- #1
adrian116
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the questions is that:
An astronaut inside a spacecraft , which protects her from harmful radiation, is orbiting a black hole at a distance of 120 km from its center. The black hole is 5 times the mass of the sun and has a Schwarzschild radius of 15 km. The astronaut is positioned inside the spaceship such that one of here 0.03 kg ears is 6 cm farther from the black hole than the center of mass of the spacecraft and the other ear is 6 cm closer.
a) What is the tension between her ears? Would the astronaut find it difficult to keep from being torn apart by the gravitational forces? (Since her whole 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.)
b) Is the center of gravity of her head at the same point as the center of mass?. Explain
my question is that can i use the formula F=GMm/r^2 directly? So i could find two force acting to the ears respectively. Then get the difference,
is it the way to work out part 1 of (a)?
Also , why one ear is moving too slowly and the other is moving too fast?
Finally, i totally do not how to answer part (b)...
thx for attention~
An astronaut inside a spacecraft , which protects her from harmful radiation, is orbiting a black hole at a distance of 120 km from its center. The black hole is 5 times the mass of the sun and has a Schwarzschild radius of 15 km. The astronaut is positioned inside the spaceship such that one of here 0.03 kg ears is 6 cm farther from the black hole than the center of mass of the spacecraft and the other ear is 6 cm closer.
a) What is the tension between her ears? Would the astronaut find it difficult to keep from being torn apart by the gravitational forces? (Since her whole 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.)
b) Is the center of gravity of her head at the same point as the center of mass?. Explain
my question is that can i use the formula F=GMm/r^2 directly? So i could find two force acting to the ears respectively. Then get the difference,
is it the way to work out part 1 of (a)?
Also , why one ear is moving too slowly and the other is moving too fast?
Finally, i totally do not how to answer part (b)...
thx for attention~