What is the escape speed from Jupiter?

검증된 단계별 안내

Understand the concept of escape speed: Escape speed is the minimum speed an object must have to break free from the gravitational pull of a planet without further propulsion. The formula for escape speed is derived from the conservation of energy principle.

Write the formula for escape speed: \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \), 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 planet, and \( R \) is the radius of the planet.

Identify the values for Jupiter: The mass of Jupiter \( M \) is approximately \( 1.898 \times 10^{27} \ \text{kg} \), and the mean radius \( R \) of Jupiter is approximately \( 6.991 \times 10^7 \ \text{m} \).

Substitute the values into the formula: Replace \( G \), \( M \), and \( R \) in the formula \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \) with their respective values.

Simplify the expression: Perform the calculations step by step to find the escape speed, ensuring units are consistent throughout (e.g., meters, kilograms, seconds).

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주요 개념

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Escape Velocity

Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without any additional propulsion. It depends on the mass and radius of the body, calculated using the formula v = √(2GM/R), where G is the gravitational constant, M is the mass of the body, and R is its radius.

Gravitational Constant

The gravitational constant (G) is a fundamental physical constant that quantifies the strength of gravitational attraction between two masses. Its value is approximately 6.674 × 10^-11 N(m/kg)^2. This constant is crucial in calculating escape velocity, as it directly influences the gravitational force exerted by a planet like Jupiter.

Jupiter's Mass and Radius

Jupiter is the largest planet in our solar system, with a mass of about 1.898 × 10^27 kg and a mean radius of approximately 69,911 km. These parameters are essential for determining its escape velocity, as a larger mass and radius result in a higher gravitational pull, necessitating a greater speed for an object to escape its influence.