How gravity holds us down and keeps planets in orbit
Newton’s universal law of gravitation states that every two masses attract each other with a force F = Gm₁m₂/r², where G = 6.67 × 10⁻¹¹ N m² kg⁻². Near Earth’s surface this force gives every falling object the same acceleration, g ≈ 9.8 m/s², if air resistance is ignored. The weight of a body is W = mg, so it changes from place to place, while mass stays the same. On the Moon, g is about one-sixth of its value on Earth.
At higher levels, g decreases with height above the surface and with depth below it, and it is slightly less at the equator than at the poles. Gravitational potential energy of a mass m at distance r from Earth’s centre is −GMm/r. A satellite in a circular orbit has orbital speed v = √(GM/r), and the escape speed from Earth’s surface is √(2GR), about 11.2 km/s. Kepler’s laws describe elliptical orbits, equal areas swept in equal times, and T² ∝ r³.
Why it matters
Gravity explains tides, the orbits of the Moon and planets, and why astronauts feel weightless in free fall around Earth. Communication and weather satellites are placed in carefully calculated orbits, and geostationary satellites match Earth’s rotation so dishes can point at one spot. This topic connects mechanics with astronomy and space science.
Key terms
- Gravitational constant
- The universal constant G that sets the strength of gravitational attraction between masses.
- Acceleration due to gravity
- The acceleration of a freely falling body near a planet, about 9.8 m/s² on Earth.
- Escape speed
- The minimum speed an object needs to escape a planet’s gravity without further propulsion.
- Geostationary orbit
- An orbit in which a satellite takes 24 hours to circle Earth and stays above the same point on the equator.