Calculate the escape velocity of Titan.
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![**Calculate the Escape Velocity of Titan**
In the study of celestial mechanics, the escape velocity is the speed at which an object must travel to break free from the gravitational pull of a celestial body without further propulsion. To calculate the escape velocity of Titan, Saturn's largest moon, you can use the formula:
\[ v = \sqrt{\frac{2GM}{r}} \]
Where:
- \( v \) is the escape velocity.
- \( G \) is the gravitational constant (\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\)).
- \( M \) is the mass of Titan.
- \( r \) is the radius of Titan.
The specific values for Titan's mass and radius are:
- Mass (\( M \)): \( 1.3452 \times 10^{23} \, \text{kg} \)
- Radius (\( r \)): \( 2,575,000 \, \text{m} \)
Plugging these values into the formula will yield the escape velocity for Titan.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc44715e-e997-4081-aac6-58f75fd336c7%2Fc53b71a3-0d14-42b5-a1e1-dcc0571a9f5c%2F4da681y_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate the Escape Velocity of Titan**
In the study of celestial mechanics, the escape velocity is the speed at which an object must travel to break free from the gravitational pull of a celestial body without further propulsion. To calculate the escape velocity of Titan, Saturn's largest moon, you can use the formula:
\[ v = \sqrt{\frac{2GM}{r}} \]
Where:
- \( v \) is the escape velocity.
- \( G \) is the gravitational constant (\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\)).
- \( M \) is the mass of Titan.
- \( r \) is the radius of Titan.
The specific values for Titan's mass and radius are:
- Mass (\( M \)): \( 1.3452 \times 10^{23} \, \text{kg} \)
- Radius (\( r \)): \( 2,575,000 \, \text{m} \)
Plugging these values into the formula will yield the escape velocity for Titan.
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