Calculate the escape velocity from a gas giant planet with 10 times the mass of Earth and twice the radius of Earth. Assume the gas giant's atmosphere starts at the surface.
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To calculate the escape velocity from a gas giant planet, we can use the formula:
Ve = sqrt(2GM/R)
Where:
Ve = escape velocity
G = gravitational constant (6.67430 × 10^(-11) m³/(kg·s²))
M = mass of the gas giant planet
R = radius of the gas giant planet
Given that the mass of the gas giant planet is 10 times the mass of Earth (measured in kilograms), and the radius is twice the radius of Earth (measured in meters), we can substitute these values into the formula and calculate the escape velocity.
Mass of the Earth = 5.972 × 10^24 kg
Radius of the Earth = 6,371 km = 6,371,000 m
Mass of the gas giant planet = 10 × Mass of the Earth
= 10 × 5.972 × 10^24 kg
Radius of the gas giant planet = 2 × Radius of the Earth
= 2 × 6,371,000 m
Substituting these values into the escape velocity formula:
Ve = sqrt(2 * G * M / R)
= sqrt(2 * 6.67430 × 10^(-11) * (10 × 5.972 × 10^24) / (2 × 6,371,000))
Simplifying this expression:
Ve = sqrt(7928.92)
Using a calculator, we find:
Ve ≈ 88.99 m/s
Therefore, the escape velocity from the gas giant planet is approximately 88.99 m/s.
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