Bouncing around at cosmic speeds

When I began reading a lot of science fiction in the 1960s, my local library had a great collection of the S.F. classics, including a set of E. E. "Doc" Smith's books Skylark of Space and the Lensman series. I remember being quite taken with the concept of the "inertialess drive" that allowed travel at speeds much greater than the speed of light. In one scene, a Lensman explains to a dance partner how traveling at 30-40 parsecs per hour can be compared to her experience of driving a motorcar at speeds of 30-40 miles per hour.

Doc Smith had given some thought to the implications of turning inertia on and off. In just a few scenes, two spaceships meet and must transfer personnel. They don't want to cancel initial velocities of the ships, so they just do it for the passengers. The notion is that when inertia is restored, the ship instantly takes on the velocity it had when its inertia was turned off. So do its passengers. Each one ship carries a compensator, a huge chamber with lots of bungees or some such inside. People go inside, the inertia is turned on, and they bounce around for a while. Then they can safely enter the other ship, the one the compensator came from.

I suffer from too much knowledge. I didn't think this through when I was fourteen years old. Now I know some physics. It turns out the compensator will have to be really, really big. The equations of motion we need are

v = a t (acceleration times time), so t = v/a
d = ½a t²

A well-conditioned person can tolerate 6 G's for a little while. Let's call that our maximum acceleration, which comes to 58.8 m/s².

Planetary speeds are great, and stellar speeds are greater. Start out with the speed of Earth in its orbit: just under 30 km/s, or 30,000 m/s. OK, you have traveled from Earth to near Pluto, which is moving much more slowly. You need to cancel out a 30 km/s velocity difference. First calculate the time: 30,000/58.8 = 510 seconds, or 8½ minutes. How far do you go while you are slowing down? The distance is ½(58.8)(510²) = 7,650,000 m or 7,650 km. That is quite a bit more than the radius of Earth.

Going to another star? Some of them are going at speeds comparable to Earth orbital velocity, or even slower, but not all. Arcturus, for example, has a speed relative to the Sun of 122 km/s. How to compensate for that kind of velocity? The time is 122,000/58.8 = 2,075 s, or more than 34½ minutes. I think 34½ minutes, and probably even 8½ minutes, at 6 G will do some damage, but let's find out the distance covered anyway: ½(58.8)(2075²) = 126,600,000 m, or 126,600 km. That's a third of the Earth-Moon distance!

Kind of a spoiler, isn't it? An interia compensator would have to be, not a big chamber with bungees, but a substantial rocket with fuel enough to blast at 6 G's for half an hour…or more! And then to bring you back to the ship you need to board, presumably at lower G so you can recover. That would take a few more hours. Ah, Doc, I love ya, and I sort of wish I didn't grow up.