2GM What is the escape velocity from the surface of Rhea if its mass is 2.3 x 1021 kg and its radius is 7.7 × 102 km? (Hint: Use the formula for escape velocity, V. = V km/s
2GM What is the escape velocity from the surface of Rhea if its mass is 2.3 x 1021 kg and its radius is 7.7 × 102 km? (Hint: Use the formula for escape velocity, V. = V km/s
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There is one part to this question. I need to know the km/s. Thank you!
![**Problem Statement:**
What is the escape velocity from the surface of Rhea if its mass is \(2.3 \times 10^{21}\) kg and its radius is \(7.7 \times 10^{2}\) km?
*Hint: Use the formula for escape velocity, \(V_e = \sqrt{\frac{2GM}{r}}\)*
**Answer Field:**
\[ \_\_\_\_\_\_ \text{ km/s} \]
**Explanation:**
To solve this problem, you will need to use the escape velocity formula:
\[ V_e = \sqrt{\frac{2GM}{r}} \]
where:
- \( G \) is the gravitational constant (\(6.674 \times 10^{-11} \, \text{m}^3\, \text{kg}^{-1}\, \text{s}^{-2}\)),
- \( M \) is the mass of the body (in this case, Rhea, which is given as \(2.3 \times 10^{21}\) kg),
- \( r \) is the radius of the body (Rhea's radius is \(7.7 \times 10^{2}\) km, which should be converted to meters for the calculation).
To compute the escape velocity, substitute the given values into the formula, remembering to convert the radius into meters:
\[ r = 7.7 \times 10^2 \text{ km} = 7.7 \times 10^5 \text{ m} \]
Plug these into the formula to find \( V_e \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10987a05-6004-4fb1-8846-eb9d55f60d7e%2F877c5660-7a49-4fcd-925e-5b2019ad9af1%2Fzys0p7_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
What is the escape velocity from the surface of Rhea if its mass is \(2.3 \times 10^{21}\) kg and its radius is \(7.7 \times 10^{2}\) km?
*Hint: Use the formula for escape velocity, \(V_e = \sqrt{\frac{2GM}{r}}\)*
**Answer Field:**
\[ \_\_\_\_\_\_ \text{ km/s} \]
**Explanation:**
To solve this problem, you will need to use the escape velocity formula:
\[ V_e = \sqrt{\frac{2GM}{r}} \]
where:
- \( G \) is the gravitational constant (\(6.674 \times 10^{-11} \, \text{m}^3\, \text{kg}^{-1}\, \text{s}^{-2}\)),
- \( M \) is the mass of the body (in this case, Rhea, which is given as \(2.3 \times 10^{21}\) kg),
- \( r \) is the radius of the body (Rhea's radius is \(7.7 \times 10^{2}\) km, which should be converted to meters for the calculation).
To compute the escape velocity, substitute the given values into the formula, remembering to convert the radius into meters:
\[ r = 7.7 \times 10^2 \text{ km} = 7.7 \times 10^5 \text{ m} \]
Plug these into the formula to find \( V_e \).
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