## February 10, 2013

### Q: I heard that in space, if you don't have a rope attach you to the space ship, you will just float/fly away. Why does that happen? and what kind of force is it? Derek

Actually, while we're on the subject of gravity, let's consider the case in which the space ship is in orbit around the Earth. The Earth's gravity weakens as you go away from the center of the Earth, inversely proportional to the square of the distance. If an astronaut is separated from his spaceship by a tiny distance, then the acceleration due to gravity will be slightly different and they will follow slightly different orbits, drifting apart.

If the astronaut has an initial velocity with respect to his spaceship which points away from the center of the Earth, his new orbit around the Earth will be elliptical with almost the same period, but the radius will oscillate outwards and inwards and back again. But even a small change in the period of the astronaut's orbit will take him far away from his spaceship.

Forces arising from the different strengths of gravity from one place to another are called "tidal" forces, because it is the variation of the sun's and the moon's gravitational fields across the size of the Earth that cause the tides.

These gravitational effects are quite small compared to what velocities can be picked up just by the astronaut stepping away from the spacecraft with some velocity, or by tossing a wrench, say in one direction and recoiling in another.