I thought this only affected the free-floating cameras, and not actual ships.
Without doing so would result in a perpetual orbit of the Earth...
Well, yes. The Moon is in orbit around the Earth. One just needs an elliptical orbit to reach the Moon.
I looked up some numbers — not in-depth research, but I found some info on the Apollo 8 mission on Wikipedia. Started with a somewhat-circular parking orbit at about 185.2 km. Orbital velocity was 7.793 km/s. Orbital period was 88.7 minutes.
I parked a ship in Earth orbit at about 185 km. Circular orbit velocity reported by SE at that altitude was 7.79 km/s. Orbital period turned out to be 1hr 28min and some odd seconds. Pretty good so far.
Apollo 8 apparently reached a speed of 10.822 km/s after its transfer orbit burn. That is less than escape velocity.
So I burned (does anybody know the g-forces involved in a Saturn-IV stage burn?) prograde at about 1g. When I got 10.82 km/s, I checked my orbit. I looked a little off, so I burned a little more. I think I should have left it (I'll try it again later), because now my apoapsis was just past the Moons orbit. Turns out my orbital inclination was quite a bit off with the Moons.
Anyway... as you can see from the attached screenshot, I will reach said apoapsis in 5.745 days. I think I am going to scrub this mission, and try better alignment for a Moon intercept. I'm sure nearing the Moon will affect orbital parameters.
Also, it would seem that Apollo 8 performed its Lunar orbit insertion burn at 2 days, 21 hours, 8 minutes into the mission.
Oh... another thing to keep in mind, along with the free-floating camera velocity being dependent on framerate, the free-floating cameras are not affected by gravity, but the ships are. As soon as I shut down the engine, I am decelerating. The free-floating cameras are moving in a straight line (more or less — I know they may be following a planet in orbit).
The mission continues:
As you can see from the system clock, it is now some four and half hours after the first screen shot. The most notable thing is how much I have slowed down already, now only doing 3.14 km/s. I'm also some 68,121 km from the Earth (its center, rather), and was 6,800 km away in the first pic.
Still some five and a half days to apoapsis.
(Note: I did close down the program between posts, and the orbital parameters were slightly different when I fired it up again. Original apoapsis was 423,725.37 km and the period was 11.495 days. After I started it up again, the apoapsis changed to 424,051.75 km and the period 11.508 days. Not much of a change, but I guess that depends on how S.E. stores the parameters. None of these parameters changed, however, during the time it was running.)
One thing I have not checked is if the S.E. clock actually matches the real world clock. I never had any reason to doubt it, so I leave that for somebody else to check.