How do scientists tell the size and distance from Earth a celestial object is?

I tired to tell my brother that if you are traveling at the speed of a bullet (roughly 280 m/s) that it would take 40 hours to go around Earth, and nearly half a year to go around the sun. But when ever I try to tell him he always asks how, he is quite stubborn and and close minded. But then it hit me that I don't know how they do it either. Surely the data is accurate, but how do they acquire it? I need something to retaliate with.