An engineer wants a satellite to orbit the earth with a period of 28 hours. Hint: You need to find an equation for r in terms of givens (T, M and G only). Start by setting your two equations for acceleration equal. Then rearrange the orbital period equation to solve for T and substitue. Finally, solve for r and plug in! You may enter answers in scientific notation as shown: 1.23 x 105 - 1.23e5 At what orbital radius must the satellite orbit? m How far is this above the earth's surface? m At what speed does the satellite need to orbit? m/s 8 earth data mass: 5.97 x 1024kg radius: 6.37 x 106m
An engineer wants a satellite to orbit the earth with a period of 28 hours. Hint: You need to find an equation for r in terms of givens (T, M and G only). Start by setting your two equations for acceleration equal. Then rearrange the orbital period equation to solve for T and substitue. Finally, solve for r and plug in! You may enter answers in scientific notation as shown: 1.23 x 105 - 1.23e5 At what orbital radius must the satellite orbit? m How far is this above the earth's surface? m At what speed does the satellite need to orbit? m/s 8 earth data mass: 5.97 x 1024kg radius: 6.37 x 106m
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![**Title: Calculating the Orbital Requirements for a Satellite with a 28-Hour Period**
**Objective:** Determine the orbital radius and speed for a satellite to orbit the Earth with a period of 28 hours.
---
**Instructions:**
An engineer aims to position a satellite in orbit around Earth with a specified orbital period of 28 hours. To achieve this, you'll need to derive the equation for the orbital radius \( r \) using the given values (orbital period \( T \), Earth's mass \( M \), and gravitational constant \( G \)). Follow these steps:
1. Set the equations for gravitational and centripetal acceleration equal.
2. Rearrange the orbital period equation to solve for \( T \), and substitute the values.
3. Calculate the orbital radius \( r \) and plug in your values.
*Note:* You may enter answers in scientific notation (e.g., \( 1.23 \times 10^5 \) as 1.23e5).
---
**Questions:**
1. **At what orbital radius must the satellite orbit?**
Enter your answer: [______] m
2. **How far is this above the Earth's surface?**
Enter your answer: [______] m
3. **At what speed does the satellite need to orbit?**
Enter your answer: [______] m/s
---
**Diagram Explanation:**
The diagram illustrates a satellite in orbit around Earth. It highlights the following:
- The satellite’s orbit is depicted as a gray dashed circle.
- The line labeled \( r \) represents the orbital radius from the center of the Earth to the satellite.
- **Earth data:**
- Mass: \( 5.97 \times 10^{24} \) kg
- Radius: \( 6.37 \times 10^6 \) m
Using the values provided, calculate the necessary orbital parameters to maintain a 28-hour orbit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3775607-704b-46c9-9d82-255ef12a8c56%2F2b3d7057-7e15-4f5e-878c-a3f6884ffd03%2Ft17tf7j_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Orbital Requirements for a Satellite with a 28-Hour Period**
**Objective:** Determine the orbital radius and speed for a satellite to orbit the Earth with a period of 28 hours.
---
**Instructions:**
An engineer aims to position a satellite in orbit around Earth with a specified orbital period of 28 hours. To achieve this, you'll need to derive the equation for the orbital radius \( r \) using the given values (orbital period \( T \), Earth's mass \( M \), and gravitational constant \( G \)). Follow these steps:
1. Set the equations for gravitational and centripetal acceleration equal.
2. Rearrange the orbital period equation to solve for \( T \), and substitute the values.
3. Calculate the orbital radius \( r \) and plug in your values.
*Note:* You may enter answers in scientific notation (e.g., \( 1.23 \times 10^5 \) as 1.23e5).
---
**Questions:**
1. **At what orbital radius must the satellite orbit?**
Enter your answer: [______] m
2. **How far is this above the Earth's surface?**
Enter your answer: [______] m
3. **At what speed does the satellite need to orbit?**
Enter your answer: [______] m/s
---
**Diagram Explanation:**
The diagram illustrates a satellite in orbit around Earth. It highlights the following:
- The satellite’s orbit is depicted as a gray dashed circle.
- The line labeled \( r \) represents the orbital radius from the center of the Earth to the satellite.
- **Earth data:**
- Mass: \( 5.97 \times 10^{24} \) kg
- Radius: \( 6.37 \times 10^6 \) m
Using the values provided, calculate the necessary orbital parameters to maintain a 28-hour orbit.
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