What is the second cosmic speed for a planet that has the same mass as the Earth, but twice the radius?

univerkov | September 24, 2021 | education

Reference data: M (mass of the Earth) = 5.972 * 10 ^ 24 kg; R (radius of the Earth) = 6 356 863 m; G (gravitational constant) = 6.674 * 10 ^ -11 m3 / (kg * s2); R2 (planet radius) = 2R.

The second space velocity for a planet with given parameters is determined by the formula: V2 = √ (2G * M / R2) = √ (2G * M / 2R).

Let’s calculate: V2 = √ (2 * 6.674 * 10-11 * 5.972 * 10 ^ 24 / (2 * 6356863)) = 7918 m / s ≈ 7.9 km / s.

Answer: The second space velocity for a planet with given parameters is 7.9 km / s.

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