Forces, Energy and Motion

How Gravity Works from Newton to Einstein

Follow the idea of gravity from Newton's force acting at a distance to Einstein's curved spacetime, and see what each picture explains and where open questions remain.

On this page
  1. Before Newton
  2. Newton’s gravity: a force between all masses
  3. A problem with Mercury
  4. Einstein’s picture: curved spacetime
  5. Which theory is right?
  6. Why the story matters

Before Newton

For most of history, falling objects and moving planets were treated as separate subjects. Ancient thinkers explained a falling stone as it seeking its natural place, while heavenly bodies were thought to follow different rules. In the early 1600s, Galileo’s careful experiments on falling and rolling objects showed that, setting air resistance aside, objects fall with the same acceleration regardless of their weight. Around the same time Johannes Kepler described the planets’ elliptical orbits from observational data, but without a force-based explanation.

Newton’s gravity: a force between all masses

Isaac Newton’s 1687 book, the Principia, proposed that the same force that makes an apple fall also keeps the Moon in orbit. His theory of gravity says every object with mass attracts every other object. The attraction grows with the masses involved and weakens with the square of the distance between them. Double the distance and the force falls to one quarter.

Near Earth’s surface this produces an acceleration of about 9.8 meters per second squared for falling objects. Newton also showed that an orbit is a kind of continuous fall. Imagine firing a cannonball horizontally from a very high mountain. A faster shot lands farther away. At a high enough speed, the ground curves away beneath it as fast as it falls, and it keeps going around. This is how satellites stay up, and it is the principle behind rocket orbit missions.

The theory was a triumph of the Scientific Revolution. It explained the tides, in terms of the Moon’s and Sun’s pull on the oceans, as covered in ocean tides, and it allowed astronomers to predict the motion of planets and comets with great accuracy. In the 1800s, small irregularities in the orbit of Uranus led astronomers to calculate where an unseen planet should be, and Neptune was found close to the predicted position.

Newton himself was uneasy about one aspect: gravity seemed to act across empty space with no explanation of how. He did not claim to know the mechanism.

A problem with Mercury

By the mid-1800s, a small discrepancy had been noticed. The orientation of Mercury’s elliptical orbit slowly shifts, and a tiny part of the shift could not be accounted for by Newton’s theory, even after allowing for the pull of the other planets. The mismatch was small, but it was persistent.

Einstein’s picture: curved spacetime

Albert Einstein published his general theory of relativity in 1915. Its central idea is that gravity is not a force pulling objects through space, but a result of the shape of spacetime, which combines the three dimensions of space with time. Mass and energy curve spacetime, and objects in free fall follow the straightest possible paths through that curved geometry.

A common analogy is a heavy ball placed on a stretched rubber sheet. The sheet dips, and a marble rolled nearby curves toward the ball. The analogy has limits, since it uses a downward pull to explain gravity, and the real theory involves time as well as space. A short summary often attributed to the physicist John Wheeler is that matter tells spacetime how to curve and spacetime tells matter how to move.

The theory made testable predictions:

  • It accounted for the extra shift in Mercury’s orbit.
  • It predicted that light passing near a massive object would be bent. Measurements during a solar eclipse in 1919 were widely seen as supporting this, though the early measurements were not very precise. Later, much better observations have confirmed the effect. How such events occur is described in solar eclipses.
  • It predicted that clocks run slightly slower in stronger gravity. This has been measured with precise atomic clocks, and the effect has to be corrected for in GPS navigation, or position errors would build up.
  • It predicted gravitational waves, ripples in spacetime. They were first directly detected in 2015, from the merger of two black holes.

Which theory is right?

Newton’s formula is still used for most practical purposes, from planning spacecraft trajectories to engineering. It is an excellent approximation when gravity is weak and speeds are low compared with the speed of light. General relativity is needed for strong gravity, very precise measurements and the study of cosmic objects.

General relativity is not necessarily the final word. It does not fit together neatly with quantum physics, and physicists are still looking for a theory that combines both. Observations of galaxies also suggest more gravitational pull than visible matter can supply, which is one reason scientists propose dark matter, though other explanations are also studied.

Why the story matters

The history of gravity shows how scientific ideas change. Newton’s account was not discarded; it was found to be a special case of a deeper one. That pattern, in which a successful theory is extended rather than simply thrown out, recurs throughout science.

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