The True Doctrine of Orbits: An Original Treatise on Central Forces |
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The True Doctrine of Orbits: An Original Treatise on Central Forces H. G. Rush No preview available - 2019 |
The True Doctrine of Orbits: An Original Treatise on Central Forces (Classic ... H. G. Rush No preview available - 2017 |
Common terms and phrases
abscissa angle aphelion apse area described areas in equal attraction body moving central force centre of force centrifugal force centripetal force chord circular theory circumference comet conclusion constant curvature cycloid derived diameter diminished direction doctrine of orbits earth eccentric anomaly eccentric orbit ellipse elliptical theory epicycloid epitrochoid equation equiangular spiral finite focus force tending formula given hence hyperbola hypocycloid increased infinite law of equal law of force law of gravitation limit major axis miles per hour minor axis moon moving body negative Newton Newton's demonstrations non-eccentric orbit observed orbital motion parabola perihelion distance Perihelion velocity period planet planetary position precipitation Prop proposition quadrature radii radius vector represents result retarding revolution revolve rolling circle secondary point square straight line sun's Suppose supposition tance tendency THEOREM theory of orbits tion triangle variation whence
Popular passages
Page 115 - ... and, by approaching it, they would necessarily at the same time approach each other, and in this case their distance from each other would be diminished. Now, whenever the action of the sun would increase their distance, if they were allowed to fall towards the sun, then the sun's action, by endeavoring to separate them, diminishes their gravity to each other ; whenever the sun's action would diminish the distance, then it increases their mutual gravitation.
Page 64 - ... fixed or moving uniformly in a straight line, by radii drawn to that point, is acted on by a centripetal force tending to the same point.
Page 64 - The centripetal forces of bodies, which by equable motions describe different circles, tend to the centres of the same circles; and are to each other as the squares of the arcs* described in equal times divided respectively by the radii of the circles.
Page 64 - I. Having given the velocity with which a body is moving at any three points of a given orbit, described by it under the action of forces tending to a common centre, to find that centre. Let the three straight lines PT, TQV, VR, touch the given orbit in the points P, Q, R respectively, and let them meet in T and F.
Page 79 - If any number of bodies revolve about a common centre, and the centripetal force vary inversely as the square of the distance...
Page 76 - COB. 1. It follows from the last three propositions, that if any body move from the point P in any direction PR, with any velocity, and be at the same time acted on by a centripetal force, which is inversely proportional to the square of the distance, the body will move in some one of the conic sections, having a focus in the center of force, and conversely. For when the focus, the point of contact, and the position of the tangent are given, a conic section can be described which will have...
Page 64 - Every body, which describes areas proportional to the times of describing them by radii drawn to the centre of another body which is moving in any manner whatever, is acted on by a force compounded of a centripetal force tending to that other body, and of the whole accelerating force which acts upon that other body. Let the first body be...
Page 68 - XV. 1. A body is moving in a semicircle under the action of a force tending to a point, so distant that the lines drawn from the body to that point may be considered parallel; if the center of force be transferred to the center of the circle, when the direction of the body's motion is perpendicular to that of the force, its magnitude at that point being unaltered, prove that the body...