I read everything. I was trying to be polite, but since you insist: I don't find that argument very persuasive.
All they say at the end is that their heading takes them near "Ceti Alpha." Menkar is 250 LY from Earth, which already visited the farther (and correctly designated) Mira/Omicron Ceti system in TSOP, so I don't find that distance to be suspicious given the Enterprise's speed. I also doubt that Kirk wanted to put Khan & Co. In the main travel lanes. The real stretch is that Kirk had the authority to leave superpowered war criminals alone on a planet at all.
I'll answer you before FormerLurker does, since I will probably be more polite.
When FormerLurker wrote:
To be honest, as far out as the Botany Bay is supposed to have gotten, it couldn't be the Alpha Ceti system anyway.
FormerLurker wasn't referring to the speed of the
Enterprise or the the
Enterprise's ability to reach Alpha Ceti, but the
Botany Bay's speed and ability to reach Alpha Ceti, or anywhere close enough to Alpha Ceti that the course of the
Enterprise after finding the
Botany Bay would take it anywhere "near" to Alpha Ceti.
The distance to Menkar or Alpha Ceti is given as 249 plus or minus 8 light years, or 76 plus or minus 3 parsecs. That is about 241 to 257 light years, or 73 to 79 parsecs. Do you know how many miles are in a light year?
Almost six trillion miles. 5,878,625,000,000 miles to be a bit more precise.
So if Alpha Ceti is about 241 to 257 light years from Earth, and there are about 5,878,625,000,000 miles in a light year, Alpha Ceti should be about 1,416,748,600,000,000 to 1,510,806,600,000,000 miles from Earth.
If one assumes that the
Enterprise traveled 50 to 100 light years from the place where it found the
Botany Bay to Alpha Ceti, the
Botany Bay should have been about 141 to 357 light years from Earth when found by the
Enterprise. Therefore, the
Botany Bay should have traveled about 141 to 357 light years, or about 828,886,120,000,000 to 2,098,669,100,000,000 miles, during the time that it was on its journey.
So how long did the voyage of the
Botany Bay last?
SPOCK: Much older. DY-100 class, to be exact. Captain, the last such vessel was built centuries ago, back in the 1990s.
If the
Botany Bay and other ships of its class were built centuries ago, that should have been less than 1,000 years, and thus the
Botany Bay should have been travelling for less than 1,000 years.
(Kirk uses something metal in his hand to break the glass and open the compartment. The man is slid out on a trolley, gasping and awake. He tries to speak.)
KHAN: How long?
KIRK: How long have you been sleeping? Two centuries we estimate. Landing party to Enterprise. Come in.
KHAN: I remember a voice. Did I hear it say I had been sleeping for two centuries?
MCCOY: That is correct.
KHAN: Captain, I wonder if I could have something to read during my convalescence. I was once an engineer of sorts. I would be most interested in studying the technical manuals on your vessel.
KIRK: Yes, I understand. You have two hundred years of catching up to do.
KIRK: Name, Khan, as we know him today. (Spock changes the picture) Name, Khan Noonien Singh.
SPOCK: From 1992 through 1996, absolute ruler of more than a quarter of your world. From Asia through the Middle East.
This establishes that their belief that Khan and the
Botany Bay left during the 1990s was correct. Thus their earlier estimate of two centuries (200 years) was correct.
Assuming the widest possible meaning of two centuries, and they might have said two centuries if the actual time span was anywhere between 100 years and 300 years. If the
Botany Bay traveled 141 to 357 light years in 100 to 300 years it would have traveled at an average speed of 0.47 to 3.57 light years per year, or 2,762,953,700,000 to 20,928,690,000,000 miles per year.
Was the
Botany Bay, a DY-100 class space ship, capable of such speeds?
SPOCK: A strange, violent period in your history. I find no record what so ever of an SS Botany Bay. Captain, the DY-100 class vessel was designed for interplanetary travel only. With simple nuclear-powered engines, star travel was considered impractical at that time. It was ten thousand to one against their making it to another star system. And why no record of the trip?
MARLA: Captain, it's a sleeper ship.
KIRK: Suspended animation.
MARLA: I've seen old photographs of this. Necessary because of the time involved in space travel until about the year 2018. It took years just to travel from one planet to another.
So the DY-100 class space ships took years just to travel from one planet to anther.
Assuming that it took a DY-100 class ship 1 year to travel to Neptune, the farthest solar system planet presently recognized by the IAU. Neptune is 30.33 Astronomical Units, or 2,819,349,600 miles, from the Sun at Aphelion, when it is farthest from the Sun. If A DY-100 ship traveled to Neptune at Aphelion in one year, stayed there for months or years for research, and returned in anoterh year-long voyarge, the total trip time would be over two years. And the average speed during the voyage to Neptune would be 30.33 Astronomical Units, or 2,819,349,600 miles, per year. About one thousandth of the minimum speed necessary for the voyage of the
Botany Bay to get to a position so far from Earth that Kirk would decide to take the supermen to Alpha Ceti.
This rough calculation should show why some people, like FormerLurker, believe that it would be mathematically impossible for the
Botany Bay to reach a position close enough to Alpha Ceti for Kirk and the
Enterprise to take the supermen to Alpha Ceti.