In 2050, astronomers discover that the nearest black hole in our galaxy has a very orderly planetary system, with 3 planets in circular orbits. The planets A, B, and C have orbits with circumferences that are exactly 20, 40, and 60 times the circumference of the event horizon, respectively. Even more amazing, the planets are inhabited! On October 1, 2065, the planets all line up, and the residents of planet B decide to measure the precise distances of closest approach to their neighbors A and C. They expect these distances to be the same, but this is not what they find. Describe what they find instead, and explain the reason for the discrepancy.

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speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.

you get 2.3=1.21*\frac{a}2 or 4.6=1.21a or a=3.802 (b)

explanation: