Newton's theory of universal gravitation, formulated in his work "Philosophiæ Naturalis Principia Mathematica" in 1687, stated that every particle with mass in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This is described by Newton's law of universal gravitation, which can be expressed mathematically as:
F = G * (m₁ * m₂) / r²
where F is the gravitational force between two masses (m₁ and m₂), r is the distance between them, and G is the gravitational constant.
Einstein's theory of general relativity, on the other hand, presented a different understanding of gravity. According to general relativity, gravity is not simply a force acting at a distance, but rather a consequence of the curvature of spacetime caused by the presence of mass and energy.
In general relativity, massive objects, such as planets or stars, create a curvature in spacetime, and the motion of other objects near them is influenced by this curvature. Instead of being attracted by a force, objects move along paths determined by the curvature of spacetime. In this framework, the force of gravity experienced by an object is a result of following the geodesic (the shortest path) in the curved spacetime.
Einstein's theory of general relativity introduced a departure from Newton's concept of gravitational force as a direct action between masses. Instead, it described gravity as a geometric effect of the curvature of spacetime caused by mass and energy.
It's worth noting that Newton's theory of gravity is still considered highly accurate and applicable in many situations, especially for objects moving at low speeds and in weak gravitational fields. Einstein's theory of general relativity provides a more comprehensive and accurate description of gravity in situations involving strong gravitational fields, high speeds, and cosmological scales.