeds...
  • slowest next to a planet/star (below sublight),
  • slow up to the 3rd planetary orbit,
  • very fast in open space between systems,
  • and slows down again between galaxies...

warp-speed-curve-tos-wip-0.8-output.png


The only changes I would make today is that TOS Impulse overlaps up to TOS Warp 6 and space weather affects final speed.
 
Cosmic strings allow a variable speed of light:
https://worldbuilding.stackexchange...gravity-assisted-travel-along-a-cosmic-string

—so have it be the “center stripe” of a road to the stars as a variable speed of warp.

Old Earth and Romulan ships can therefore go much farther afield than they could on their own in free space.

My theory is that ringships are best suited to an eco cruise mode and thread the needle…but as Tom Paris says…can’t turn until an off ramp.

Twin nacelle designs can disengage and turn more quickly. In the same way SLS and Starship backers bicker…I see nacelle and ringship fans getting into arguments :)
 
My theory is that ringships are best suited to an eco cruise mode and thread the needle…but as Tom Paris says…can’t turn until an off ramp.

Twin nacelle designs can disengage and turn more quickly. In the same way SLS and Starship backers bicker…I see nacelle and ringship fans getting into arguments :)
So far, I've only discovered 8x different ways of implementing Warp Drive.

Each Warp Drive system is genuinely different than the other in design to create the Warp Field, and allows different StarShip vessel design / geometry.

Some of the other ways I haven't listed in that thread because they were a more recent discovery.

But 8x ways to implment a Warp Drive allows some genuinely flexible designs.
 
UFP achieved stable Warp 9.9 velocity with the USS Prometheus in 2374 (or at the very least, it seemed like a sustainable velocity because the ship wasn't shaking itself apart at those speeds - the only trouble is, we don't know for how long the ship could maintain Warp 9.9. I would imagine for as long as they have the resources to run the thing - plus it had multiple Warp cores, 5 Warp nacelles (in combined mode), so it certainly seemed to have the prerequisite for achieving and maintaining Warp 9.9 indefintiely - obviously some pit stops would need to be made after 3 to 5 years - depending on how long their antimatter supplies last, so they can replenish it along with deuterium and possibly dilithium - though with recrystalisation tech, I would imagine Dilithium Crystals as they are given to a ship can probably last for the entire service period of that ship).

Warp 9.9 was established on-screen to be 21,473 times speed of light (VOY on the other hand was limited to 9.75 for 12 hours as was seen on several occasions in dialogue - only 2 or 3 instances mentioned Warp 9.975, but this speed was NEVER achieved by the ship itself in practice... in fact, whenever it got closer to just 9.9, the ship was already shaking itself and the computer saying a structural collapse would be imminent in 45 seconds).

At Warp 9.9, it would have taken a ship 125.7 years to reach Andromeda (which is 2.7 million LY's away).

That of course doesn't take into account the Quantum Slipstream Drive, of which there are 2 versions.
Cruising speed of V1 QSD = around 714.2857 Ly's per day, or 260,714.2857 times speed of Light.
Maximum speed of V1 QSD = 300 Ly's per hour, or about 2,628,000 times speed of Light (this speed was implied to be something that cannot be sustained indefinitely even by the fake USS Dauntless).

V1 of QSD was adapted from Arturis fake USS Dauntless, but it never needed Benamite crystals to run and was more or less easily adapted into existing SF technology... however, VOY could not sustain the beating from quantum stresses in transit for more than 1 hour of maximum v1 Quantum Slipstream velocity (this would have been possibly easier to overcome with some R&D upon VOY return which would require say ADAPTIVE Structural Integrity fields - not necessarily to pump more power into them, but install adaptive algorithms which would adjust to the Quantum Stresses with more trips through the SLipstream).

Top speed of V2 QSD = around 10,000 Ly's per minute from what we know of what happened in Timeless episode of VOY, or 5,256,000,000 times speed of light (this version was reworked from the ground up. It had a Quantum Matrix, used Borg technology and required use of Benamite crystals which had a fast deterioration rate, but could be synthesized - though it was suggested that it COULD take years to synthesize more - there is no reason to think SF could not overcome these difficulties with automated R&D in a few years after VOY returned home and therefore reduced the time at which the crystals deteriorated and also improved times for synthesizing new crystals - though, even if SF was able to stabilize the crystals only, that would still be usable for say certain amount of trips before they would need to be replaced - in the meantime, the ship would still have access to either Warp 9.9 or QSD v1 to shorten an otherwise long trip.

Additional issue with this faster version of QSD was a phase variance which appeared after 17 seconds of flight.
It woul arguably still be usable for say 10-15 seconds 'hops' though... which would reduce the overall lightyears crossed to 1,666.666 Ly's in 10 seconds.

Automated R&D should be possible for SF to get rid of the phase variance issue a few years after VOY returned home... which is clearly indicated with the fact that SF recreated its own REAL USS Dauntless (As seen in Star Trek Prodigy, and was confirmed it had a Quantum Slipstream drive, but will need to use it sparingly - implying the phase variance issue was solved indeed, along with the benamite crystal degradation - at least in part to allow the ship multiple uses of the drive without danger).

So, using QS v1, a ship would require 10.356 years to reach Andromeda.
Using QS v2, a ship would require about 4 and a half hours to reach Andromeda galaxy.

Then of course there's the ProtoDrive from the USS Protostar... it seems this method is different compared to most others, but speed wise, it might be similar to QSD V2 from what we saw... and also, no need for benamite crystals.

There's also Warp 10 (infiinite Velocity TransWarp)... and SF does technically have access to this technology as well, and also knows of an effective treatment that can stop the mutations... however, that's the least of their issues... the issue comes to the matter of navigation because when VOY first tried it, Torres said that they'd need to figure out how to come out of TW at a specific point (and I think this would be more problematic issue to figure out - but I'd still give it no more than 20-30 odd years for SF to figure that one out too).

Right now however, Inifnite Velocity Warp 10 would be more suitable for unmanned probes and/or other larger craft such as runabouts and shuttles that could be launched at those speeds to gain a MASSIVE sum of data about the galaxy and the universe at large for scientific purposes at the very least.
Even without the ability to navigate infinite velocity, its still an invaluable tool for scientific exploration, because as we noticed, the flight WOULD result in accumulation of vast amount of data... and the moment the drive is turned off, it just returns the vessel back to the original starting point... so it has use... this can easily vastly accelerate scientific and technological R&D in just a span of a few months... and SF should be able to crack the navigation part of it too with more unmanned test flights and information they gather.
 
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I chalk it up to magnetic fields from various natural effects like stars, planets, magnetic storms and from artificial sources like civilization-built magnetic space corridors between advanced star systems. As I posted on other threads:

From WNMHGB and The Galileo Seven, magnetic potentials geometrically multiply the speed of warp drive ships. For both the SS Valiant and the shuttlecraft Galileo, it resulted in multiplying theirs speeds by 1000's to 100,000's times the speed of light.

Natural Effects: Strong magnetic storms periodically radiate from the galactic center of galaxy following the arcing shape of the galactic arms. These magnetic storms are very long, even some extending from the center of the galaxy and reaching past the galactic rim. Additionally, these magnetic storms are thin, wave-like ribbons or strings that are wiggling/drifting/moving away from the galactic center. At the origin region of these magnetic storms is a vast energy field around the galactic core called the Great Barrier, and at the terminus point, these storms dissipate at the rim of the galaxy, there interacting with some unknown energy/matter to form a negative energy field called the Galactic Barrier. Diving into one of these magnetic storms at warp draws the ship to the centerline of the ribbon and accelerates a ship geometrically along its length, either toward the galactic center or toward the galactic rim depending which direction the ship was generally moving. Once in the magnetic storm, ships can leave it at any point along its length if its impulse drive system is powerful enough to overcome the storm's magnetic potential. Finding and charting these magnetic storm ribbons is extremely important for space faring civilizations.

For both the SS Valiant and the shuttlecraft Galileo, their impulse drives weren't powerful enough to pull themselves out of those very strong magnetic storms. The SS Valiant was spit out a half lightyear outside of the galaxy by an exceptional long magnetic storm ribbon, while the Galileo was pulled into the center of a local magnetic storm and probably dislodged out of the storm by the near pass to the planet's magnetic field they crashed on. Earth's early warp ships were not knowledgable of these magnetic storms which accounts for the mysterious loss of many ships. Finding and charting these moving magnetic storm ribbons allows warp ships with powerful enough impulse drives to transverse vast distances along a galactic arm. Most storm ribbons are fragmented (only a very few light years in length) while a rare few are vast in length (10,000's light years). In WNMHGB, the Enterprise was able to get to the galactic rim possibly by riding the same magnetic storm ribbon that captured the SS Valiant, but the Enterprise got off before they exited the galaxy. This could explain how the Enterprise could be in the vicinity to find the Valiant's ship recorder, plus explain why they were near a planet set up for cracking lithium so far out on the rim; the initial explorers/developers set up the planet operations, then subsequent automated ore freighters were all using the same ribbon, too. In ST:V TFF, the Enterprise was able to travel to the galactic center in hours; using this theory, they used a charted ribbon that extended to the galactic center.

Additionally, encountering the magnetic field(s) of stars, solar flares, solar mass ejections and planets can create a "head wind" to warp speed and possibly affect the time-space continuum of ships at very high warp speed. Some of these effects can be found in various episodes such as The Naked Time, Tomorrow is Yesterday, Operation: Annihilate!, Assignment: Earth, and The Paradise Syndrome.

Artificial Effects: Advanced space civilizations, such as the Federation and the Romulan and Klingon Empires, can laboriously build magnetic corridors between important star systems using space buoys that allows warp ships to traverse the corridor in hours or days. Low warp ships even with weak impulse drives are able to use the man-made, magnetic corridor network to safely get on and get off.
 
A notable theory used by many is that there are factors which can multiply and/or divide the speed of a starship at a specificic warp factor.

And it is assumed that the strength of those factors is different in different volumes of space, so that a ship travelling at a specife warp factor will be travelling much faster in some volumes of space than in others.

Thus a starship travelling from Star System A to Star System B which is 100 light years distant might have to travel though 10 light years where its speed witll be 100 times the speed of light, and through 90 light years where its speed will be 1,000 times the speed.of light. Thus it will travel 10 light years in 0.1 year and travel 90 light years in 0.09 year for a total travel time of 0.19 year, or about 69.3975 days.

But another starship in another region of space travelling from star System C to Star Ssytem D which is 100 light years distant might have to travel through 20 light years where the speed is 1,000 times the speed of light and through 80 light years where the speed is 10,000 times the speed of light. Thus it will travel 20 light years in 0.02 year and 80 light years in year, for a total travel time of 0.028 year or 10.227 days.

And both starships might use the same warp factor in those voyages, though one ship will take about si xtimes as long to trave lthe same distance of 100 light years in a region of space where travel time is slower.

There are many aspects of this this theory which can be discussed to see how probable it is and how well it explains many time, distance, and speed paradoxes in Star Trek. But in my next post I will discuss a related but different theory.
 
I chalk it up to magnetic fields from various natural effects like stars, planets, magnetic storms and from artificial sources like civilization-built magnetic space corridors between advanced star systems. As I posted on other threads:

From WNMHGB and The Galileo Seven, magnetic potentials geometrically multiply the speed of warp drive ships. For both the SS Valiant and the shuttlecraft Galileo, it resulted in multiplying theirs speeds by 1000's to 100,000's times the speed of light.

Natural Effects: Strong magnetic storms periodically radiate from the galactic center of galaxy following the arcing shape of the galactic arms. These magnetic storms are very long, even some extending from the center of the galaxy and reaching past the galactic rim. Additionally, these magnetic storms are thin, wave-like ribbons or strings that are wiggling/drifting/moving away from the galactic center. At the origin region of these magnetic storms is a vast energy field around the galactic core called the Great Barrier, and at the terminus point, these storms dissipate at the rim of the galaxy, there interacting with some unknown energy/matter to form a negative energy field called the Galactic Barrier. Diving into one of these magnetic storms at warp draws the ship to the centerline of the ribbon and accelerates a ship geometrically along its length, either toward the galactic center or toward the galactic rim depending which direction the ship was generally moving. Once in the magnetic storm, ships can leave it at any point along its length if its impulse drive system is powerful enough to overcome the storm's magnetic potential. Finding and charting these magnetic storm ribbons is extremely important for space faring civilizations.

For both the SS Valiant and the shuttlecraft Galileo, their impulse drives weren't powerful enough to pull themselves out of those very strong magnetic storms. The SS Valiant was spit out a half lightyear outside of the galaxy by an exceptional long magnetic storm ribbon, while the Galileo was pulled into the center of a local magnetic storm and probably dislodged out of the storm by the near pass to the planet's magnetic field they crashed on. Earth's early warp ships were not knowledgable of these magnetic storms which accounts for the mysterious loss of many ships. Finding and charting these moving magnetic storm ribbons allows warp ships with powerful enough impulse drives to transverse vast distances along a galactic arm. Most storm ribbons are fragmented (only a very few light years in length) while a rare few are vast in length (10,000's light years). In WNMHGB, the Enterprise was able to get to the galactic rim possibly by riding the same magnetic storm ribbon that captured the SS Valiant, but the Enterprise got off before they exited the galaxy. This could explain how the Enterprise could be in the vicinity to find the Valiant's ship recorder, plus explain why they were near a planet set up for cracking lithium so far out on the rim; the initial explorers/developers set up the planet operations, then subsequent automated ore freighters were all using the same ribbon, too. In ST:V TFF, the Enterprise was able to travel to the galactic center in hours; using this theory, they used a charted ribbon that extended to the galactic center.

Additionally, encountering the magnetic field(s) of stars, solar flares, solar mass ejections and planets can create a "head wind" to warp speed and possibly affect the time-space continuum of ships at very high warp speed. Some of these effects can be found in various episodes such as The Naked Time, Tomorrow is Yesterday, Operation: Annihilate!, Assignment: Earth, and The Paradise Syndrome.

Artificial Effects: Advanced space civilizations, such as the Federation and the Romulan and Klingon Empires, can laboriously build magnetic corridors between important star systems using space buoys that allows warp ships to traverse the corridor in hours or days. Low warp ships even with weak impulse drives are able to use the man-made, magnetic corridor network to safely get on and get off.

I think a simpler solution that already exists can be used.

The Subspace Corridor that the Vaadwur used that they called "UnderSpace" is ALOT more common than most people give credit and it spreads across the entire Milky Way Galaxy.

It's just not fully explored.
 
In post number 7 I mentioned a well known theory that there are factors which change the speed of a starship travelling at a specific warp factor and that different regions of space have different strengths of those factors, and so a starship travelling at a specific warp facter will travel faster in some regions of space than in other regions of space..

In this post I want to suggest a related but different theory. One which I thought of yesterday, August 29, 2022, but which someone else possibly thought of long ago.

As we all know, stardates are a mystery, and many theories of stardates have been proposed, but as far as I know, none have achieved wide acceptance.

I note that it is not certain that stardates are directly related to the rate at which time passes in the universe as a whole or in a starship travelling the stars. It is possible that the length of time between two stardate units can vary over time, so that the ratio of stardate units to hours, days, or years, could vary. It might even be possible for star dates to go down over time, so that the same stardate might happen two or more times at different dates of time.

Languages change over time, and the "date" in a "stardate" might not mean a date as we think of a date. And even if the "date" in "stardate" means a date in time, it could mean the date in time when a specific scientific factor has a certain value, the numerical value of the number in the stardate. Thus a stardate 1313.13 might be the date in normal time when factor X has a value of 1313.13, and a stardate 4444.4 could be a date in normal time when factor X has the value of 4444.4.

And factor X could change with time, so that it would increase at different rates at different times, and maybe even decrease at various rates at different times.

And what factor would a starship crew consider to be so important that a stardate would be the date that factor has the numerical value given in the stardate? Maybe something which affects the speed of a starship, so that knowing the stardate would enable one to calculate how fast the starship could travel during that stardate unit.

So maybe the factor that modifies how fast a starship will travel at a specifi warp factor doesn't stay the same in each region of space, and vary between different regions of space, but instead is the same all over the galaxy, but varies over time the same all over the galaxy or maybe even the entire universe.

And if the numerical value of a stardate equals the numerical value of that factor at the moment, knowing the stardate would enable to some to estimate how how fast a starship could travel during that stardate, and how long a voyage of a specific length would take during that stardate unit..

Of course thev value of that factor would probably be changing slightly continuously during a stardate unit, and a voyage would often take several or many stardate units. So precise calculations of how long a voyage would last would have be made by computers calculating how the speed would change over time.

Maybe the higher the stardate, the faster the starship and the shorter the travel time. Or possibly the higher the stardate, the slower the starship and the longer the travel time.

So someone could corralate the possible speed ranges for the voyages in various episodes with the value of the stardates in those episodes, to see if higher or lower stardates correlate to faster travel speeds.

Such a correlation would not have been deliberately set up by the creators of various Star Trek productions, but humans can see patterns everywhere, even where they are not. So possilby such a correlation could be found, intended by the creators or not, and used by some fans to explain times, speed, and distance paradoxes.

And it is possible that some fans have thought of that theory before, but I don't remember ever reading it.
 
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In post number 7 I wrote about a well known theory to explan the many speed, time and distance paradoxes in the many Star Trek productions.

Star Trek Maps, 1980, had four large wall maps of Federation and nearby space. It also included a booklet, supposedly an Introduction to Navigation from Starfleet Academy. The booklet said that in many regions of space the "Cochrane factor" enabled a starship to travel much faster than its basic warp factor speed. That is the theory I described in post number 7.

In my post I described the generic form of that theory, without any expanation why the hypothetical "Cochrane factor" might have different strengths in different regions of space.

The booklet described the reasons for different values of the "Cochrane factor" in different regions of space. According to Einstein's Theory of Relaviity, the present of matter curves space. The booklet claims that using rocket propulsionit spaceship wouldhave to follow the curvature of space. But a starship in warp drive travels thorugh subspace and so travels in a stright line. If there are two points on the circle, the distance between them along the circumference would be longer than the distance in a straight line between them. Thus a starship using warp drive can reach their destination much soon than a ship in normal space, because it can travel a shorter distance and so appears appears ti be traveling much faster.

And of course different indentically sized volumes of space will have different amounts of interstellar gas and dust in them, which will bend space with their mass and gravity to a different degree, and so a star travelling at a specific warp factor will travel much faster in some volumes of space than in other volumes of space.

I can point out a few flaws in that explaination.

One: Diameter vs semi circumference.

Imagine a circle with a diameter across its middle from two opposite points, A & B. If Point A and Point B are on opposite sides of the circle 180 degress of arc apart, on far ends of the diameter, they will be as far from each other as any two points on the circle can be, 180 degrees apart going both ways. If they are moved to be rather apart on one side them, they will be closer ont the other side. If they are 200grees apart one way, they will be 160 degrees apart the other way,and so on. So they can only be as much as 180 degrees apart.

So Point A and Point B will be as far apart as possible when they are on opposite ends of the diameter. A diameter is two times the radius between the center point of the circle and the circumference of the circle. The formula for the circumfrence of a circle is two times Pi times the radius. Thus the distance between A & B through the diameter is two times the radius, while the distance between A & B along half the circumference is about 3.14159 times the radius, or about1.57 tiems teh discence across the diameter. Thus the distance across the diameter is 0.6366 the distance around half the circumference.

It doesn't seem plausible to travel many times faster than light by using such a long type of shortcut which just a little shorter than going around curved space.

Two: It seems plausible that the amount of Einsteinian space curvature produced by by a mass at a specific distance should be proportional to its Newtonian gavitational attraction at that distance.

At an average spot on the surface of the Earth the surface gravity is an acceleration of 9.80665 meters per second per second, or 1 g, and the escape velocity is 11.186 kilometers persecond, which could be called 1 Earth Escape Velocity or 1 eev.

At an everage spot on the surface of the Sun, the surface gravity is 28 g and the escape velocity is 617.7 kilometers per second, or 55.22 eev. Because the average density of the Sun is much less than that of the Earth, the two facors don't scale at the same rate.

The Eddington experiment was an observational test of general relativity, organised by the British astronomers Frank Watson Dyson and Arthur Stanley Eddington in 1919. The observations were of the total solar eclipse of 29 May 1919 and were carried out by two expeditions, one to the West African island of Príncipe, and the other to the Brazilian town of Sobral. The aim of the expeditions was to measure the gravitational deflection of starlight passing near the Sun.[1] The value of this deflection had been predicted by Albert Einstein in a 1911 paper; however, this initial prediction turned out not to be correct because it was based on an incomplete theory of general relativity. Einstein later improved his prediction after finalizing his theory in 1915 and obtaining the solution to his equations by Karl Schwarzschild. Following the return of the expeditions, the results were presented by Eddington to the Royal Society of London[2] and, after some deliberation, were accepted. Widespread newspaper coverage of the results led to worldwide fame for Einstein and his theories.

They photographed the starfield around the hidden Sun during the eclipse.

For light grazing the surface of the sun, the approximate angular deflection is roughly 1.75 arcseconds.[2] This is twice the value predicted by calculations using the Newtonian theory of gravity. It was this difference in the deflection between the two theories that Eddington's expedition and other later eclipse observers would attempt to observe.

So the space curvature immediately above the surface of the Sun is so slight that a light ray pass right over the surface of the Sun will be deflected only 1.75 arcseconds. A sraight chord which cuts across an arc of a circle curing only 1.75 arc seconds will be only very, very slighly shorter than the arc distance.

And of course, deep in interstellar space the Newtonian gravity and Einsteinian space curvature will be much weaker than on the surface of the Sun, and the gains by using subspace shortcut will be even more infinitesimal and meaningless.

Three: A much more serious objection is that astronomers have mapped the density of interstellar gas and dust in various regions and will continue to do so in the future. It is quite posible that someday the interstella desnity regions will be mapped so precisely that someone will be able to calculate that any formula which makes one Star Trek voyage take the right amount of time will make another Star Trek voyage take a much longer or shorter time that it should.

It is possible that astronomical research has or will prove interstellar density regions don't have the right locations or densities to make any possble formula work with all the Star Trek voyages in various productions.

I think that together, the previous three objections to that theory are fatal to it. But they w are really minor objections compared to the dext objeciton to that objection to that explaination of varying warp speeds in different reigons of space. That theory ignores an obvious and fundimental law of physics. I will explain it in a later post.

And maybe some of you will want to think about what obvious and fundimental law of physics the Introduction to Navigation explaination for the various warp speeds in different regions of space ignores before I post that objection...
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I chalk it up to magnetic fields from various natural effects like stars, planets, magnetic storms and from artificial sources like civilization-built magnetic space corridors between advanced star systems. As I posted on other threads:

From WNMHGB and The Galileo Seven, magnetic potentials geometrically multiply the speed of warp drive ships. For both the SS Valiant and the shuttlecraft Galileo, it resulted in multiplying theirs speeds by 1000's to 100,000's times the speed of light.

Natural Effects: Strong magnetic storms periodically radiate from the galactic center of galaxy following the arcing shape of the galactic arms. These magnetic storms are very long, even some extending from the center of the galaxy and reaching past the galactic rim. Additionally, these magnetic storms are thin, wave-like ribbons or strings that are wiggling/drifting/moving away from the galactic center. At the origin region of these magnetic storms is a vast energy field around the galactic core called the Great Barrier, and at the terminus point, these storms dissipate at the rim of the galaxy, there interacting with some unknown energy/matter to form a negative energy field called the Galactic Barrier. Diving into one of these magnetic storms at warp draws the ship to the centerline of the ribbon and accelerates a ship geometrically along its length, either toward the galactic center or toward the galactic rim depending which direction the ship was generally moving. Once in the magnetic storm, ships can leave it at any point along its length if its impulse drive system is powerful enough to overcome the storm's magnetic potential. Finding and charting these magnetic storm ribbons is extremely important for space faring civilizations.

For both the SS Valiant and the shuttlecraft Galileo, their impulse drives weren't powerful enough to pull themselves out of those very strong magnetic storms. The SS Valiant was spit out a half lightyear outside of the galaxy by an exceptional long magnetic storm ribbon, while the Galileo was pulled into the center of a local magnetic storm and probably dislodged out of the storm by the near pass to the planet's magnetic field they crashed on. Earth's early warp ships were not knowledgable of these magnetic storms which accounts for the mysterious loss of many ships. Finding and charting these moving magnetic storm ribbons allows warp ships with powerful enough impulse drives to transverse vast distances along a galactic arm. Most storm ribbons are fragmented (only a very few light years in length) while a rare few are vast in length (10,000's light years). In WNMHGB, the Enterprise was able to get to the galactic rim possibly by riding the same magnetic storm ribbon that captured the SS Valiant, but the Enterprise got off before they exited the galaxy. This could explain how the Enterprise could be in the vicinity to find the Valiant's ship recorder, plus explain why they were near a planet set up for cracking lithium so far out on the rim; the initial explorers/developers set up the planet operations, then subsequent automated ore freighters were all using the same ribbon, too. In ST:V TFF, the Enterprise was able to travel to the galactic center in hours; using this theory, they used a charted ribbon that extended to the galactic center.

Additionally, encountering the magnetic field(s) of stars, solar flares, solar mass ejections and planets can create a "head wind" to warp speed and possibly affect the time-space continuum of ships at very high warp speed. Some of these effects can be found in various episodes such as The Naked Time, Tomorrow is Yesterday, Operation: Annihilate!, Assignment: Earth, and The Paradise Syndrome.

Artificial Effects: Advanced space civilizations, such as the Federation and the Romulan and Klingon Empires, can laboriously build magnetic corridors between important star systems using space buoys that allows warp ships to traverse the corridor in hours or days. Low warp ships even with weak impulse drives are able to use the man-made, magnetic corridor network to safely get on and get off.

This reminds me of the space period of the Dick Tracy comic strip from from about 1963 to 1969. Inventor Diet Smith invented a space coupe with magnetic propulsion, leading to moon flights and contact with Moon people.

https://dicktracy.fandom.com/wiki/Moon_Period#:~:text=The Moon Period (also referred,Moon Valley on the Moon.

It is true that magnetism can be stronger than gravity - a magnet can lift iron or steel against the force of gravity.

There are four fundamental forces at work in the universe: the strong force, the weak force, the electromagnetic force, and the gravitational force. They work over different ranges and have different strengths. Gravity is the weakest but it has an infinite range. The electromagnetic force also has infinite range but it is many times stronger than gravity. The weak and strong forces are effective only over a very short range and dominate only at the level of subatomic particles. Despite its name, the weak force is much stronger than gravity but it is indeed the weakest of the other three. The strong force, as the name suggests, is the strongest of all four fundamental interactions.

https://home.cern/science/physics/standard-model#:~:text=There are four fundamental forces,it has an infinite range.

But it seems just as difficult to create a magnetic drive spaceship as a gravity drive spaceship. Maybe more diffcult, since only some matter is magnetically charged. A magnetic drive can only attract or repel othe rcharged matter, while all matter should be gravitating.

I note that there are magneticallcy charged regions of space which accelerate tiny charged particles to vast speeds, almost to the speed of lgiht. But an entire spaceship would be accerated to a tiny fractino of those speeds by the forces in those regions of space, since it will be vastly more massive than a subatomic particle. And not all of manned spaceship could have strong magnetic charge - changing the magnetic charges of humans in major way would probably kill them. In any case there is way for those electromagnetic charged regions of space to accelerate particles or objects to the speed of light or to almost the speed of light.

So I find it hard to believe that any sort of magnetic storm could accelerate spaceship like the SS Valiant in "Where No Man Has Gone Before" to many times the speed of light and keep them at that velocity while they travel hundreds, or thousnds, or tens of thousands, of light years from Earth to the edge of the galaxy.

There is very little information about the voyage of the SS Valiant in "Where No Man Has Gone Before". In the opening narraton Kirk never says why he considers the distress signal "impossible"

Captain's log, Star date 1312.4. The impossible has happened. From directly ahead, we're picking up a recorded distress signal, the call letters of a vessel which has been missing for over two centuries. Did another Earth ship once probe out of the galaxy as we intend to do? What happened to it out there? Is this some warning they've left behind?

Since doesn't explain why he thinks the impossible has happened, we learn nothing about the voyage of the older ship from his worls. We can only speculate.

When Spock reports what the recorder says:

SPOCK: Decoding memory banks. I'll try to interpolate. The Valiant had encountered a magnetic space storm and was being swept in this direction.
KIRK: The old impulse engines weren't strong enough.
SPOCK: Swept past this point, about a half light year out of the galaxy, they were thrown clear, turned, and headed back into the galaxy here. I'm not getting it all. The tapes are pretty badly burned. Sounds like the ship had encountered some unknown force. Now, orders,

So apparently the magnetic storm struck the SS Valiant where the Enterprise was then, or possibly farther back into the galaxy,and swept it half a light year out of the galaxy. And when the storm calmed or the SS Valiant was thrown out of the storm, it headed back into the galaxy.

I would like to propose an alternative interpretation of those words. Possibly the hull of the SS Valiant had less insulation against magnetic effects and the magnetism in the magnetic storm affected the electrical controls of the SS Valiant , somewhat similar to, but inot identical to, their effect on the nstruments and controls of the Enterprise. Possibly the SS Valiant got to the edge of the galaxy using warp drive and then was struck by the magnetic storm which got the ship's warmp engines stuck at full speed until they could be shut off, and so took the SS Valiant half a light year out of the galaxy.

Kirk's statement about the "old impulse engines" could mean that the various generations of warp engines had complex official designatinos, but werre usually called just "warp drive" or "warp engines " for short. KIrk might have thought that the date of the voyage of the SS Valiant indicated it should have had "impulse warp drive engines" instead of "original warp drive engines" or "first generation warp drive engines", or "generation three warp drive engines", or whatever.

Or possibly the SS Valiant travelled to the edge of the galaxy using actual impulse engines and was struck by the magnetic strom there. Maybe some generatons of impulse engines had faster than light capability, even though they wre depicted being used only for slower than light travel in various movies and tv shows.

I note that some time ago I decided tha the stardates in "Where No Man Has Gone Before" indicate that less than a full stardate unit passed aboard the Enterprise while the Enterprise made a voyage of several light days to Delta Vega, while a stardate unit seems to lake less than one day in "Where No Man Has Gone Before" Thus the Enterprise seems to travel several light days while using impulse power which should be slower than light.

There are several solutions to this paradox.

One) That Delta Vega was several light days away, but the starship happened to be near the mouth of a space tunnel which let to the Delta Vega system, and thus the Enterprise could travel through much less than the full several light days to the Delta Vega system. Post number 1 above suggests the possible existence of such a system in Star Trek. And if that ws the case, maybe the SS Valiant found a route to the edge of the galaxy thorugh that system of space tunnels, and so could reach a place hundreds or thousands of light years from Earth while actually traveling though only a few light days or light months of space with a slower than light impulse drive.

Two) Or maybe the energy supply to the warp drive engines was damaged, but the actual warp drive engines were not. Thus the Enterprise could travel severa light days to Delta Vega in less than a day using the faster than light warp engines powered by the power supply for the impulse engines. If the impulse power supply had much less power, Enterprise would be travelling at faster than light warp drive but still at only a tiny faction of her normal speed.

So when Kirk says:
Captain's log, Star date 1312.9. Ship's condition, heading back on impulse power only. Main engines burned out. The ship's space warp ability gone. Earth bases which were only days away are now years in the distance. Our overriding question now is what destroyed the Valiant? They lived through the barrier, just as we have. What happened to them after that?

Maye the Enterprise can still travel faster than light, but much slower than when the power supply to the warp engines was functional.

Three) Or maybe the Enterprise has dual mode time warp (as in "The Menagerie") and space warp warp engines, and uses them with both space warp and time warp running when it travels at the upper warp factors. And maybe the Galactic Barrier knocked out the spacee warp mode of the warp engines but left the time warp mode functioning.

So when Kirk says:

Captain's log, Star date 1312.9. Ship's condition, heading back on impulse power only. Main engines burned out. The ship's space warp ability gone. Earth bases which were only days away are now years in the distance. Our overriding question now is what destroyed the Valiant? They lived through the barrier, just as we have. What happened to them after that?

Maybe the Enterprise can still travel faster than light to Delta Vega, but much slower than when both the space warp and the time warp are running.

Four) The mention of "our time warp, factor seven" in "The Menagerie" indicates that time warps can be generated. So even if tthe Enterprise in "Where No Man Has Gone Before" doesn't use time warps in its warp drive, it might be able to generate time warps using some other devices, for some purposes. So possibly the the Enterprise took days or weeks to travel to Delta Vega using the slower than light impulse engines, but used a time warp to slow down time within the saucer section and the sick way where Mitchell was so that only a few hours passed instead of the days or weeks that passed outside the aea in the time warp.

SPOCK: We'll never reach an Earth base with him aboard, Jim. You heard the mathematics of it. In a month he'll have as much in common with us as we'd have with a ship full of white mice.

MItchell almost became too powerful while developing his powers for only a few hours after that meeting according to the stardates. So if it took days, weeks, or months to reach Delta Vega they would have had to slow down the passage of time about the ship using some sort of time warp so that only a few hours passed aboard.

Five) Or as I suggested above, maybe the Valiant used old "impulses warp drive engines" for faster than light travel. And maybe the Enterprise has has a much more recent generation of warp drive engines to power the warp drive, and some backp old "impulse warp drive engnes" which are usually called just impulse engines, and which are usually used for slower than light travel but can be used for faster than travel, even if much slower than the later generation main warp engines.

Six) Or, as I suggested above, maybe both the Valiant and the Enterprise have faster-than-light capable impulse engines totally different from warp drive engines. The has only impusle engiens, and so has to use the impulse engines for faster than light travel. But the Enterprise has both impulse engines and warp engines, and so usually uses the warp engines for faster than light travel, since they are superoor for that, and ususally uses the impulse engines for slower than light travel because they are better for that. But the impulse engines of the Enterprise can be used for faster than light travel in an emergency, and the Enterprise uses them to travel faster than light to ge to Delta Vega before Mitchell becomes too powerful.

Seven) Maybe the voyage to Delta vega took days or weeks,and Mitchell's powers developed greatly during those days or weeks. And only a fraction of a stardate unit changed during those days of weeks, since at that time there were many days in a stardate unit for some reason. And then as they reached Delta Vega, for some reason the ratio of stardate units to days changed, and there would be a few stardate units in a day aboard the Enterprise and on Delta Vega. I note that my pos tnumber 9 above discusses thepossilitity of the ratio between stardate units and units of time changing,and suggested a reason for such a stardate unit, reason which could have helped the SS Valiant get to delta Vega without being pushed all the way by a magnetic storm.

And I note that possibilites one, five, six, and seven are consistent with the Valiant reaching the edge of the Galaxy hundreds or thousands of light years from Earth under its own power without being swept from the Solar system to edge of the galaxy by a highly implausible magnetic storm.. The miniumum magnetic storm I suggested is implausible enough.

As I said there are some spsce phenomena which can accelerate charged particles to almost the speed of light. But there is a big difference between accelerating many tiny chargde particles to almost the speed of light and accelerating a massive starship to speeds many times the speed of light.

I think that powrful magnetic storms would highly detectable if they existed in our galaxy. Phenenomena which accelerate charged particles are lot like hypothetical charged particle weapons. If someone fired a powerful charged particle ray gun in Earth's atmosphere the charged particles will strike gas molecules in the air and would excite them to emitt radiation at various frequencies from radio to visible to X-Rays to Gamma rays. The cylinder of air struck by the charged particle ray would glow in many frequencies and would look a lot like a phaser beam.

But there aren't any gas molecules in interstellar space for a charged particle beam to strike. Thus nobody could see a charged particle beam in outer space from the side, because the cylindrical space occupied by the beam wouldn't be glowing in infra-rad, uLtraviolet, or visible light, but would be totally invisible from the side. Right?

Actually there is extremely rarified gas and dust in interstellar space, which will glow in many frequencies if struck by a strong enough beam of light or of charged particles.

And contempory enthusiasts for the concept of particle beam weapons would probably go crazy with frustration if they knew that somewhere in the universe there was an incredibley, unbelieveably, powerful particle beam that makes any built on Earth seem infinitely weak by comparison..

Here is a link to images of the jet of M87.

https://www.astrobin.com/244741/

Notice that it is viewed from the side and is visible. If it was pointed straight at us it would look like a point of light.

The German-American astronomer Walter Baade found that light from the jet was plane polarized, which suggests that the energy is generated by the acceleration of electrons moving at relativistic velocities in a magnetic field. The total energy of these electrons is estimated at 5.1 × 1056 ergs[92] (5.1 × 1049 joules or 3.2 × 1068 eV). This is roughly 1013 times the energy produced in the entire Milky Way in one second, which is estimated at 5 × 1036 joules.[93]

So charged particles accelerated to almost the speed of light and colliding with the intersellar medium do emit visible light, as well as X-Rays and radio waves.

The interaction of relativistic jets of plasma emanating from the core with the surrounding medium gives rise to radio lobes in active galaxies. The lobes occur in pairs and are often symmetrical.[106] The two radio lobes of M87 together span about 80 kiloparsecs; the inner parts, extending up to 2 kiloparsecs, emit strongly at radio wavelengths. Two flows of material emerge from this region, one aligned with the jet itself and the other in the opposite direction. The flows are asymmetrical and deformed, implying that they encounter a dense intra-cluster medium. At greater distances, both flows diffuse into two lobes. The lobes are surrounded by a fainter halo of radio-emitting gas.[107][108]

https://en.wikipedia.org/wiki/Messier_87#Jet

In 1947 M87 was discovered to be one of the strongest sources of astronomical radio waves, after the Sun. M87 is a giant galaaxy about 52 to 55 million light years from Earth.

No physicist would think that the jet of M87 could be strong enough to accelerate a starship like Valiant to many times the speed of light.

If a magnetic storm was in our galaxy 53,000 light years away, it would be as strong a radio source as seen from Earth as M87 even if it emitted only 1 millioneth as much radio energy as M87.

If a magnetic storm was in our galxy 5.3 light years away, it would be as strong a radio source as seen from Earth as M87 even if it emitted only 1 hundred trillioneth as much radio energy as M87.

So the idea that magnetic storms capable of pushing starships faster than the speed of light for hundreds or thousands of light years from the Solar System to the edge of the galaxy would not have been detected already if they existed in our galaxy is not rational or plausible.

To say nothing of what would have happened to Earth if such a powerful magnetic storm came close enough to carry the Valiant all the way from the solar system to the edge of the galaxy.
 
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In post number 1 in this thread, and in post number 1 in the thread https://www.trekbbs.com/threads/distance-speeed-and-time-in-tmp.312160/#post-14252735 I mentioned a theory to explain the many problems with the "galactography" of Star Trek and the many distance, time, and speed pardoxes in Star Trek.

That theory is that sometmes starships use their warp drive to taravel all of the distance betwen Star A and Star B, but often, especially for longer voyages, they travel though a system of wormholes, gateways, space tunnels, portals, or whatever you want to call them. They can enter a mouth of the phenonemon in one star system and instantly appear in another mouth of the phenomenon in another star sytem. And maybe they can make a short voyage in that system to enter the mouth of another such phenonomenon and instantly emerbe from the other mouth of the second phenonomenon in a third system, that of Star C. Thus by leapfrogging, or side stepping, or avoiding, travelling though all the space betweent star A and Star C they can reach star C in much less time that it would take if they traveled the entire distance in space between Star A and Star C.

And one time i was watching "The Galileo 7" where Kirk takes the time to study a "quasr like phenomenon" even though the Enterprise is involved in a mission to carry medicines to a plague stricken world.

FERRIS: I remind you, Captain, I'm entirely opposed to this delay. Your mission is to get those emergency medical supplies to Makus Three in time for their transfer to the New Paris colonies.
KIRK: No problem, Commissioner. And may I remind you that I have standing orders to investigate all quasars and quasar-like phenomena wherever they may be encountered. Besides, it's three days to Makus. And the rendezvous doesn't take place for five.
FERRIS: I don't like to take chances. The plague is out of control on New Paris. We must get those drugs there on time.

So the Enterprise picked up the drugs at a planet A, and is going to take the drugs to Makus Three, and wait for about two days there,and then transfer the drugs to another ship which will take them to New Paris . Apparently the Enterprise will lhave to wait at Makus Three for the other ship to arrive, and then transfer the drugs to the other ship. I can't see why the Enterprise couldn't just simply take the drugs straight from Planet A to New Paris, and skip the rendezvouz at Makus Three.

And then I thought of that theory of the space shortcuts, and thought of a variation on it.

Possibly the system of space shortcuts isn't always arranged the same, Possibly, for some reason, the system periodically rearranges itself. So the shortcut which once led from system 1 to system 2 now leads to system 3. And maybe in the future that shortcut will switch to lead to system 4, and so on, before eventually switching back to leading to system 2 again. And possibly all of the shortcut system switches destinations at the same time.

Or maybe the system of space shortcuts switches on and off periodically, so it can be used to travel thorugh many star systems rapidly when it is switched on and won't take you to even a single star system when it is switched off.

So maybe the parameters of the system of shortcuts was such that it woudn't be possible for the drugs to get to New Paris any sooner than the second ship arived to take them after picking them up at New Paris. Perhaps in two and a half days the parameters of the system would change, and the Enterprise would then be able to reach Makus Three in half a day, making Kirk's three days the earliest possible arrival time. And then maybe they would have to wait another two days at Makus three for the second ship to arrive and have a fast route to new Paris.

That still doesn't explain why the Enterprise couldn't wait two days at Makus Three for the system to change and open up a fast route for the New Paris and then take the drugs there themself, instead transferring the drugs to a second ship to take them to Makus Three. I can't imagine any spatial arrangement of the planet the Enterprise picked up the drugs at, New Paris, and the original location of the second ship that make the drugs get there faster by transferring them between the two ships. But at least it would explain why Kirk had time to spare investigating Murasaki 312 instead of hurrying to meet the other ship sooner at a place closer to New Paris.

And some time laker I was thinking about stardates and my opinion that stardates are not necessarily related to Earth time units. Maybe stardates are connected to time units more important to Starfleet and other space travellers. And the thought occured to me that possibly the length of stardate units was connected to the length of time that the system of shortcuts through space maintained the same configuration - the interval between successive changes in the configuration of that system.

It would be handy to have a quick reminder of what configuration that system of spatial shortcuts was in at the moment. That way a captain could avoid embarrassng himself by ordering a trip from Planet D to Planet E, thinking it will take only three hours, only to be told that with the current arrangement of the system of space shortcuts it will take 2 years to get from system D to system E, and they wil lhave to wait for the system to rearrange itself for the short route to system E to be open.

So I decided it was possible that the stardate system was devised to make it easier to tell what configuration the system of subspacial shortcuts was arrainged in at the moment.

Adn then, on Teusday, August 29, 2022, I wrote post number 9 in this thread discussing a different theory to explain the speed, time, and distance paradoxes. And I wrote in part:

Languages change over time, and the "date" in a "stardate" might not mean a date as we think of a date. And even if the "date" in "stardate" means a date in time, it could mean the date in time when a specific scientific factor has a certain value, the numerical value of the number in the stardate. Thus a stardate 1313.13 might be the date in normal time when factor X has a value of 1313.13, and a stardate 4444.4 could be a date in normal time when factor X has the value of 4444.4.

And factor X could change with time, so that it would increase at different rates at different times, and maybe even decrease at various rates at different times.

And I thought that possibly factor X which changed over time, could be the arrangement of the system of space shortcuts that enabled a starship to go from Star A to Star B without travelling through all of the space between them, and thus getting there much faster than if it travelled through all that space even at its highest warp factor.

So possibly sometimes the interval between successive switching of the system of space shortcuts could 1.2 Earth hours, and sometimes it could be 7.5 hours, and sometimes 1.25 days (30 hours), and sometimes 15.4 hours, and sometimes half an hour, and so on.

And the stardate would increase by one digit every time the system changed, so sometimes a stardate unit might be 1.2 hours, sometimes 7.5 hours, sometimes 30 hours, and sometimes 0.5 hour,and so on.

I think that a year or two ago I started a thread about time in TOS. And one of my concerns was the ratio between stardate units and time aboard the Enterprise. I only did the first season and 1 episode of the 2nd season. I found that some episodes didn't have enough evidence to calculate such a ratio, most had evidence sufficient to calculate only a very broad range of possible ratios, and four had evidence to deduce rather narrow ranges of possible ratios. And if I remember correctly, those four rather narrow ranges of possible ratios didn't overlap at all.

And so on Tuesday, August 29, 2022 I suddenly had an eureka moment. Possibly the length of a stardate unit varies with time to mark the rather irregular intervals between successive changes in the arrangement of the hypothetical system of space shortcuts and thus in the voyages it will be possible to make at the moment. And I couldn't help feeling stupid for not thinking of such a simple and obvious theory decades earlier.

Of course with a possible theory why the period of a stardate unit varies given in post number 9 and a different theory for why the period of stardates units varies given in this post, someone might despair at the thought that stardates change randomly, with no rhyme or reason.

Here is are links to images of sine waves:

https://www.investopedia.com/terms/s/sinewave.asp

https://commons.wikimedia.org/wiki/File:Simple_sine_wave.svg

http://www.maxmcarter.com/sinewave/fatter_trace.html

Notice that they don't have the same shape. There is vast variation in the possible shapes of sine waves representing fluctuations in a variable.

Suppose that the period of a stardate unit depends on a factor which varies according to a sine wave. In that case it should be rather easy for Starfleet to calculate the sine wave and then predict the value of the factor at specified future times,and plot out the future relationship between stardates and the time on shps and planets.

But maybe several factors affect the period of the phenomenon that stardates are linked to. Suppose those different factors vary according to sine waves with different forms. When different sine waves are superimposed on each other, they create a very wierd looking wave that seems totally chaotic and unpredictable. But I expect that a somewhat more complicated mathematical analysis could find a formula for the compound sine wave and predict the future changes, and thus the stardates linked to them, before they happen.
 
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I can't see why the Enterprise couldn't just simply take the drugs straight from Planet A to New Paris, and skip the rendezvouz at Makus Three.

A simple answer could be that New Paris is outside of the Enterprise's assigned patrol zone. It seems to be similar to the scenario in "Obsession" where the Yorktown is to transfer vaccines to the Enterprise to take to Theta Seven. With the Enterprise ending up almost 2 days late for the rendezvous then Yorktown could've used those days to take the drugs to Theta Seven on her own. But since we know ships have their assigned patrol zones that could prevent them from leaving those zones as they would likely need another ship to be available to cover for them.
 
The Starship schedule is a serious and critical factor for Starfleet. An early example is from Conscience of the King:
Captain's log, star date 2817.6. Starship Enterprise diverted from scheduled course. Purpose, to confirm discover by Doctor Thomas Leighton of an extraordinary new synthetic food which would totally end the threat of famine on Cygnia Minor, a nearby Earth colony.
KIRK: You mean to tell me you've called me three light years off my course just to accuse an actor of being Kodos?
LEIGHTON: He is Kodos. I'm sure of it.
KIRK: You said you discovered a new food concentrate. What am I supposed to put in my log, that you lied? That you diverted a starship with false information? You're not only in trouble, you've put me in trouble, too.
...
KIRK: And I have to get back to my ship and figure out how I'm going to enter all this in my log.
(later)
SPOCK: I have no information on that, Captain. We are ready to leave orbit.
KIRK: We'll delay departure for a time. I'm beaming back down to the planet.
(later after Tom Leighton is dead)
SPOCK: Ready to resume course, Captain.
KIRK: I think we're due for a pick-up.
...
KIRK: Mister Spock, prepare to leave orbit as soon as the Karidian company is aboard the ship.
(Lenore and her escort enter the turbolift)
SPOCK: May I inquire as to our course, Captain?
KIRK: Benecia Colony.
SPOCK: Benecia Colony is eight light years off our course.
KIRK: If my memory needs refreshing, Mister Spock, I'll ask you for it. In the meantime, follow my orders.
Kirk is first upset that he was diverted only 3 light years off-course, then later, Spock wanting to get back on course and then concerned over another 8 light years off-course (even after a murder of the person whom diverted the ship in the first place). Yikes, the ship's schedule is more important than solving a murder mystery and worrying about ending your career if you miss it. Orders are orders!:vulcan:
 
did a bit of flying years ago
say a aircraft travelling at 100 miles hour known as true air speed according to aircraft gauges
with a headwind of 20 miles a hour so over ground (known as ground speed )it is now doing 80miles a hour
with a tailwind 20 miles a hour so over ground is now doing 120 miles a hour ,note gauge speed has not changed(100miles hour)so as pointed out above different area of space may have a different effect on warp speed numbers
 
Trek ships move at the speed of plot. (Whatever the official warp scale happens to be). For Voyager it was important that the crew be faced with a very long trip home.
 
Here is another theory to explain the speed, dstance, and time paradoxes in Star Trek.

The closest thing in real science to the fictional warp drive is the highly theoretical Alcubierre drive. And it may be noted that the theoretical Alcubierra drive would pick up particles in its warp bubble as it traveled through space.

Brendan McMonigal, Geraint F. Lewis, and Philip O'Byrne have argued that were an Alcubierre-driven ship to decelerate from superluminal speed, the particles that its bubble had gathered in transit would be released in energetic outbursts akin to the infinitely-blueshifted radiation hypothesized to occur at the inner event horizon of a Kerr black hole; forward-facing particles would thereby be energetic enough to destroy anything at the destination directly in front of the ship.[38][39]

https://en.wikipedia.org/wiki/Alcubierre_drive#Damaging_effect_on_destination

This is another example of how a highly advanced spaceship could be used as a weapon, even if it wasn't equipped with weapon systems.

One way to avoid destroying the destination would be to make a U turn right before reaching the destination and then turn off the Alcubierre drive, thus shooting the destructive radiation back the way you came instead at at the destination.

Another way would be to turn the Alubierre drive on and off fairly rapidly during the trip to dischage the acquired particles fairly often, and thus to avoid building up a major accumulation of them to discharge at the end of the voyage.

Since the theoretical Alcubierre drive is the closest thing to Star Trek warp drive in science, it seems fairly possible that the warp bubble of a starship using warp drive would also sweep up much matter and radiation during a warp drive voyage.

And in any case interstellar matter should interact via electromagnitism and gavity with matter - such as a starship and interstellar matter near to it - inside the moving warp bubble of the starship. And it seems probable that such interactions between rapitidly moving matter and slower moviing matter might result in a transfer of momentium between them, thus accelerating the matter outside the warp bubble and slowing the matter inside the warp bubble, slowing down the starship.

And thus it is possible that a starship at warp in a pure vacuum would travel much faster than a starship in interplanetary, interstellar, or even intergalactic, space, because the extremely rarified matter in space will slow down a starshp and its warp bubble passing through.

And possibly the actual speed of a starship is extremely sensitive to the density of matter, so that even the extremely minor differences in the density of interstellar matter compared to, for example, air, will make important differences in the velocity of a starship.

So possibly a starship travelling in a vacuum would travel much faster than at its warp scale. Posssibly warp scale is an average speed for a warp factor. In space in Earth's region of the galaxy, the average velocity of a starship at warp factor 3 in the TOS scale will be about 27 times the speed of light, but a starship at warp factor 3 can travel many times as fast in regions of low density and only a fraction as fast in regions of high density.

And possibly interstellar civilizations are not satisified with the natural low density regions of space, but create their own even lower density regions of space to enable starships to travel much faster than even in the lowest density natural regions.

An Alcubierre drive would sweep up interstellar matter as traveled interstellar space. So if an Alcubierre drive starship travels in the precise path that another Alcubierre drive ship travelled earlier, it should travel through a total vacuum emptied by the previous ship.

I don't know whether a Star Trek warp drive starship would sweep up interstellar matter like an Alcubierre drive ship. But even if it wouldn't, perhaps there are special starships designed to clear vacuum corridors and open up fast space lanes.

We could call those special starships vacuum cleaner starships, since they clean up the interstellar matter or "dirt" and make intersellar space a truce vacuum.

A vacuum cleaner starship could have a powerfull antigravity generator installed, which repelled interstellar matter from its position. Thus as it travelled between Star A and Star B, it would repell matter away from the cylinder of space it traveled through, creating a widening cylinder of pure vacuum, where starships could travel at the fastest possible speeds for their warp factors.

So if an interstellar government claimed both Star A and Star B, it would broadcast a claim to rule all space within a radius of - for example - one light year from each of those stars. And if it sent vacuum cleaner starships between Star A and Star B to clear a cylinder of space between them of all matter so travel would be very fast between them, it would also claim a cylinder of space around the the space lane it created, and ships from other rralms would need permission to use that space lane without being considered hostile.

I don't know how wide an area would be cleared around the path of a vacuum clearner starship, so I don't know how wide the cylinderical space that would be claimed would be. Maybe 10 percent of a light year in diameter, maybe 1 percent, maybe 0.01 percent, or whatever. A cylinder 1 Astronoiical Unit (AU) in diameter would be very wide by human standards, about 93,000,000 miles, or precisely 149,597,870.7 kilometers, which would be very difficult to clear of all interstellar matter. But it would be only 0.0000158 of a light year.

So a map of a space grovernment might look like a bunch of bubbles floating in three dimensional space, with very thin cylinders of space connecting them, somewhat like some models of molecules.

And possibly some space governments occupy highly overlapping volumes of space without much problems. It might take a year to travel through uncleaned space between a star belong to Realm A and a star belonging to Realm B that is only 5 light years away, while it might take only a week to travel 100 light years thorugh the cleaned space in the space lanes.

And of course since intersellar particles have many different velocities in space, eventually some will drift back into a cleaned space lane. Eventually travel in the space lane will become slow enough that a space vacuum cleaner ship will have to make another voyage thorugh the space lane to clean it again.

Since stars orbit the galactic center, the direction between two stars slowly changes. So the mouths of the cleared space in a space lane will slowly move relative to the two star systems it connects. As time passes, a starhip leaving system A will have to make aslight detour to reach the mouth of the cylinder of cleaned space and enter it, and when it exits from the cylinder of cleaned space at the other end it will have to travel a distance to catch up with System B.

Eventually the two systems will move far enough from the mouths of the cylinder of cleared space that a space vacuum cleaner ship will have to make a new cylinder of cleared space between the two stars. This should happen much less often than clearing the space lane of interstellar particles which drifted into it.
 
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Another good idea. Just think if you put an enormous matter deflector on your Starship to self clean out space in front of the ship...
 
Another good idea. Just think if you put an enormous matter deflector on your Starship to self clean out space in front of the ship...

Yes but a deflector probably only clears out a tunnel with about the width and height of the starship, or of the warp bubble, And I was thinking that those space clear ships could clear out a much wider tunnel thourgh space, with space for starshps to pass each other, etc., and with it taking much more time or space dust to drift back in.
 
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