How do the astronauts know exactly where to re-enter earth?

Answer 1

The computers tell them.

Answer 2

Spaceships' orbits are ellipses. There is one point of the ellipse where the spaceship is farthest from Earth, called the apoapsis, and another point, opposite to the apoapsis, where the spaceship is closest to Earth, we call it periapsis.

Th procedure to reentry is quite complex. First they modify the orbit with small burns of their rockets so the orbit is aligned with the landing point. So they can flay exactly overhead the entry point in the last orbit.

Then they have to get the periapsis of their orbit to "touch" the landing point.

The trick here is to modify the elliptical orbit so that the periapsis is at the Earth's surface at the point of landing. That is what the astronauts do with the so-called "deorbit burn", where they light up their rocket to slow down the spacecraft so the periapsis of their orbit goes down to let's say Cape Canaveral. The burn must be done at the apoapsis. It sounds complicated. Well, it really is. Rocket science.

You may practice this with a space simulator if you have time. I recommend Orbiter, a free space simulator. Not a game, looks like one, but is real physics behind it running the show. Check the link.

Answer 3

The people at NASA mapped the re-entry area mathematically, so the ares where they are suppose to land is going to be be pretty close to the projected area.

Answer 4

When you fire a rocket change your orbit, the orbit change is greatest at the point opposite the point where you changed it. So, if you want to come down at a certain point, you wait until you are on the exact opposite side of the earth and fire your retro-rockets at that point.

Answer 5

Simple,

They enter through the ozone hole

Answer 6

...did you see the tragic firey re-entry...it is all a calculated risk...really good guessing...really brave people...