Gravitational attraction

If you were inside a massive hollow sphere, in a perfect vacuum, with edges of uniform thickness, which direction would you go because of gravitational pull between you and the edge of the sphere? PS. You don't start right in the middle.

This sounds suspiciously like an extra credit problem... but since the question is over three weeks old I guess it's safe to answer it! ;-)

The answer may surprise you. Almost 400 years ago, Isaac Newton derived the basic equations for gravitational attraction. He was also curious about gravity inside a spherical shell, so he worked out the math. To his surprise, he found that there is no net gravitational attraction anywhere inside the sphere! In other words, no matter where you are in the sphere-- in the middle, or really close to the wall-- you feel no gravity.

The math to solve this problem is a bit tricky, and is usually given as a homework problem in college physics (I had to solve it once, and it took me a long time!). Think of it this way: if you are in the exact center, you feel an outward pull in all directions, right? But suppose you are off center: then you might think you'd feel a larger pull towards the part of shell nearest to you. However, now there is more mass on the other side of the shell pulling you that way! As it turns out, the effects exactly cancel, leaving you feeling no net pull.