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 \( V_e \).
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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