Gravitation

An apple falls to the ground, the Moon circles the Earth, and the planets orbit the Sun. Newton's great insight was that all of these are caused by the same force: gravitation, the attraction between every pair of masses in the universe. This single idea ties together events on Earth and in the heavens. It explains weight, falling and floating.

Newton's universal law of gravitation states that every object in the universe attracts every other object with a force that is:

• directly proportional to the product of their masses, and
• inversely proportional to the square of the distance between them.

So heavier objects attract more strongly. The force also falls off rapidly as objects move apart. Doubling the distance makes the force one-quarter as strong. This is the inverse-square law. The force is the same on both bodies. We notice the Earth's pull on us, not ours on the Earth, because the Earth is so vastly more massive.

Physicists trace every interaction in nature to just four fundamental forces. Gravitation is one of them. Each force has its own job and its own range:

• Gravity: the attraction between masses. It has infinite range and shapes orbits, tides and the structure of the universe. Yet it is the weakest of the four forces.
• Electromagnetism: acts only on particles that carry an electric charge. It binds electrons to nuclei, holds atoms together in molecules and produces light. Its range is also infinite.
• Strong nuclear force: the strongest of the four. It holds protons and neutrons together inside the nucleus of an atom, overcoming the electric repulsion between protons. It works only over the tiny distances inside a nucleus.
• Weak nuclear force: causes radioactivity, the spontaneous decay of unstable nuclei. It too acts only over very short ranges.

The order of strength is a favourite test point. From strongest to weakest it runs: strong nuclear force, electromagnetism, weak nuclear force, gravity. Gravity feels powerful in daily life only because the Earth is enormous. Between two small objects its pull is almost immeasurably small.

When an object falls towards the Earth under the pull of gravity alone, it is in free fall, and it speeds up at a steady rate called the acceleration due to gravity, written g. Near the Earth's surface g is about 9.8 metres per second squared.

A famous and surprising fact: in free fall, all objects accelerate at the same rate regardless of their mass. A heavy stone and a light one, dropped together (with no air resistance), hit the ground at the same instant. The value of g is slightly greater at the poles than at the equator, and it decreases with height.

It is vital not to confuse mass and weight:

• Mass is the amount of matter in an object. It is constant: the same on the Earth, on the Moon or in space. It is measured in kilograms.
• Weight is the force with which gravity pulls on that mass. It is given by W = m × g, measured in newtons, and it changes with g. On the Moon, where gravity is about one-sixth of the Earth's, an object weighs only one-sixth as much, even though its mass is unchanged.

Gravity also helps explain how things float. A force acting on a surface produces:

• Thrust: the force acting perpendicular to a surface.
• Pressure: the thrust per unit area (pressure = force ÷ area). A sharp knife or a nail tip cuts easily because a small area gives high pressure.

When an object is placed in a fluid, the fluid pushes up on it with an upward force called buoyancy (or upthrust). Archimedes' principle states that this buoyant force equals the weight of the fluid the object displaces. An object floats if it is less dense than the fluid. It sinks if it is denser. That is why a ship of steel can float while a steel nail sinks.