THE EARTH ORBITING A BLACK HOLE

The simplest kind of black hole is a Schwarzschild black hole, which is a black hole with mass, but with no electric charge, and no spin. Karl Schwarzschild discovered this black hole geometry at the close of 1915 within weeks of Einstein presenting his final theory of General Relativity.

The animation nicely illustrates gravitational lensing. The black hole here is taken to have a radius equal to that of the Earth, which requires that the mass of the black hole be about 2,000 suns. The Earth orbits at 3 Schwarzschild radii (the minimum stable circular orbit), and we observe at rest from a distance of 5 Schwarzschild radii. For these parameters, we would see the Earth orbit the black hole 80 times per second.

This animation is not realistic! The Earth would be tidally torn apart in about one orbit if it were orbiting this close to a black hole of this mass.
Notice that when the Earth recedes from us, it appears reddish (redshifted) and slowed, and conversely when the Earth approaches us it appears blue (blueshifted) and speeded up.

Sources & references:
http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html
http://ipht.cea.fr/Phocea-SPhT/ast_visu_spht.php?id_ast=18

Animation credit and specific info via JILA Science
https://jila.colorado.edu/.

Corina Marinescu