Escape velocity on Earth is 11.2 km/s. What would be the escape velocity on a planet whose mass is 1000 times and radius is 10 times that of Earth?
Answer: 112 km/s
Explanation
Escape velocity (vₑ) is given by:
vₑ = √(2GM/r)
where:
G = gravitational constant
M = mass of the planet
r = radius of the planet
Given:
M₂ = 1000M₁ (mass of the new planet is 1000 times that of Earth)
r₂ = 10r₁ (radius of the new planet is 10 times that of Earth)
Escape velocity on the new planet (vₑ₂) is:
vₑ₂ = √(2GM₂/r₂)
= √(2G(1000M₁)/(10r₁))
= √(200G(M₁/r₁))
= √200 × √(2GM₁/r₁)
= √200 × vₑ₁
Given vₑ₁ = 11.2 km/s:
vₑ₂ ≈ √200 × 11.2 km/s
≈ 112 km/s
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