The other modes aren't too bad, but Epicycles is extremely tricky. Doing well in this mode actually requires a basic understanding of orbital mechanics, which are extremely unintuitive to humans. To use a physics term, when you are in orbit you are not in an "inertial frame of reference". Objects near you behave strangely, and (from your point of view) they do not satisfy Newton's first law (moving in a straight line with constant speed). Also, it doesn't help that the line which projects your path ahead of you is in relation to the "sun", when for most of the time you are actually in orbit around the "planets", making it somewhat useless. (What would be a lot more helpful is a point of view that assumes the "planet" stays still and projects your orbital path around it... but you don't have that.)
So you're mostly on your own, and you'll need to understand a little about how orbits work to navigate. You don't need a physics degree, but you might want to, say, read the Wikipedia article on "orbital mechanics". And, of course, practice helps a lot, since most of us don't pilot spaceships in everyday life. :)
Important facts:
- Every orbit is an ellipse with only two important parameters: "energy" and "eccentricity" (how elongated the ellipse is). You're pretty much a prisoner to these two values; you can't cheat without wasting a LOT of energy.
- Smaller circular orbits have less energy (since you're closer to the planet), larger circular orbits have more. Elliptical orbits have about the same energy as an averaged circular orbit.
- Thrusting along your movement vector adds energy to the orbit. Thrusting against it removes energy from the orbit. Thrusting directly towards or away from the planet DOES NOT change the energy, but affects the eccentricity a lot. So unless you specifically want to get into/out of a very elliptical orbit, in general you shouldn't do this. Stick to firing forwards and backwards only.
- It bears repeating because it's so strange: if you're trying to get closer to the planet, DON'T thrust towards it! The more you try, the more eccentric your orbit will become, probably against your wishes. Instead, gently thrust against your movement vector to leech energy away from your orbit; when you're at the desired distance, thrust in the direction of motion to make your orbit circular again. (This is a "Hohmann transfer orbit"; Wikipedia it.)
- Similarly, to move further away from the planet, thrust in the direction you're moving; at the desired distance, thrust against your motion.
- Objects in a smaller orbit (closer to the planet) move faster. Objects in a larger orbit move slower. If you're trying to reach an object closer to the planet than you, let it catch up. If you're trying to reach an object further from the planet than you, catch up to it. Trying to do anything else will waste a lot of energy, might not work, and could even leave you falling into the planet with a ruined orbit. :)
- Trying to hit something by thrusting towards it only works if it's close to you and in roughly the same orbit. Only do this for fine-tuning.
- To leave the planet's orbit, use the sun. Thrust in the direction of motion when you're further away from the sun than the planet; this will create an elliptical orbit that brings you close to the sun, which will then capture you. (And once you're orbiting the sun, the path prediction line becomes useful again. :)
- Even if you want to get to another planet, it's easiest to get into the sun's orbit first, then approach the other planet in the usual way.
With those basics down, here's my overall strategy:
1. Gobble up the moons circling your current planet as quickly as possible. Intentionally creating a very elliptical orbit helps with this, as it will intersect a lot of their (mostly circular) orbits. Speed up time until something comes close, then slow down time and do some fine-tuning to gobble it up.
2. Switch orbits to the sun. Hopefully you've done #1 fast enough that there are still some objects circling it that are small enough to gobble up. Use cautious circular orbits to collect them without hitting anything else. If you're lucky, they'll be able to step you up in size until you can eat almost everything surrounding the sun.
3. Switch orbits to the largest attractor, eat everything orbiting it, and then gobble it up.
4. You should be large enough to eat the central sun at this point. Eat it.
5. The remaining attractors should now hit the sides and be destroyed.
6. ???
7. Profit!