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The second law establishes that when a planet is closer to the Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the longer its orbital period. Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System as a consequence of his own laws of motion and law of universal ...
That is, the individual gravitational forces exerted on a point at radius r 0 by the elements of the mass outside the radius r 0 cancel each other. As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere.
The net result is that an object at the Equator experiences a weaker gravitational pull than an object on one of the poles. In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sea-level gravity increases from about 9.780 m/s 2 at the Equator to about 9.832 m/s 2 at the poles, so an ...
One must choose the one dominant gravitating body in each region of space through which the trajectory will pass, and to model only that body's effects in that region. For instance, on a trajectory from the Earth to Mars, one would begin by considering only the Earth's gravity until the trajectory reaches a distance where the Earth's gravity no ...
It is also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, [a] denoted by the capital letter G. In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their ...
(As planets and natural satellites form pairs of comparable mass, the distance 'r' is measured from the common centers of mass of each pair rather than the direct total distance between planet centers.) If one mass is much larger than the other, it is convenient to take it as observational reference and define it as source of a gravitational ...
The equation of motion for the particle derived above = + + can be rewritten using the definition of the Schwarzschild radius r s as = [] + + (+) which is equivalent to a particle moving in a one-dimensional effective potential = + (+) The first two terms are well-known classical energies, the first being the attractive Newtonian gravitational ...
The gravitational field equation is [7] = = = | | =, where F is the gravitational force, m is the mass of the test particle, R is the radial vector of the test particle relative to the mass (or for Newton's second law of motion which is a time dependent function, a set of positions of test particles each occupying a particular point in space ...