Earth's pull is not the same everywhere, and Einstein says it isn't a pull
Drop a hammer and a feather in a vacuum and they land together: in the same gravitational field, everything falls at the same rate whatever its mass or material. Yet the rate itself differs across Earth's surface, and in Einstein's picture a falling object is not really accelerating at all.
Gravitational acceleration is the steady gain in speed of something falling freely with no air to slow it. On Earth's surface it ranges from about 9.764 to 9.834 metres per second squared, depending on height, latitude and longitude, partly because the planet's spin adds a slight outward push that weakens the effect. For calculations scientists use an agreed standard of exactly 9.80665. Places that depart noticeably from that figure are called gravity anomalies, and measuring such differences is the science of gravimetry.
Isaac Newton described gravity as a force between any two masses, pulling each toward the other, growing with their masses and weakening with the square of the distance between them. When one body vastly outweighs the other, as a planet outweighs a person, it is handy to treat the big one as the source of a field. The acceleration it produces depends only on its own mass and how far away you are, not on the mass of whatever is falling.
That simple rule works well at a distance, but up close the shape of a body matters. Detailed models include the bulge around Earth's equator and lumpy concentrations of mass left by ancient impacts on the Moon. The GRACE mission, launched in 2002, sent two probes nicknamed Tom and Jerry into polar orbit, where tiny changes in the gap between them mapped Earth's gravity and tracked how it shifts over time.
General relativity tells a different story. For Einstein, mass bends spacetime around it, and free-falling objects simply follow the straightest available paths through that curved geometry. In this view gravity is not a genuine force, and something in free fall undergoes no real acceleration at all.
Source: Gravitational acceleration
