Putting gravity together

Imagine four objects near Earth: a stone held above the ground, a second stone just released, a ball thrown upwards and a satellite in orbit. They have different motions, but we can account for all four using the same surrounding spacetime geometry.

Two parts of the explanation

In general relativity, matter and energy are related to spacetime geometry. The geometry describes measurable relationships between distances, elapsed times and paths. Earth’s mass is the main source in our example.

A freely moving object follows a geodesic through that geometry. Its starting position and velocity determine which geodesic it follows. A hand, floor or engine can exert a force that takes it away from free fall.

This gives us a way to describe both motion and support. It also explains why different objects can follow different paths around the same Earth.

Falling, rising and orbiting

The released stone gains downward speed relative to the ground. The thrown ball initially rises, slows and returns. The satellite has enough sideways motion for its path to continue around Earth without reaching the surface.

All three are in free fall while other forces are negligible. Free fall includes the upward part of the ball’s flight and the satellite’s entire orbit. It describes the absence of support or propulsion, rather than a particular direction of travel.

Objects with different masses but the same starting position and velocity follow the same free-fall path in this approximation. Their own gravitational influence is too small to change the surrounding geometry appreciably. This connects the geometric picture with the heavy-and-light experiment earlier in the series.

Standing and feeling weight

The held stone follows a different path because the hand keeps it at one height. A scale beneath it measures that support.

Your feet experience the same kind of support from the ground. Remove it and you begin to fall freely. An accelerometer falling with you reads zero, even while your speed relative to Earth changes.

That zero reading does not make gravity disappear. Compare two nearby freely falling objects and their separation can still change. These tidal effects reveal the curvature that a single small falling room cannot remove from the wider picture.

Where clocks and light fit

Clocks held at different heights record different amounts of time. This is one way to measure the geometry around Earth. For slow motion in a weak, steady gravitational field, the change in their rate with height gives the familiar downward acceleration.

The clocks do not supply a pull. Their readings and the object’s motion are related predictions of the same theory. Light deflection provides another test, one that requires more of the spacetime description than the simple slow-fall calculation.

What we mean by gravity

In Newton’s account, gravity is an attractive force between masses. This remains an accurate and convenient description for many everyday and orbital calculations.

In general relativity, gravity is described through spacetime geometry and the free motion that follows from it. Falling, orbiting, clock differences and tides belong to that description. The pressure we feel as weight comes from the support that prevents us from following a free path.

Einstein’s theory tells us how to calculate these effects and connect them with observations. It does not settle every deeper question about nature, including how gravity should fit with quantum physics. Understanding the theory’s account of a falling stone does not require those further questions to have been answered.

Return to the four objects and follow one through its motion. Identify its starting velocity, whether anything supports or propels it, and whose viewpoint the diagram uses. Those three checks let you explain each case using the same picture of gravity.