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An astronaut inside a spacecraft, which protects her from harmful radiation, is orbiting a black hole in a circular orbit at a distance of 120 km from its centre. The black hole mass is 5 times the mass of the sun, and it has a Schwarzschild radius of 15 km. The astronaut is positioned inside the spacecraft such that one of her 30 g ears is 6 cm farther from the black hole than the centre of mass of the spacecraft and the other 30 g ear 6 cm closer. What is the amount of force (in newtons N) between her ears?

An astronaut inside a spacecraft, which protects her from harmful radiation, is orbiting a black hole in a circular orbit at a distance of 120 km from its centre. The black hole mass is 5 times the mass of the sun, and it has a Schwarzschild radius of 15 km. The astronaut is positioned inside the spacecraft such that one of her 30 g ears is 6 cm farther from the black hole than the centre of mass of the spacecraft and the other 30 g ear 6 cm closer. What is the amount of force (in newtons N) between her ears?

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any help would be much appreciated thanks

11. An astronaut inside a spacecraft, which protects her from harmful radiation, is orbiting a black hole in a circular orbit at a distance of 120 km from its centre. The black hole mass is 5 times the mass of the sun, and it has a Schwarzschild radius of 15 km. The astronaut is positioned inside the spacecraft such that one of her 30 g ears is 6 cm farther from the black hole than the centre of mass of the spacecraft and the other 30 g ear 6 cm closer. What is the amount of force (in newtons N) between her ears? (Hint: Since her entire body orbits with the same angular velocity, one ear is moving too slowly for the radius of its orbit and the other is moving too fast. Hence her head must exert forces on her ears to keep them in their orbits.)
Transcribed Image Text:11. An astronaut inside a spacecraft, which protects her from harmful radiation, is orbiting a black hole in a circular orbit at a distance of 120 km from its centre. The black hole mass is 5 times the mass of the sun, and it has a Schwarzschild radius of 15 km. The astronaut is positioned inside the spacecraft such that one of her 30 g ears is 6 cm farther from the black hole than the centre of mass of the spacecraft and the other 30 g ear 6 cm closer. What is the amount of force (in newtons N) between her ears? (Hint: Since her entire body orbits with the same angular velocity, one ear is moving too slowly for the radius of its orbit and the other is moving too fast. Hence her head must exert forces on her ears to keep them in their orbits.)
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