Gravitational waves (radiation) are not that weird. They're kind of like electromagnetic waves. If you accelerate an electric charge it will radiate. Likewise

Gravitational waves (radiation) are not that weird. They're kind of like electromagnetic waves. If you accelerate an electric charge it will radiate. Likewise a mass should radiate gravitational waves. Two objects gravitationally orbiting each other will spiral into each other due to the loss of energy to grav radiation. This is due to the finite speed of light. Basically each object 'sees' the other object slightly behind due to light propagation.