Warmup Exercises

Imagine throwing (or launching) a ball off a platform that uses rockets to remain suspended at a constant height above the black hole. What happens to the ball? Does the ball get sucked into the black hole, go into orbit, or completely escape the attraction of the black hole? If the ball does go into orbit, what are the possible shapes for the orbit? As you might imagine, the answers to these questions depend on the height of the platform, and on the speed and direction with which the ball is thrown.

The animation to the right lets you investigate the fate of the ball. The bottom of the display has areas where you can input values for three parameters:

r - the patform's "distance" from the singularity at the centre of the black hole;

v - the ball's launch speed with respect to the platform;

angle - the launch angle with respect to the horizontal platform.

Launch speed is given as a fraction of the speed of light. For example, v = 0.2 corresponds to 60,000 kilometres per second, and v = 1 corresponds to 300,000 kilometres per second. The speed of light is nature's speed limit, so values of v greater than 1 are not accepted.

The ball starts directly above the platform. Starting the ball with angle = 0 launches it horizontally to the right. Starting the ball with angle = 90 launches it vertically straight up. Starting the ball with angle equal to some value between 0 and 90 launches it up and to the right. Starting the ball with a negative angle launches the ball in a downwards direction, with -90 being straight down.

You can start the animation with the input parameters set to any desired values by editing the numbers and then clicking on the Start button. Typing the "Enter" key is not required and has no effect. If trail is checked, then the particle leaves a trail as it orbits; if trail is not checked, then the particle leaves no trail as it orbits. The initial input parameters are such that a pretty display forms (this may take a few minutes) after trail is checked. Trail and each of the input parameters r, v, angle can be changed independently of the others. Changing trail has immediate effect, while any changes to the input parameters r, v, and angle only take effect after clicking the Start button.

If the display turns white, checking trail or clicking the Start button will restore the display to black. Unfortunately, any trail that has built up will be lost.

Give it a try!

Enter 200 in the area for r, .3 in the area for v, and 60 in the area for angle. Click the Start button. After briefly disappearing off the diplay, the black hole sucks up the ball.

Without changing anything else, check (by clicking) trail, and click the Start button. This shows you the path of the ball.

Without changing r, v, or trail, set angle to 10. Click the Start button, and watch a complicated pattern build up as the ball orbits the black hole.

Now you're ready to try some of the experiments, or to experiment with your own choices for r, v, and angle.

Home

Experiment 1: Falling Into a Black Hole

Experiment 2: Escape Velocity

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