Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Ask your questions and receive precise answers from experienced professionals across different disciplines. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine the orbital period of Jupiter using the stated equation \( P^2 = A^3 \), where \( A \) is the semi-major axis of Jupiter's orbit in astronomical units (AU) and \( P \) is the orbital period in years, follow these steps:
1. Identify the Given Value:
- The semi-major axis \( A \) for Jupiter is 5.2 AU.
2. Calculate \( A^3 \):
[tex]\[ A^3 = 5.2^3 = 140.608 \][/tex]
3. Set Up the Equation \( P^2 = A^3 \):
[tex]\[ P^2 = 140.608 \][/tex]
4. Solve for \( P \) by Taking the Square Root of Both Sides:
[tex]\[ P = \sqrt{140.608} \approx 11.8578 \][/tex]
5. Examine the Multiple-Choice Options:
- The options provided are 5 years, 11 years, 110 years, and 500 years.
6. Determine the Closest Match to the Calculated \( P \):
- The closest value to \( 11.8578 \) among the given choices is 11 years.
Therefore, the orbital period of Jupiter is approximately 11 years.
1. Identify the Given Value:
- The semi-major axis \( A \) for Jupiter is 5.2 AU.
2. Calculate \( A^3 \):
[tex]\[ A^3 = 5.2^3 = 140.608 \][/tex]
3. Set Up the Equation \( P^2 = A^3 \):
[tex]\[ P^2 = 140.608 \][/tex]
4. Solve for \( P \) by Taking the Square Root of Both Sides:
[tex]\[ P = \sqrt{140.608} \approx 11.8578 \][/tex]
5. Examine the Multiple-Choice Options:
- The options provided are 5 years, 11 years, 110 years, and 500 years.
6. Determine the Closest Match to the Calculated \( P \):
- The closest value to \( 11.8578 \) among the given choices is 11 years.
Therefore, the orbital period of Jupiter is approximately 11 years.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.