Let's say I would want to light up Venus, such that we can see Venus all day long and not have to wait for a Venus Transit. What kind of light would I need for it? How powerful would it need to be?
I assume you are interested in using light sent from Earth. You could use a laser which does not spread out so much as it travels and so less of it would be wasted. If you used some bulb radiating in one direction, you would use the inverse square law to get the power at a distance $x$, the distance to Jupiter. Then multiply the power per unit area at that distance by the area of the circle formed by Jupiter's radius to get the reflected power. Then use the square law again in the same way to find the power returned to earth. The power you will need will depend on the sensitivity of the photodiode, used to measure the light. The laser is better because the power per unit area goes down way slower with distance.