Hitching a ride on a black hole, part III: Edge of your seat
Last time we designed our literal-star-drive-based space ship:
and figured out that to provide 10g of acceleration in the frame of the star while surfing its gravitational wake in free-fall, we would have to trail the star drive by about a million kilometers (or miles, the calculations were not very precise). We also noticed that the tidal gravity from the star limits the size of the crew module to tens of kilometers, or the size of a really small moon, like Phobos. Anything larger is going to be stretched beyond breaking point and ripped into pieces. This size is certainly nothing to sneeze at, but it has certain limitations. For example, if you want to travel comfortably without leaving your home planet and instead use it at the crew module, it is probably too large to remain in one piece. So even the largest possible crew module does not provide enough natural gravity to feel comfortable.
Of course, gravity does not have to be natural. One can always produce enough centrifugal forces by spinning the module fast enough. Many sci-fi stories rely on that. A ring of 1 km in radius only needs to make a full turn once a minute to give the illusion of 1g gravity on the inside of its surface. “Only”? Seems a bit dizzying, to see the world around you complete a full rotation in barely one minute. Just over 3 min for a 10 km ring. Still not a lot of fun. Imagine all those distant stars zipping around you every minute. So, just for fun, let’s consider other alternatives. After all we’ve been playing with gravity for some time in this series, why stop now?
But first… Let us return to the issue of stability. If you ever surfed, skied or even walked (and I hope you have done at least that last activity, otherwise you are probably just a brain in a jar), you realize that it requires some effort to remain on the sweet spot of the wave. If you goof, you are either too far down or too far up and probably off your board. And that’s assuming you don’t fall over sideways. This is because the equilibrium you achieve is unstable. It’s more like balancing a long stick vertically on your finger than holding it hanging down. You can do it, but you have to constantly compensate for the damn thing trying to fall. It is the same with our star-drive setup. If the crew module lags a bit behind the sweet spot, it would tend to keep lagging farther and farther, until it is left behind in the darkness, forever lost. If the crew module slides a bit forward, the star’s gravity will pull it harder and it will plunge toward it and disintegrate in the short order, which is also a suboptimal outcome. So we have to maintain constant vigilance and compensate for random deviations from the optimal surfing location. How would we do that? One obvious solution is to have small rocket engines — maneuvering thrusters — to provide course corrections. This means having to carry extra fuel, maintain the engines, etc. While inescapable in other circumstances, using on-board engines for course correction seems a bit silly when we are literally blowing up a star for fuel just ahead of us.
Note that in the diagram above I carefully drew the exhaust skirting the crew module. Mainly because I did not want the crew members to be incinerated by a stream of radiation strong enough to accelerate a star-massed object at freaking 10 gravities! We will get to the question of how terrifyingly awesome this exhaust must be later in this post series. For now let us note that if the star drive goes out of alignment only a little bit and the propellant hits the crew module, the crew does not stand a chance in hell, because hell is what it would feel like for the scant few seconds until they get evaporated. However, in homeopathic doses this same exhaust might be helpful, rather than harmful. (Who said homeopathy doesn’t work?)
If only a small amount of exhaust hits our crew module, it nudges us backward. This can be good if we stray too close to the star. A useful side effect is that it provides some acceleration, which to the people inside would feel like gravity. Isn’t it nice to kill two birds with one stone? Umm, this metaphor might be a bit cruel and dated. Throwing stones at birds might have been considered good clean fun a couple of centuries ago, but not by the enlightened standards of the present day. Anyway, I digress. We want to use a small amount of starlight to stabilize the crew module and to simulate gravity. Again, this idea is not new, using solar sail for interplanetary travel has been discussed for some 100 years. A German-Russian-Soviet scientist and engineer Friedrich Zander was apparently one of the first to do a serious calculation of the solar sail propulsion, during his downtime between designing one of the first liquid-fuel rockets (well, second, after Goddard in the US, but before von Braun in Germany) and figuring out the details of a gravitational slingshot, a now-standard technique for interplanetary travel.
There is at least a couple of ways we can design our solar sail: we can put it in front of the crew module, like a rocket:
or behind it, like a parachute:
There are advantages and disadvantages in both cases, as evident by the fact that both approaches are in use. A parachute-style sail provides stability for free, while a crew module equipped with a reflector would have to be actively stabilized, the way planes and rockets are. On the other hand, a heavy module precariously suspended on something like ropes… What if one of them breaks? And how will they fair while being bombarded by the exhaust rays? In either case, as you can see, the direction toward the star becomes “down”. The preferred location of the crew module would be somewhat ahead of the free-fall point. How far ahead? Not very much. If the star drive provides 10g acceleration, we only need to get to the 11g zone to get 1g apparent gravity. And since the gravitational force is proportional to the inverse square of the distance, we only need to be 5% closer to the star to get that extra 1g, or around 50,000 km closer.
Interestingly, the solar sail provides us something like a neutral equilibrium: if we get closer to the star, its gravity gets stronger, but so does the exhaust density, which also falls off as inverse square of the distance, or close to it. So we still need to do some course correction, but not nearly as much. There are also some other small effects which affect the crew module, like a slight blueshift of the exhaust during the time it took for it to reach the sails, the gravitational effects of the exhaust left behind, and a few others. However, we cannot properly address them without doing a fully general-relativistic analysis, and they are too small to matter, anyway.
So, as promised, we have improved our star ride to make it more stable, easier to control and more comfortable by diverting a tiny fraction of the ejecta toward the solar sail. We have not yet calculated how big or strong the sail would have to be. Hopefully next time. We will also look into how far 10g acceleration gets us and how fast. In the meantime, please feel free to comment or ask questions!