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.
v = sqrt(G × M / r)
LaTeX: v = \sqrt{\frac{GM}{r}}
| Symbol | Meaning | Unit |
|---|---|---|
| v | Orbital velocity of the satellite | m/s |
| G | Universal gravitational constant (6.674 × 10⁻¹¹) | N·m²/kg² |
| M | Mass of the central body (Earth: 5.972 × 10²⁴ kg) | kg |
| r | Orbital radius from centre of Earth | meters (m) |
Problem
Calculate the orbital velocity of the International Space Station, which orbits at an altitude of 400 km above Earth's surface. (Earth's radius R_E = 6.371 × 10⁶ m, M_E = 5.972 × 10²⁴ kg, G = 6.674 × 10⁻¹¹ N·m²/kg²)
Solution
Step 1: Find orbital radius: r = R_E + altitude = 6.371 × 10⁶ + 4.00 × 10⁵ = 6.771 × 10⁶ m. Step 2: Apply the orbital velocity formula: v = sqrt(G × M / r). Step 3: Numerator: G × M = 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ = 3.986 × 10¹⁴ m³/s². Step 4: v = sqrt(3.986 × 10¹⁴ / 6.771 × 10⁶) = sqrt(5.888 × 10⁷) = 7674 m/s.
Answer
Orbital velocity v ≈ 7,674 m/s ≈ 7.67 km/s (approximately 27,600 km/h)
| Orbit Type | Altitude | Orbital Period | Applications |
|---|---|---|---|
| LEO | 160–2,000 km | 90–127 min | ISS, Earth observation, Starlink |
| MEO | 2,000–35,786 km | 2–24 hours | GPS, GLONASS, Galileo |
| GEO | 35,786 km | 24 hours | TV broadcast, weather, comms |
| HEO (Molniya) | Elliptical (500–40,000 km) | ~12 hours | High-latitude communications |
| SSO | 600–800 km | ~100 min | Earth imaging, reconnaissance |
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From Latin artificialis (made by human skill, from ars/artis meaning "skill") and satellitem (an attendant or bodyguard, from satellite). The term "satellite" for orbital bodies was introduced by Johannes Kepler in 1610 to describe the moons of Jupiter.