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Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [1]
Before Newton's law of gravity, there were many theories explaining gravity. Philoshophers made observations about things falling down − and developed theories why they do – as early as Aristotle who thought that rocks fall to the ground because seeking the ground was an essential part of their nature. [6]
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The resulting Newton–Cartan theory is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system. [30] In this geometric description, tidal effects —the relative acceleration of bodies in free fall—are related to the derivative of the connection, showing ...
Most modern approaches to mathematical general relativity begin with the concept of a manifold. More precisely, the basic physical construct representing gravitation — a curved spacetime — is modelled by a four-dimensional, smooth, connected, Lorentzian manifold. Other physical descriptors are represented by various tensors, discussed below.
The equivalence between inertia and gravity cannot explain tidal effects – it cannot explain variations in the gravitational field. [10] For that, a theory is needed which describes the way that matter (such as the large mass of the Earth) affects the inertial environment around it.
This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept.
1902 – Paul Gerber explains the movement of the perihelion of Mercury using finite speed of gravity. [31] His formula, at least approximately, matches the later model from Einstein's general relativity, but Gerber's theory was incorrect. 1902 – Henri Poincaré questions the concept of simultaneity in his book, Science and Hypothesis. [32] [33]