# Do mass and motion affect space-time differently?

Mass is said to create curvatures in space-time thereby creating gravity, yet technically the smallest movements, even on Earth, create gravitational waves. Are there different "types" of disturbances of space-time? How?

So I’ll answer your other question by talking in terms of mass. If a distribution of mass is sitting still, it creates a static gravitational field that decreases at large distances like $$1/r^2$$. But if it is moving in a certain way, it radiates a gravitational wave whose field decreases like $$1/r$$. In order to radiate, the quadrupole moment of the mass distribution must have a nonzero third time derivative. (Or the octupole moment can have a nonzero fourth derivative, etc.) This means, for example, that a spinning sphere does not radiate, but a dumbbell spinning end over end does.