A gas eventually will escape from a planet's atmosphere if the average velocity of the atoms exceeds 1/6 times the escape velocity of the planet. If the average velocity of water vapor in Venus's atmosphere is 0.9 km/s, would it eventually escape into outer space? Note that Venus's mass is 5 * 10²⁴ kg and its radius is 6,050 km. A) Water vapor would escape because 1/6 times the escape velocity is 0.51 km/s. B) Water vapor would not escape because 1/6 times the escape velocity is 1.7 km/s. C) Water vapor would escape because 1/6 times the escape velocity is 0.42 km/s. D) Water vapor would not escape because 1/6 times the escape velocity is 2.6 km/s. E) Water vapor would escape because 1/6 times the escape velocity is 1.3 km/s.

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Quizplus · Accepted Answer

The escape velocity $ v_e $ is calculated using the formula $ v_e = \sqrt{\frac{2GM}{R}} $. For Venus, $ G = 6.674 \times 10^{-11} \, \text{m}^3/\text{kg}\cdot\text{s}^2 $, $ M = 5 \times 10^{24} \, \text{kg} $, and $ R = 6,050,000 \, \text{m} $. Calculating gives $ v_e \approx 10.36 \, \text{km/s} $. Therefore, $ \frac{1}{6} \times v_e \approx 1.73 \, \text{km/s} $. Since the average velocity of water vapor (0.9 km/s) is less than 1.73 km/s, it would not escape.

A Gas Eventually Will Escape from a Planet's Atmosphere If