Escape Velocity
Escape velocity is the minimum speed an object must achieve to escape the gravitational field of a massive body without any further propulsion, assuming no atmospheric drag and a radial (straight-up) trajectory. It is derived by equating the kinetic energy of the object to the magnitude of its gravitational potential energy. Escape velocity is a critical concept in rocketry and planetary science: Earth's escape velocity is approximately 11.2 km/s, while the Sun's is about 617.5 km/s, and a black hole's escape velocity at the event horizon equals the speed of light.
Key Formula
v_e = sqrt(2 × G × M / r)
LaTeX: v_e = \sqrt{\frac{2GM}{r}}
| Symbol | Meaning | Unit |
|---|---|---|
| v_e | Escape velocity | m/s |
| G | Universal gravitational constant (6.674 × 10⁻¹¹) | N·m²/kg² |
| M | Mass of the central body | kg |
| r | Distance from the centre of the body | meters (m) |
Worked Example
Problem
Calculate the escape velocity from the surface of Mars. (Mass of Mars M = 6.417 × 10²³ kg, Radius of Mars R = 3.390 × 10⁶ m, G = 6.674 × 10⁻¹¹ N·m²/kg²)
Solution
Step 1: Write the formula: v_e = sqrt(2 × G × M / r). Step 2: Calculate numerator: 2 × G × M = 2 × 6.674 × 10⁻¹¹ × 6.417 × 10²³ = 8.566 × 10¹³. Step 3: Divide by r: 8.566 × 10¹³ / 3.390 × 10⁶ = 2.527 × 10⁷ m²/s². Step 4: Take square root: v_e = sqrt(2.527 × 10⁷) = 5027 m/s.
Answer
Escape velocity from Mars ≈ 5,027 m/s ≈ 5.03 km/s
Escape Velocities of Solar System Bodies
| Body | Mass (kg) | Radius (km) | Escape Velocity (km/s) |
|---|---|---|---|
| Moon | 7.34 × 10²² | 1,737 | 2.38 |
| Mars | 6.42 × 10²³ | 3,390 | 5.03 |
| Earth | 5.97 × 10²⁴ | 6,371 | 11.2 |
| Saturn | 5.68 × 10²⁶ | 58,232 | 35.5 |
| Jupiter | 1.90 × 10²⁷ | 69,911 | 59.5 |
| Sun | 1.99 × 10³⁰ | 696,000 | 617.5 |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Artificial Satellite
An artificial satellite is any human-made object intentionally placed into orbit around a celestial body — most commonly Earth — to perform specific functions such as telecommunications, Earth observation, weather monitoring, navigation (GPS), scientific research, or military surveillance. Satellites follow orbital paths determined by the balance between gravitational attraction and their tangential velocity; they are classified by orbital altitude into Low Earth Orbit (LEO: 160–2000 km), Medium Earth Orbit (MEO: 2000–35,786 km), and Geostationary Orbit (GEO: 35,786 km). Sputnik 1, launched by the Soviet Union on 4 October 1957, was the first artificial satellite, marking the beginning of the Space Age.
Black Hole
A black hole is a region of spacetime where gravity is so extreme that nothing — not even light or other electromagnetic radiation — can escape once past the event horizon, the point of no return. Black holes form when massive stars collapse at the end of their lives (stellar black holes), or may grow supermassive through accretion and mergers in galactic centres. The boundary of a black hole is described by the Schwarzschild radius (for non-rotating black holes), and their properties are encapsulated by the "no-hair theorem": a black hole is fully described by only three parameters — mass, charge, and spin.
Orbital Mechanics
Orbital mechanics (also called astrodynamics) is the branch of aerospace engineering and applied physics that studies the motion of spacecraft, satellites, and celestial bodies under the influence of gravitational forces. It is governed by Newton's law of universal gravitation and Kepler's three laws of planetary motion, and it underpins the planning of satellite launches, orbital transfers, interplanetary trajectories, and re-entry profiles. Mastery of orbital mechanics is essential for mission design, ground-track prediction, and spacecraft manoeuvring.
From Latin escapare (to escape) and velocitas (speed, from velox meaning "swift"). The concept was mathematically formalized by British mathematician and natural philosopher John Michell in 1783, who used it to reason about "dark stars" (precursors to black holes), and independently by Pierre-Simon Laplace.