Escape velocity
Universal gravitation · Physics
Solar system
Interactive 3DAll 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.
Related topics
- Kepler's laws of planetary motion
- Newton's universal law of gravitation
- Gravitational constant and its measurement (Cavendish experiment)
- Acceleration due to gravity and its variation (altitude, depth, rotation of Earth)
- Gravitational field and field intensity
- Gravitational potential and potential energy