The only differences between the beginning of this experiment and the start of Experiment 3 are the values of r and v.
An observer stands on a platform that is stationary with respect to the black hole, and that is positioned at r = 68.4 km. The observer throws a ball horizontally in an attempt to put the ball into circular orbit. Thus, set r = 68.4 and angle = 0. The speed of an object in a circular orbit at this radius is 0.625, so set v = 0.625 and click Start.
Again, a beautiful circle results when trail is checked.
Try slightly different values for v - maybe 0.62501 and 0.62499. When v = 0.62499, the object spirals into the black hole. When v = 0.62501, the object spirals out to a much larger distance, spirals back in to r = 68.4, spirals out, etc.
In this experiment, unlike what happened in Experiment 3, any change, no matter how small, from the circular orbital speed produces a large change from a circle for the shape of the orbit. This is an unstable circular orbit.
Find the v required for a circular orbit at r = 53.4375 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.
This unstable circular orbit is even more unstable than the previous unstable circular orbit at r = 68.4. In what sense? Answers.
Experiment 1: Falling Into a Black Hole
Experiment 3: Investigation of Stable Circular Orbits
Experiment 5: Investigation of Spiral Orbits
Experiment 6: Gravity Bends Light Rays!