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**Problem 3: International Space Station (ISS) Calculations** The International Space Station (ISS) is in orbit at a radius of 6,800 km and completes one full circle in 90 minutes. Its size is about 100 m in the longest direction. **Tasks:** a. Calculate the centripetal acceleration on the ISS. b. Calculate the orbital (tangential) speed \( v \) of the ISS. c. Calculate the angular velocity of the ISS. d. For an observer on Earth, what viewing angle is the ISS taking up? e. According to special relativity, a second on the ISS (\( \Delta t' \)) is longer than a second on Earth (\( \Delta t \)) as described by the equation below. Here, \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light. Over the course of a one-year stay on the ISS, how much less have the astronauts aged compared to had they stayed on the ground? \[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} \]
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Transcribed Image Text:**Problem 3: International Space Station (ISS) Calculations** The International Space Station (ISS) is in orbit at a radius of 6,800 km and completes one full circle in 90 minutes. Its size is about 100 m in the longest direction. **Tasks:** a. Calculate the centripetal acceleration on the ISS. b. Calculate the orbital (tangential) speed \( v \) of the ISS. c. Calculate the angular velocity of the ISS. d. For an observer on Earth, what viewing angle is the ISS taking up? e. According to special relativity, a second on the ISS (\( \Delta t' \)) is longer than a second on Earth (\( \Delta t \)) as described by the equation below. Here, \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light. Over the course of a one-year stay on the ISS, how much less have the astronauts aged compared to had they stayed on the ground? \[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} \]
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