Question

A black hole has an event horizon radius of 3.00

Answer 1

A) The Schwarzschild radius of a black hole (which is the same same as the radius of its event horizon) is given by the formula where is the radius, is the black hole's mass, is the gravitational constant and is the speed of light. You should easily be able to solve this for the mass of the body and plug in the numbers.

B) If you're outside the event horizon of a black hole, it behaves exactly like any other object with mass. To an excellent approximation, the acceleration it produces will be given by Newton's Law of Gravity:

where is your distance from the center and I went ahead and substituted in the expression for the hole's mass in terms of its Schwarzchild radius. Again, just plug in the numbers.

C) Again, we can use regular Newtonian physics to solve this problem. The escape velocity is the velocity needed to come to rest infinitely far from the black hole's center. If you're a distance from the hole's center and traveling at speed , then your total energy is the energy due to the hole's gravity plus your kinetic energy: E. We are interested in the case where when is infinitely large; when that happens, . Hence, when you began your journey (at escape velocity), conservation of energy implies that you had zero energy then, too. Therefore, the escape velocity must be given by .