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Imagine you are an astronaut in a circular orbit around the Earth. Let's say you have a mass of 100 kg. You are orbiting at a radial distance of 10,000 km (10° km, or 10' m) from the center of the Earth (Radius of Earth is 6400 km (6.4 x 10° km, or 6.4 x 10 m), so you are 3600 km above the surface). It takes you two hours and 45 minutes to complete each orbit. 7. What is the acceleration of gravity at your location (in m/s)? (Hint: "G*M" for Earth = 4 x 1014) 8. What was your weight (in Newtons) on Earth? WE = 9. What is your weight (gravitational force), compared to what it was on Earth? (in other words, I want the ratio, like your did for # 1 - 6)

Imagine you are an astronaut in a circular orbit around the Earth. Let's say you have a mass of 100 kg. You are orbiting at a radial distance of 10,000 km (10° km, or 10' m) from the center of the Earth (Radius of Earth is 6400 km (6.4 x 10° km, or 6.4 x 10 m), so you are 3600 km above the surface). It takes you two hours and 45 minutes to complete each orbit. 7. What is the acceleration of gravity at your location (in m/s)? (Hint: "G*M" for Earth = 4 x 1014) 8. What was your weight (in Newtons) on Earth? WE = 9. What is your weight (gravitational force), compared to what it was on Earth? (in other words, I want the ratio, like your did for # 1 - 6)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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## Exploring Circular Orbits and Gravitational Forces **Scenario:** Imagine you are an astronaut in a circular orbit around the Earth. Let's say you have a mass of 100 kg. You are orbiting at a radial distance of 10,000 km (10⁴ km, or 10⁷ m) from the center of the Earth. (Radius of Earth is approximately 6400 km (6.4 x 10³ km, or 6.4 x 10⁶ m), so you are approximately 3600 km above the surface). It takes you two hours and 45 minutes to complete each orbit. **Questions:** 7. **What is the acceleration of gravity at your location (in m/s²)?** - Use the hint: "G*M" for Earth = 4 x 10¹⁴. - Provide the calculation for \( g \). ``` g = ``` 8. **What was your weight (in Newtons) on Earth?** - Provide the calculation for your weight on Earth, \( W_E \). ``` W_E = ``` 9. **What is your weight (gravitational force) compared to what it was on Earth?** - In other words, determine the ratio, similar to your calculation for questions #1-6. ``` Weight Ratio = ``` **Detailed Explanation of the Scenario:** - **Radial Distance:** Your orbital distance (10,000 km) includes Earth's radius. Since Earth's radius is approximately 6400 km, your orbit is about 3600 km above the surface. - **Time for One Orbit:** You complete an orbital revolution in 2 hours and 45 minutes. This exercise illustrates the application of gravitational principles and orbital mechanics. It helps understand how gravity diminishes with distance and affects weight calculations in different gravitational fields. **Note:** The text above provides clear, educational information suitable for understanding gravitational forces and orbital mechanics. It is structured to guide students in solving related physics problems.
Transcribed Image Text:## Exploring Circular Orbits and Gravitational Forces **Scenario:** Imagine you are an astronaut in a circular orbit around the Earth. Let's say you have a mass of 100 kg. You are orbiting at a radial distance of 10,000 km (10⁴ km, or 10⁷ m) from the center of the Earth. (Radius of Earth is approximately 6400 km (6.4 x 10³ km, or 6.4 x 10⁶ m), so you are approximately 3600 km above the surface). It takes you two hours and 45 minutes to complete each orbit. **Questions:** 7. **What is the acceleration of gravity at your location (in m/s²)?** - Use the hint: "G*M" for Earth = 4 x 10¹⁴. - Provide the calculation for \( g \). ``` g = ``` 8. **What was your weight (in Newtons) on Earth?** - Provide the calculation for your weight on Earth, \( W_E \). ``` W_E = ``` 9. **What is your weight (gravitational force) compared to what it was on Earth?** - In other words, determine the ratio, similar to your calculation for questions #1-6. ``` Weight Ratio = ``` **Detailed Explanation of the Scenario:** - **Radial Distance:** Your orbital distance (10,000 km) includes Earth's radius. Since Earth's radius is approximately 6400 km, your orbit is about 3600 km above the surface. - **Time for One Orbit:** You complete an orbital revolution in 2 hours and 45 minutes. This exercise illustrates the application of gravitational principles and orbital mechanics. It helps understand how gravity diminishes with distance and affects weight calculations in different gravitational fields. **Note:** The text above provides clear, educational information suitable for understanding gravitational forces and orbital mechanics. It is structured to guide students in solving related physics problems.
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