What present of the earth can be lighted by the sun at any time?

Present? You mean percent?

Do a thought experiment - if you shine a flashlight on a tennis ball from a few feet away how much of the tennis ball can the flashlight light up at once? Or when you look at a tennis ball, how much of it can you see at one time?

The pursists out there may note that the sun actually lights up a bit more of the earth than the above would imply, due to refraction of light through the earth's atmosphere. But that's a detail.