Why planets follow curved paths

In general relativity, matter and energy change the geometry of spacetime—the combined description of space and time. A planet moving near a star then follows the straightest path available in that curved geometry, called a geodesic. To us, that path looks like an orbit bending around the star, even though the planet is not being pulled by an invisible rope.

An orbit also depends on the planet’s motion. Earth has forward speed as well as a path shaped by the Sun’s gravity. It continually falls toward the Sun, but keeps moving sideways, so it keeps missing. Without that sideways motion, it would fall inward; with a different speed, its path could be wider or less stable.

Why the trampoline picture is incomplete

A stretched sheet makes curvature easy to picture, but it can also mislead. The sheet bends downward because Earth’s gravity pulls the ball on it; that uses the very gravity the analogy is meant to explain. And the sheet is a two-dimensional surface bending through an imagined extra direction. Spacetime’s curvature is not a dent in a material cosmic fabric that objects sink into.

Time is part of the mechanism, too. Gravity changes how time passes from place to place, and this curvature of time helps determine the paths of planets and falling objects. The familiar image of a star making a hollow in space captures only part of what relativity describes.

When the older picture still works

For everyday motion and most planetary calculations, Newton’s account of gravity as a force gives extremely accurate results. Relativity becomes important when gravity is especially strong or measurements are precise enough to reveal small differences. It does not make Newton’s picture useless; it explains why that picture works so well in ordinary conditions.

The key shift is from asking what invisible pull steers a planet to asking what path spacetime’s geometry makes natural. Earth’s orbit is not a track laid around the Sun: it is the route Earth follows while moving through a changing geometry.