There isn't a need to [keep the solar panel] pointed at the sun.
Actually, there still is, although it is much easier to do.
I was going to mention Space Elevators, but Maggarg has already done so. Some engineering problems to sort out. Including
over-engineering in order to deal with some of the more obvious dangers from the more obvious failure conditions. (And then some more thought about how to deal with the less obvious dangers... indeed, what the less obvious dangers might be!)
There's a trilogy of books that includes a failure of a non-Terran space elevator system, but to namecheck it would be a spoiler for those not yet having read the series. There are more than enough trilogies that might well qualify against all that I have deigned to describe, and so it causes me absolutely no grief mentioning these bare bones.
Obviously, space elevators are themselves going to take effort to make, so we need to continue with both materials science and space science in order to be able to hoist up the spool of appropriate material (or the means to produce it while up there, from hoisted or captured materials), possibly gather in a suitable counterweight asteroid (if not relying upon accretion of various bits of space-junk onto the hoisting-mission left-overs), and then after the original tether is made taught (from ground to geosynchronous station to counterweight) use whatever we've just created to spin further threads up and down from to create something suitable for heavy lifting purposes.
Though I must admit that the last time I seriously engaged in discussions with various parties (some 'merely' space-interested, some actually space-professionals!) about this kind of project, it was... 1990, I think, so I might be a couple of decades behind in the thinking. IIRC, "carbon nanotubes" were still a little hypothetical (or
very recently confirmed), although I've fairly certain that significant lengths of them (by human scale, never mind orbital ones) remain so to this day.
I think one of the other ideas at that time (that could, even at the time, have been made with existing metal wire technologies) was to have a series of tether-type vehicles in various orbits, spinning two 'arms' of chord around their barycentre as they orbit, such that a high-flying vehicle (e.g. one of these new-fangled Scaled Composites/SpaceShipOne-style craft, lifting to "space, but not orbit") could rendezvous with the lower spinning arm, attach and be dragged up further before being slung onto a meeting with a higher-orbiting construct of a similar nature, and perhaps a further slingshot or two after that...
The slingshot-sats, themselves, would lose orbital altitude in turn (though could be provided with the mass to reduce the amount of loss and allow proportionally more in the slung-ship's gain), but by using solar power to send a given current along the tether, as it moves through the Earth's magnetic field, it could regain its altitude without the need for reaction mass. Not sure if that idea is still in vogue, or not.
On the case for colonisation[1], I'm of the "eggs in one basket" school. (i.e., don't keep them all there!) I'm unfortunately nowhere on track to become space-borne by any common contemporary route (test pilot, practical scientist of significant note or billionaire) and would probably have to work to pass the physicals in the event I get the chance to be lofted upwards in any lucky-dip approach (e.g. the path that the likes of Christa McAuliffe got, conveniently stepping around the fact that this meant she was involved in that particular disaster), but I'm currently more than willing to put up with the risk that
having non-terrestrial colonies out there might mean someone (colonial, or an interested party down here who knows the colonies can continue in their stead) is more willing to endanger the planet, because humanity will
eventually find itself in a situation where having someone 'out there' means either that they continue as a species, on our behalf, even when the Big One comes and brings us to our knees (if not lower), or that we actually have some people handily situated out there (and at least partially experienced enough) that can quickly get in there and avert certain disaster with a good and steady but sustained nudge. (Or paint half the thing white, if that's the solution...)
PS Lagrange Points. Particularly L1. That's where I'd put the solar array. Not
so far away from Earth, but closer to the sun, and stable in the direction of the orbital path and perpendicular to the orbital plane, even if it needs a
little effort to keep steady in the sunward/earthward direction. And unless it was a tag larger than the Earth itself it wouldn't cast significant shadow (although I don't see why something couldn't also be set up to make it double up as large-scale sun-shade that could block a few percent of the Sun's light, if required, to help buffer against whatever rampant greenhouse effect might be occurring in the near-future decades that it gets built in[3].
PPS. I keep getting "while you were typing" messages, and now Maggarg's ninjaed me again with the "one graveyard" comment! Post, darn you, post!
PPPS. Forgot to say, Nuclear submarines with Eden Project strapped on? Reminds me of
Silent Running.
[1] Sorry, I stick to this English spelling as a force of habit in the case of just about every instance of interchangable -ise/ize words and their derivatives. The exceptions mainly being generally along the lines of Sid Meier's various games given that they are names with the zed[2]-like spelling.
[2] "Zee", if you wish.
[3] Especially if the availability of "unbounded electrical energy" also ends up contributing to global warming, by a slightly indirect route... Not that I've done the maths regarding that, but could it be something to consider..?