If you angle the sail to send light in front of you, you will speed up and fall towards the Sun. If you angle the sail to send light behind you, you will slow down and move away from the Sun. Aim to either side and you will move away from the light and also move up slightly. Between these effects you can manage to get from any orbit you might be in to any other possible orbit. It will just take a while.
This is all assuming that there is not enough force from reflecting the light back into the Sun to beat the Sun's gravity.
This is a kind of thing that is totally counterintuitive until you spend a few (dozen) hours in Kerbal Space Program. Basically keep sails angled at 45 degrees so that the light reflects in the direction you're moving, and you'll be getting closer and closer.
It wouldn't be called "the satellite paradox" if it did what you would naively expect. :-)
If you have 2 objects in the same orbit and one accelerates backwards, that one winds up below and in front of the first. This happens because accelerating backwards causes it to lose energy, so it falls, and in falling picks up more kinetic energy than it had before.
It depends on the frame of reference. Obviously we're talking about a solar reference frame here with respect to linear velocity (it's the only other object), but it will also be rotating.
If the reference frame is initially rotating at with your orbit or a closer one, "speed up" is accurate. If it's rotating with some more distant orbit, "slow down" is accurate.
This, by the way, is one reason why physicists tend to just say "accelerate" in both cases: then, it's technically true for any external reference frame.
There's gravity from the sun but not the planet, and yes, that ought to be worth adding. I'm not sure what'd help the most to turn this into a fun game, though, so I'm working on other things. Thanks for the suggestion; a time control's probably a good idea too.
Ah yes some kind of normalization for the sail's velocity would be cool. The whole systems dynamics gets a lot slower as you get away from the sun, so it gets frustrating to see what happens with those; and it is hard to execute manuevers near the sun. (Maybe normalize for constant angular speed and display e.g. 'Time at 3.5x'?)
You can angle the sail to be close to your retrograde vector, which will allow you to decrease your orbital altitude around the sun. You could use this to move closer to the sun or to the inner planets (or to return from a distant mission).
On the other hand, you have a constant accelleration towards the sun, so you can use parabolic orbits to move sunward (at least, until you reach Voyager I).
Are you sure about this? If you have a sail in a heliocentric orbit, I would think you could increase or decrease your orbital speed based on the direction you deflect the solar wind, thus slowly increasing/decreasing altitude. I would assume it's possible to modify orbits around other bodies in a similar fashion.
Indeed. To explain the technical term, retrograde is the reverse of where you're going (where your velocity vector is pointing). Accelerating retrograde (against the direction of your movement) = dropping your current orbital velocity = when you "slingshot" to the other side, you'll be closer to the Sun.
Of course, no spacecraft will ever be at rest with regards to the Sun -- it would take 30km/s of delta-v to get there, and there's rather little point. They will be orbiting, starting from leo, which means that the meagre acceleration from a sail is more than enough to get basically anywhere.
