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Escape velocity

Universal gravitation · Physics

Solar system

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All eight planets in orbit around the Sun, with Saturn's rings and Earth's Moon.

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Study notes

Calculate the escape velocity from the Moon. (M_moon = 7.35 × 10²² kg, R_moon = 1.74 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²) Step 1: v_e = √(2GM/R) = √(2 × 6.67 × 10⁻¹¹ × 7.35 × 10²² / 1.74 × 10⁶). Step 2: Numerator: 2 × 6.67 × 7.35 × 10^(−11+22) = 98.0 × 10¹¹ = 9.80 × 10¹². Step 3: Divide by 1.74 × 10⁶: 9.80 × 10¹² / 1.74 × 10⁶ ≈ 5.63 × 10⁶. Step 4: Square root: √(5.63 × 10⁶) ≈ 2370 m/s ≈ 2.37 km/s. Answer: ≈ 2.4 km/s — nearly five times smaller than Earth's 11.2 km/s, which is why the Moon could not hold on to an atmosphere.

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