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is the radial coordinate of the observer within the gravitational field (this coordinate is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate; the equation in this form has real solutions for >), is the speed of light,
The orbit of every planet is an ellipse with the Sun at one of the two foci. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Kepler published the first two laws in 1609 and the third ...
Newton proposed that the orbits of planets about the Sun are largely elliptical because the Sun's gravitation is dominant; to first approximation, the presence of the other planets can be ignored. By analogy, the elliptical orbit of the Moon about the Earth was dominated by the Earth's gravity; to first approximation, the Sun's gravity and ...
The equivalence between gravitational and inertial effects does not constitute a complete theory of gravity. When it comes to explaining gravity near our own location on the Earth's surface, noting that our reference frame is not in free fall, so that fictitious forces are to be expected, provides a suitable explanation. But a freely falling ...
Approximate solutions may also be found by perturbation theories such as linearized gravity [60] and its generalization, the post-Newtonian expansion, both of which were developed by Einstein. The latter provides a systematic approach to solving for the geometry of a spacetime that contains a distribution of matter that moves slowly compared ...
In the context of general relativity, it means the problem of finding solutions to Einstein's field equations — a system of hyperbolic partial differential equations — given some initial data on a hypersurface. Studying the Cauchy problem allows one to formulate the concept of causality in general relativity, as well as 'parametrising ...
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.
The Sun is 1.4 million kilometers (4.643 light-seconds) wide, about 109 times wider than Earth, or four times the Lunar distance, and contains 99.86% of all Solar System mass. The Sun is a G-type main-sequence star that makes up about 99.86% of the mass of the Solar System. [26]