Centripetal Forces their Definitions r Dif ferential Equations of Motion caused by their Action. Trans formation of those Equations into others more convenient for Astronomical purposes. Three Equations necessary for determining the Length of the Radius Vector, the Latitude and Longitude of the Body Consequences that follow from the Diferential ations of Motion when the Forces acting on a Body in motion are Centripetal, or are directed to one point only Keplers Law of the Equable Description of Areas demonstrated. Variation of the Velocity. The Equable Description of Areas necessariIy disturbed, when the Body is acted on by Forces, some of which are not directed to the same Point or Centre.The Centripetal Force is supposed to act inversely as the Square of the i s t a n c e . Co sequencethsa t flow from it. The Orbit, or the Curve described by the moving Body round the Central, an Ellipse. Keplers Law i f the Squares of the Periodic Times varying ss the Cubes of the Major Axes. Keplerb

...Problem for determining the true from the mean Anomaly. IIis Law re specting the Periodic T i e s not exactly true.The Elliybica Elements of s Planets Orbit determined its hlajor Axis, Eccentricity, Longitude of the Perihelion, Inclination of its Plane, Longitude of the Node, Epoch of the Passage of the Perihelion. The Elements of the Orbit considered as the Arbitrary Constant Quantities introduced by the Integration of the Differential Equations, Their invariabiIity in the System of two Bodies. Expression forthe Velocity in an Ellipse in a Circle in s Right Line, the Centripetal Force varying inversely as the Square of the Distance. AIodification of the preceding llesults, by considering the Masses of the Revolving atid Cer tral Body.. , 35 A third attracting Body introduced into the System of two Bodies. Its Effects in disturbing the Laws of filntion and the Elements of that System. Expressions of the Values of the resolved Parts of the disturbing Force the Ablatitious the Addititious the Force in the direction of the Jladius Vector the Tangen tial Force EFects of these Forces in altering Keplers Laws, c, Approximate Values of the 1 orres when the disturbing Body is very remote. Expressions for the Forces, in the Problem of. the Three Bodies, by means of the Partial Differentials of a Func tion of the Eodys Parallax, Longitude and Latitude The Motion of the Centre of Gravity of two or more nodies not affected by their mutual Action their Cenhre of Gravity nt tractcd by a distant Externd Body the Systern revolving round it by a Force nearly as the Inverse Squrtre nf the Distance it describes therefore an Ellipse, nearly, roui d that Body. The Centre of Gravity of the Earth and Moon, the Centres of Gravity of Jupiter and his Satellites, of SaLurn and his, all de scribe, very nearly, Ellipses round the Sun, and Areas proportional to the Times. Values of the Disturbing Forces that prevent the exact Description. The Rloons RIenstrual Motion Values of the Perturbations of her Parallax and Longitude by the Earths Action Value of the Menstrual Parall Pale Elimination of d t from the Differential Equations. The Three Equations illat belong to the Theory of the Rfoon, and the Problem of the Three Bodies. The Approximate Integration of these Equations by the Method called the Variation of the Parameters...

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