When does space curve pdf?

The question usually stems from searching for a document about relativity, but the answer doesn't depend on a date. In Einstein's theory, space and time form a single four-dimensional entity whose geometry is set by the content of matter and energy. Wherever there is mass, spacetime is deformed; bodies passing nearby follow the straightest possible lines within that curved geometry, and that is what we perceive as gravitational attraction. Earth orbits the Sun not because a force pulls on it, but because it follows the curvature the Sun imprints around itself.

The deformation is minuscule for everyday objects and only becomes noticeable with enormous or dense masses. The Sun deflects a light ray grazing its edge by just 1.75 arcseconds, the figure Eddington measured during the 1919 eclipse. Near a neutron star or a black hole, the curvature is so intense that light can trace closed orbits. And the theory predicts that accelerating masses emit ripples in the geometry itself: gravitational waves, detected by LIGO in September 2015.

Curvature isn't a blackboard abstraction. GPS satellites orbit at about 20,200 km, where spacetime is less curved than at the surface: their clocks run fast by about 45 microseconds a day due to this effect, and another 7 slow due to their speed; without correcting for it, position would drift by kilometers within a few hours. NASA's Gravity Probe B mission measured, between 2004 and 2005, how Earth deforms and drags space around itself, and the gravitational lenses photographed by Hubble and Webb show distant galaxies distorted by the mass of intervening clusters.