How about discussing the technical details of the voyage of the SS
Botany Bay?
Hunters, target shooters, soldiers, and automatic weapons systems "lead the target". They don't aim at where the target is now, they aim at where the target will be when the projectile arrives there. As different stars orbit around the center of the galaxy, the directions between them change slowly. So if a spaceship is relatively slow compared to the speed of the stars, it has to aim where the destination star will be when the spaceship gets there.
So the SS
Botany Bay would have been aimed at where the destination star would be centuries in the future. But after warp drive was invented, the new warp ships didn't have to lead the target as much for their much faster voyages. So they would not aim as far ahead of the present position of the destination star as the SS
Botany Bay had to, and so they didn't pass close enough to the SS
Botany Bay to detect it.
But as decades and centuries passed, the direction to the destination star slowly inched closer and closer to where the SS
Botany Bay had aimed, and ships headed for that destination star passed closer and closer to the SS
Botany Bay. And their sensors constantly improved and could scan larger and larger volumes of space. And finally the USS
Enterprise traveled toward the destination star with more advanced sensors, and closer to the path of the SS
Botany Bay than ever before, and detected the SS
Botany Bay..
This implies that the USS
Enterprise was traveling from our Solar System, after some rare visit to Earth, toward the destination star of the SS
Botany Bay, when it detected the SS
Botany Bay.
In "Space Seed" Khan Noonian Singh is described as:
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.
MCCOY: The last of the tyrants to be overthrown.
So Khan was overthrown sometime in 1996 SS (in the calendar used in "Space Seed"), and left Earth some time in 1996 SS or later.
In
Star Trek II: The Wrath of Khan, Khan says:
KHAN: Captain! Captain! Save your strength. These people have sworn to live and die at my command two hundred years before you were born. Do you mean he never told you the tale? To amuse your Captain? No? Never told you how the Enterprise picked up the Botany Bay, lost in space in the year nineteen hundred and ninety-six, myself and the ship's company in cryogenic freeze?
So Khan and his "supermen" left Earth in the year 1996 WOK (in the calendar used in
Star Trek II: The Wrath of Khan). If they are the same calendar, Khan left Earth in the same year that he was deposed.
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?
SCOTT: Definitely Earth-type mechanism, sir. Twentieth century vessel. Old type atomic power. Bulky, solid. I think they used to call them transistor units. I'd love to tear this baby apart.
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.
As a historian, McGivers would remember the exact date, or remember an event as being about a numerically significant date. If much faster space travel began in 2015 she would say it was introduced in 2015 or about 2015. If much faster space ships were introduced in 2020 she would say they were introduced in 2020 or about 2020. So I guess that space travel became much faster sometime in the period of about 2016 to 2019 SS (in the calendar used in "Space Seed")
And before about the year 2018 SS, suspended animation was necessary in space travel because it used to take years just to travel from one planet to another.
So perhaps I should refresh some people's memories about distances in space.
A light second is the distance light travels in one second of time, and is 299,792.458 kilometers or 186,282 miles..
There are 60 seconds in a minute, and 60 minutes in an hour (3,600 seconds), and 24 hours in a day (86,400 seconds), and in a average Julian calendar year 365.25 days long there are 31,557,600 seconds.
A light minute is about 17,987,5477 kilometers or 11,180,000 miles. Earth is about 8.3 light minutes from the Sun.
A light hour is about 1,079,000,000 kilometers or 670,600,000 miles. The semi-major axis of Pluto's orbit is about 5.4 light hours.
A light day is about 2,590,000,000 kilometers or 1.609,000,000 miles. The dwarf planet Sedna is currently about 0.52 light days from the Sun.
A light year is 9,461,000,000,000 kilometers or 5,879,000,000,000 miles. Proxima Centauri, the nearest star to the Sun is about 4.24 light years from the Sun.
A basic unit in astronomy is the Astronomical Unit or AU, the semi-major axis of the orbit of Earth around the Sun, though it is now defined as precisely 149,597,870.7 kilometers. A light year is 63,241 AU, and a parsec is 206,284.8 AU.
Since Pluto is not officially a planet now, the longest possible d distance of an interplanetary voyage would be between Uranus and Neptune when they were on opposite sides of the Sun, a total distance of about 49.2 AU. And if you count Pluto as a planet, in the 1990s AD it was actually only about as far from the Sun as Neptune, anyway.
Assume that a spaceship accelerated halfway, or about 25 AU, and then began decelerating in the second half of the journey. If a journey of about 50 AU took exactly one year, the average speed during the voyage would be about 50 AU per year, or 0.13 AU per day. The spaceship would have the average speed at two points during the journey, when halfway through accelerating and when halfway through decelerating. Its top speed would be reached just when it switched from accelerating to decelerating,and would be twice the average speed, or about 100 AU per year.
So the spaceship would change its velocity by 100 AU per year while accelerating, and again by 100 AU when decelerating, for a total capacity of velocity change of 200 AU per year. And if the spaceship didn't acquire any fuel or propellant for the return trip at the destination planet, it would have to bring that along. Thus the spaceship would have a total ability to change its velocity of 400 AU per year.
So if Khan's people hijacked a spaceship with a total velocity change capacity of 400 AU per year or 1.09 AU per day, or 0.04 AU per hour, they could use half of that to accelerate to a velocity of 200 AU per year, coast for many years, and then decelerate as they arrived at their destination. So for most of the trip they would be coasting at 200 AU per year. If they were headed for the closest star Proxima Centauri, at a distance of 4.24 light years or 268,142 AU, it would take them about 1,340.71 years plus years of acceleration and deceleration..
If Khan's people brought along a solar sail or magnetic anchor to decelerate at the end of their journey, they could use all 400 AU per year velocity change to accelerate at the beginning of the voyage. At an average speed of 400 AU per year, a voyage to Proxima Centauri would take about 670.35 years.
I note that the map of our solar system in "The Changeling" shows nine planets in our solar system..The hypothetical Planet Nine recently suggested would be about 400 to 800 AU from the Sun. if an interplanetary voyage from Earth to the as yet purely hypothetical Planet Nine took as little as one Earth year, that would involve speeds eight to 16 times as great as in a one year voyage from Uranus to Neptune when they were on opposite sides of the Sun. A ship built for a hypothetical one year voyage to the hypothetical Planet Nine would require velocity change capabilities of 3,200 to 6,400 AU per year.
Depending on whether Khan's people brought along a solar sail or a magnetic anchor to decelerate, they could have made the voyage at an average speed between 1,600 to 6,400 AU per year. Assuming that the 200 years that they spent in suspended animation was actually between 100 and 300 years, they would have traveled 160,000 to 640,000 AU (2.53 to 10.12 light years in 100 years, 320,000 to 1,280,000 AU (5.06 to 20.24 light years) in 200 years, and 480,000 to 1,920,000 Au (7.59 to 30.36 light years) in 300 years.
I see no reason why interplanetary ships that took years to journey between planets would have much more velocity change ability than required to travel to the most distant planet, the hypothetical Planet Nine, in one year's time and return in another year's time. Any greater ability to change their velocity would be inconsistent with the words of Marla McGivers.
Since a light year is 63,241 AU, light travels 63241 AU per year. Thus speeds of 1,600 to 6,400 AU per year would be about 0.0253 to 0.1012 of the speed of light, two and a half to ten percent of the speed of light. At such speeds time dilation would not significantly change the amount of time elapsed on the SS
Botany Bay during the voyage, as some people have suggested from time to time..