Answers

Experiment 3. An object in stable circular orbit at r = 123.75 km has an orbital speed of v = 0.4.

Experiment 4. An object in unstable circular orbit at r = 53.4375 km has an orbital speed of v = 0.8. This orbit is more unstable than the unstable circular orbit at 68.4 kilometres in the sense that any horizontal launch speed greater than the circular orbital of v = 0.8 results in escape from the black hole.

Experiment 5. An object launched horizontally at r = 240 km with a speed of v = 2/9 = 0.2222222... will be captured in an unstable circular orbit.

Experiment 6. Circular light orbit occurs at r = 45 km. Since a small change in r either sends the light spiraling into the black hole or spiraling out to infinity, this orbit is unstable.

Experiment 7. The boundary between 1) and 2) occurs at r = 60 km; the boundary between 2) and 3) occurs at r = 90 km.

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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