Experiment 5: Investigation of Spiral Orbits

The existence of unstable circular orbits gives rise to an interesting phenomenon - orbits that start near edge of the display and then spiral down to unstable circular orbits.

For example, setting r = 270 km, v = 0.2, and angle = 0 should result in an orbit that approaches an unstable circular orbit at 67.5 km. This is best seen with the trail off. Enter these number, click Start, and see what ensues.

The initial conditions given start the object at 270 km with the exact velocity necessary to spiral down to the unstable circular orbit at 67.5 km. The computer animation shows the object spiraling into the black hole after almost being captured in circular orbit at 67.5 km. The animation does not show actual capture because the computer solves equations approximately, and there is a tradeoff between the accuracy of the animation and the speed of the animation. An exact animation would run infinitely slowly, and would be a very boring animation!

Find the horizontal (angle = 0) launch speed necessary for capture in a circular orbit after launch at r = 240 km. Hint: find a launch speed such that the object ends up in the black hole, and then increase the speed until the object does not end up in the black hole. Narrow the gap between those speeds that result in the object being swallowed by the black and those that don't. Answer.

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Warmup Exercises

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 6: Gravity Bends Light Rays!

Experiment 7: Boundaries Between Orbits of Various Kinds

Experiment 8: Orbital Precession and Closed Orbits