Sorry about that; I mistakenly plugged in 1,000,000 instead of 500,000. Those earlier numbers were correct, and not quite so close to the calculator's limits. The acceleration is 20.923425515 g. with a maximum speed of .999,999,999,999,982,9 c.

I wanted to edit that last post to strike out the wrong part. Apparently, there ain't much you can do to edit a post, is there?

The "time on earth" part of the calculator says, "500,000.092622 years, which is just 33.8 days longer than it took for the light pulse which left at the same time as the ship to reach Midway in Earth coordinates. That represents the time it takes for the ship to reach Midway (500,000 ly from Earth) in Earth coordinates.

For an Earth-based observer 500,000 years after launch, the ship is just 33.8 light-days behind the light flash that left Earth at launch time. So the next light flash from Earth must now be 0.907378 ly, or 331 light days, behind the ship, in Earth coordinates. In other words, the ship crosses Midway long before the next flash from Earth is seen from the ship. The light flashes from Earth are redshifted and stretched farther apart, but not uniformly so. The distance between flashes from Earth, in ship's coordinates, varies because Earth clocks (and the Earth year) gradually got slower as the ship accelerated. As Earth clocks got slower, the flashes were emitted less often, in ship's coordinates.

No light flashes from Earth pass the ship before Midway; only two flashes pass the ship after it Midway; the third flash just catches up at Planet X. That third flash from Earth tells Planet-Xians to celebrate the year 1,000,003. (They set their clocks at 0, not 3000, at liftoff from Earth.) In Planet X coordinates, same as Earth coordinates, Earthians are celebrating the year 1,003,000; I guess there was a slight delay from the original launch schedule.

The flashes passing the ship from Planet X are blueshifted and pancaked together, from the ship's perspective, as the relative speed increases. This is the inverse of the redshift behind the ship. At Midway, the ship has passed 500,000 light flashes from Planet X. Flash #500,001 is just milliseconds ahead. For a while, flashes from Planet X pass the ship in rapid succession. Deceleration gradually stretches the flashes farther apart, so the ship passes them less often. They arrive just as the 1,000,003rd flash is being sent.

What I'm looking for is, what is the time on Earth and on Planet X in ship's coordinates when the ship crosses Midway?