An observer stands on a platform that is stationary with respect to the black hole, and that is positioned at r = 270 km. The observer throws a ball horizontally in an attempt to put the ball into circular orbit. Therefore, set r = 270 and angle = 0. The speed of an object in a circular orbit at this radius is 0.25, so set v = 0.25 and click Start.
Look at the beautiful circle that results when trail is checked.
What happens if the ball is thrown with speed a little more than or a little less than 0.25? To find out, leave r and angle alone, change v to 0.26, and click Start. After letting the image build up for a while, a band of yellow results. Do the same for v = 0.24. In both cases, the orbit changes from a circle, but not by much.
Try v = 0.251, and note the smallness of the band. A small change from the circular orbital speed produces a small change from a circle in the shape of the orbit. For this reason, a circular orbit with r = 270 km is said to be stable.
Find the orbital velocity for a stable circular orbit at r = 123.75 km. Hint: when the object moves closer to the black hole after clicking Start, v is too small, and when the object moves farther from black hole after clicking Start, v is too large. Narrow the gap between speeds that are too small and too large. Answer.
Experiment 1: Falling Into a Black Hole
Experiment 4: Investigation of Unstable Circular Orbits
Experiment 5: Investigation of Spiral Orbits
Experiment 6: Gravity Bends Light Rays!