So I was just reading about satellites burning up in the atmosphere. The book pointed out that it wasn't the gravitational velocity (towards the earth) that caused objects to burn up (which makes sense since the thinner air means less air friction which balances out the increase in terminal velocity [at a guess]), but the parallel (tangent) velocity that kept it in orbit to burn up. If that's the case, shouldn't the heat (visually), be on the side of falling object as opposed to the bottom?
What is "side?" What is "bottom?" The meaning of those words is somewhat arbitrary when you're talking about spacecraft.
Spacecraft that are designed to survive re-entry and atmospheric braking typically turn so that the shielded part faces "forward" during the re-entry maneuver. When it's a manned spacecraft, the shielded/forward-facing side typically will be the side that is "under" the crew seats, so that the braking force will tend to push the crew "down" into their seats instead of making them hang from the straps.
P.S., The heat generated during atmospheric braking isn't due to friction. It's mostly due to the air being compressed as the spacecraft pushes its way through.