How Gravity Works

Newton's Law of Universal Gravitation

Isaac Newton formulated the law of universal gravitation in 1687. The law 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 their centers. Mathematically, F = G times m1 times m2 divided by r squared, where G is the gravitational constant (approximately 6.674 times 10 to the minus 11 N m squared per kg squared).

The inverse-square relationship means gravity weakens rapidly with distance. Double the distance between two objects and the gravitational force drops to one quarter. Triple the distance and the force drops to one ninth. This rapid decrease explains why we feel Earth's gravity strongly but barely notice the gravitational pull of distant stars.

The gravitational constant G is remarkably small, which is why gravity is the weakest of the fundamental forces. Two one-kilogram masses placed one meter apart attract each other with a force of only 6.674 times 10 to the minus 11 newtons, a force so tiny it is undetectable without extremely sensitive equipment. Gravity only becomes significant when at least one of the objects has enormous mass, like a planet or star.

Gravitational Acceleration and Free Fall

Near Earth's surface, gravity accelerates all objects downward at approximately 9.8 m/s squared, a value commonly labeled g. This means that every second an object is in free fall, its downward velocity increases by 9.8 meters per second. After one second, a dropped ball moves at 9.8 m/s. After two seconds, it moves at 19.6 m/s. This acceleration is constant as long as the object remains near Earth's surface.

A critical insight is that gravitational acceleration is independent of mass. A bowling ball and a marble dropped from the same height hit the ground at the same time, provided air resistance is negligible. Galileo demonstrated this principle in the early 1600s, contradicting the centuries-old Aristotelian belief that heavier objects fall faster. Apollo 15 astronaut David Scott famously confirmed it on the Moon by dropping a hammer and a feather simultaneously in the airless lunar environment.

In everyday conditions, air resistance does affect falling objects, which is why a feather falls more slowly than a hammer on Earth. But this difference comes from air resistance, not from gravity itself. Gravity pulls both objects with the same acceleration. The feather's large surface area relative to its mass means air resistance slows it much more than the hammer.

Weight Versus Mass

Mass and weight are related but fundamentally different quantities. Mass is the amount of matter in an object, measured in kilograms, and it does not change with location. Weight is the gravitational force acting on an object, measured in newtons, and it depends on the local gravitational field. The relationship is W = mg, where W is weight, m is mass, and g is the gravitational acceleration.

A person with a mass of 70 kilograms weighs about 686 newtons on Earth (70 times 9.8). The same person on the Moon, where g is about 1.6 m/s squared, would weigh only 112 newtons but would still have a mass of 70 kilograms. On Jupiter, where g is about 24.8 m/s squared, they would weigh 1736 newtons. Their mass, and therefore their inertia, remains the same everywhere.

This distinction matters practically. Bathroom scales measure weight, not mass. An astronaut floating in the International Space Station appears weightless because the station and everything in it are in free fall together, but the astronaut's mass has not changed. Moving heavy equipment in orbit still requires significant force because the inertia (determined by mass) is unchanged.

Orbits and Gravity

An orbit is the result of an object falling toward another object while simultaneously moving sideways fast enough to keep missing it. The Moon is constantly falling toward Earth, pulled by gravity. But it also has a sideways velocity that carries it forward. The combination of these two motions produces a curved path that circles the Earth continuously. If gravity suddenly vanished, the Moon would fly off in a straight line at its current velocity.

Newton realized that the same force that makes an apple fall from a tree keeps the Moon in orbit. The apple falls straight down because it has no sideways velocity. If you throw the apple sideways fast enough, it would curve around the Earth and come back to where it started, forming an orbit. This thought experiment, sometimes called Newton's cannonball, shows that orbital motion and falling are the same phenomenon at different scales.

Orbital speed depends on altitude. Satellites in low Earth orbit (about 400 km altitude) travel at approximately 7.7 km/s and complete an orbit in about 90 minutes. Geostationary satellites at 35,786 km altitude travel at about 3.1 km/s and take exactly 24 hours to orbit, allowing them to remain above the same point on Earth. The farther from Earth, the slower the required orbital speed and the longer the orbital period.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. Near Earth's surface, this energy is calculated as PE = mgh, where m is mass, g is gravitational acceleration, and h is the height above a chosen reference point. Lifting a 5-kilogram object 2 meters high gives it 98 joules of gravitational potential energy (5 times 9.8 times 2).

This energy is recoverable. When the object falls, its potential energy converts to kinetic energy. At the bottom of its fall, all the potential energy has become kinetic energy (ignoring air resistance). This exchange between potential and kinetic energy is the basis of many mechanical systems, from pendulums to roller coasters to hydroelectric dams.

For objects far from Earth, the simplified formula PE = mgh is not accurate because g varies with distance. The general formula is PE = minus G times m1 times m2 divided by r. The negative sign indicates that gravitational potential energy is zero at infinite distance and becomes more negative as objects move closer together. Escaping a gravitational field requires adding enough energy to bring the total from its negative value to zero, which defines the concept of escape velocity.

Gravity Beyond Newton

Newton's law of gravitation works extremely well for most practical purposes, but it is not the complete picture. In 1915, Albert Einstein published his general theory of relativity, which describes gravity not as a force but as a curvature of spacetime caused by mass and energy. Objects follow the straightest possible paths through curved spacetime, and what we perceive as gravitational attraction is actually this curvature guiding their motion.

For everyday situations and even most astronomical calculations, Newton's formula and Einstein's theory give identical predictions. The differences become significant only in extreme conditions: near very massive objects like black holes, at very high speeds approaching the speed of light, or when measuring extremely precise effects like the precession of Mercury's orbit. GPS satellites must account for relativistic corrections to maintain accuracy, because time runs slightly faster at their altitude than on Earth's surface.

Despite these refinements, Newton's gravitational theory remains the standard tool for engineering, orbital mechanics, and nearly all practical physics. Its simplicity and accuracy in normal conditions make it indispensable. General relativity provides the deeper understanding, but Newton's equations do the daily work.

Common Misconceptions About Gravity

The most common misconception is that there is no gravity in space. Gravity exists everywhere in the universe. Astronauts aboard the International Space Station experience about 90% of Earth's surface gravity. They appear weightless because they and the station are in free fall together, constantly falling around the Earth. The correct term is microgravity, not zero gravity.

Another misconception is that gravity requires air or atmosphere. Gravity acts through empty space with no medium needed. The Sun's gravity holds planets in orbit across millions of kilometers of vacuum. This is fundamentally different from sound, which does require a medium to travel through.

People sometimes believe that heavier objects have stronger gravity, which is technically true but misleading. Every object with mass produces a gravitational field. Your body gravitationally attracts everything around you, but the force is immeasurably small because your mass is tiny compared to Earth. The asymmetry in everyday experience comes from Earth's enormous mass, not from any special property of large objects.