When the first solar driven aeroplane now has made a round trip of the globe, could we build a space craft driven by sunlight that could reach orbit?
No, not for quite a while. There are 2 ways that solar power can be used in an airless environment:
- Ion Drives
- Solar Sails
Neither of these produces a high thrust. To improve the thrust, they both would need to collect a huge amount of solar power, which would increase the drag through the atmosphere, making it even harder. Getting these in to orbit is quite impossible.
The only system that could remotely be possible would be to concentrate solar power from the ground on to a single point on the rocket, and heat water or something similar to let it escape. This would be very difficult to do, and in fact, wouldn't really be any more efficient than just using a chemical rocket. It would also require very accurate tracking, and large mirrors, to make it work.
A few other schemes that could do something:
- Send power by laser to the rocket, similar to the large mirror concept.
- Send power via wires (Space elevator concept)
- Space gun concept, with a barrel higher than the atmosphere, although the achieving full orbit would still be difficult.
As SF mentioned in the comments, the best way would be to fuel/ manufacture the rocket using solar power, and otherwise launch it as is. But that doesn't really seem to count, I suppose.
This depends a lot on what you define as "solar driven". If you imagine a rocket covered in solar cells or some solar-thermic power plant, then the answer is clearly "No".
To put a ton of material into LEO, we need about 32 GJ of energy (2 GJ to lift the object, 30 GJ to accelerate to orbital velocity). Unfortunately the rocket equation is not that simple and we have to spend more than 100 GJ on a typical rocket (How much Energy is required to put 1 kg in LEO? gives a rough estimate, but has a very high Isp and calculates for a single-staged rocket). This energy needs to be spent within few minutes (Falcon9 needs about 8 minutes until SECO), giving a power requirement of 220 MW. To generate this power under optimal circumstances we need a solar array of about 1 million square meters per ton of payload. That is a square of 1 km side length which we would need to attach to the rocket.
Reducing power requirements by prolonging the transfer time doesn't help as you need to fight gravity during the full time, thus increasing energy requirements. One option as @RussellBorogove mentioned is a solar powered plane to reach orbital speed. Unfortunately I can't calculate any meaningful number for drag for a large disc at supersonic speeds to see how much power you need to maintain altitude and speed.
Theoretical transportation methods like a space elevator do not have this limitation and could be powered from photo-voltaic cells easily.
But there are other ways to build a solar driven rocket: Take any conventional rocket based on Hydrogen/Oxygen fuel. These can easily be produced by electrolysis using electricity from a solar power plant. In this sense, the answer to your question is: "Yes, easily" - all it needs is a signature in the right place (i.e. sign up for electricity from a solar power plant)