Experiment 2: Escape Velocity

An observer stands on a platform that is stationary with respect to the black hole and throws a ball straight up. Just as if he were on the surface of the Earth, when observer throws the ball fast enough, the ball escapes the gravity of the black hole. If the ball is thrown with less than escape velocity, the ball will reach a maximum height, and then fall back down.

To experiment with this situation, set angle = 90, which means that the ball is being thrown straight up. Now, for example, suppose the platform is at r = 120 km. Turn the trail off, set v = 0.4, click Start, and watch the ball go up and down.

Change v to 0.45. The ball now goes off the display, but still comes back. Wait for it!

Set v = 0.6. Don't wait too long for the ball to come back, because 0.6 is greater than the escape velocity.

Try and verify that the escape velocity from a platform at r = 120 km is half the speed of light. This means that for v less than 0.5. the ball falls into the black hole, and for v greater than 0.5, the ball escapes the black hole's influence.

Verify that the escape velocity approaches the speed of light as the launching point approaches the event horizon (r = 30) by finding approximate escape velocities for various values of r. Don't bother if you find this to be too tedious!

Home

Warmup Exercises

Experiment 1: Falling Into a Black Hole

Experiment 3: Investigation of Stable Circular Orbits

Experiment 4: Investigation of Unstable Circular Orbits

Experiment 5: Investigation of Spiral Orbits

Experiment 6: Gravity Bends Light Rays!

Experiment 7: Boundaries Between Orbits of Various Kinds

Experiment 8: Orbital Precession and Closed Orbits