|MadSci Network: Astronomy|
The word "power" is used in physics to denote the rate that work is done over time. It has the units of (energy per second), and so is appropriate for describing the rate that energy is radiated by an astronomical body.
The Sun, for example, emits energy at a rate of about 4 × 1026 Watts (that's a 4 followed by 26 zeros). This is called the Sun's radiant power.
Black holes, however, hardly emit any radiation, so their radiant power is nearly zero.
Now the word "power" is used in everyday speech to mean anything that is fast or strong. This use of the word may have nothing to do with the rate that energy is emitted. People will use the word "powerful" to mean that the gravity of a black hole is very strong when you are close to it. In other words (in informal speech) a black hole has very powerful gravity.
Black holes indeed have extremely strong gravity close up. If you drop a stone to the Earth from a very great height (say from out in space), the stone will land on the earth at a high speed. Ignoring the fact that our atmosphere would slow the stone as it approached, one can calculate that the stone would land at a speed of about 11 kilometers per second.
On the other hand, if you drop a stone onto a black hole made from a dead star (about 10 times the mass of the Sun), it will be traveling at nearly the speed of light (300,000 kilometers per second) by the time it gets close to the black hole.
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