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Introducing physical explanations for movement in space beyond just geometry, Kepler correctly defined the orbit of planets as follows: [1] [2] [5]: 53–54 The planetary orbit is not a circle with epicycles, but an ellipse. The Sun is not at the center but at a focal point of the elliptical orbit.
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
a (km) is the average orbital distance between the centers of the two bodies; r 1 (km) is the distance from the center of the primary to the barycenter; R 1 (km) is the radius of the primary r 1 / R 1 a value less than one means the barycenter lies inside the primary
r a is the radius at apoapsis (also "apofocus", "aphelion", "apogee"), i.e., the farthest distance of the orbit to the center of mass of the system, which is a focus of the ellipse. r p is the radius at periapsis (or "perifocus" etc.), the closest distance.
According to Einstein's theory of general relativity, particles of negligible mass travel along geodesics in the space-time. In uncurved space-time, far from a source of gravity, these geodesics correspond to straight lines; however, they may deviate from straight lines when the space-time is curved.
All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M can be derived as follows:
All three planets (red, blue and green) are at the same distance r from the center of force C. It is required to make a body move in a curve that revolves about the center of force in the same manner as another body in the same curve at rest. [42] Newton's derivation of Proposition 43 depends on his Proposition 2, derived earlier in the ...