Question

1.Alyssa and Victoria are sent to study a 10 solar mass black hole (it's mass is 10 times bigger than the Sun). Victoria loses the game of paper-rock-scissors, and so must descend to a distance 29,498 m away from the black hole while Alyssa watches Disney + in the Command shuttle from a safe distance. If Victoria only stays there for an hour, and then returns to the Command shuttle, how many hours of Disney + will Alyssa have watched? (The Sun's mass is 1.99 x 10^30 kg)

2.Merari is jealous that Ethan got to be the first person to visit another star. So he joins NASA and volunteers to be sent to AD Leonis, which is 16.2 light-years away and is in the Leo constellation. Which is much further than Proxima Centauri. But he doesn't want to age that much, so convinces NASA to make a rocket for him that sends him there and back at a speed 0.99c! How much older will Merari be when he returns to Earth?

Answer 1

Solution

1. Please check the distance r of Victoria from black hole. The provided time is too close such that time would have almost frozen. I have calculated the time for some distance 10^4 times that of given. You can use the same formula for any given distance r.

2. This question is actually paradoxical. We need general relativity to answer this question. And we need the deceleration felt by Merari at the point of return (where special relativity breaks down) to answer the question. The final expected result would be the same that Merari would be not as much as aged as he is expected to be due to relativistic effects.