When a large star gets old, it explodes, instantly releasing as much energy as the Sun outputs in ten billion years. This is called a supernova, which is Latin for "Wow, no really, wow."
After the explosion, what's left at the center is a neutron star, which is an extremely dense object with just slightly more mass than our own Sun, crammed into a space the size of New Orleans. A neutron star is so dense that a teaspoonful of one would weigh as much as ten million Oprahs.
Occasionally, a pair of neutron stars will wind up orbiting each other. In 2003, a pair was discovered orbiting about half a million miles apart. This is twice the distance between the Earth and the Moon. Because neutron stars are so massive, however, each orbit takes only two and a half hours.
The astronomers who discovered this binary neutron star system gave it the name PSR J0737-3039. I wonder what these guys name their pets.
Every day, the two neutron stars in PSR J0737-3039 get a quarter of an inch closer together, because of energy loss due to gravitational waves. 85 million years from now, they'll merge together. One minute before this happens, the neutron stars will be only a few hundred miles apart, and orbit around each other 30 times per second. In the final few moments, they'll get much closer together, and extremely angry, and the orbital frequency will increase to 1000 times per second.
This is totally insane. Two city-sized objects, each with the mass of the Sun, whirling around each other 1000 times per second. If you don't think this is impressive, you might as well go back to bed now.
When the neutron stars in PSR J0737-3039 merge, they will probably form a black hole, which is an exotic astronomical object whose gravity is so strong that even humor cannot escape it.