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Calculate the escape velocity of Titan.

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.
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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