An Elementary Treatise on Astronomy. ..., Volume 2Smith, 1818 - 487 pages |
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Page iv
... sole Disturbing Force acting in the Direction of the Radius Vector . Remarkable Result obtained by the first Integration of the Differential Equation . Dalembert's Method of indeterminate Coefficients , for finding the Value of the ...
... sole Disturbing Force acting in the Direction of the Radius Vector . Remarkable Result obtained by the first Integration of the Differential Equation . Dalembert's Method of indeterminate Coefficients , for finding the Value of the ...
Page xii
... solely from the will of the mathematician , or for mere convenience ; but from the absolute insufficiency of the art of Calculation . We may at this point discern the several sorts of explanation . that may be admitted into a Treatise ...
... solely from the will of the mathematician , or for mere convenience ; but from the absolute insufficiency of the art of Calculation . We may at this point discern the several sorts of explanation . that may be admitted into a Treatise ...
Page xiii
... solely those which have been detected by the nicety of modern research , but such as the principal Lunar in- equalities , which , previously to Newton , had been discovered by Tycho Brahé and others . Of explanations towards the other ...
... solely those which have been detected by the nicety of modern research , but such as the principal Lunar in- equalities , which , previously to Newton , had been discovered by Tycho Brahé and others . Of explanations towards the other ...
Page xv
... sole source of attraction being supposed to be the central body , the orbit of the revolving body , is not approximately , but exactly , an ellipse : but other heavenly bodies , besides the Sun , attract Mars . The former theory ...
... sole source of attraction being supposed to be the central body , the orbit of the revolving body , is not approximately , but exactly , an ellipse : but other heavenly bodies , besides the Sun , attract Mars . The former theory ...
Page xvi
... sole agency of a centripetal force , is more simple than that of their derangement according to the real circumstances that take place in nature . If we feign the Sun and Jupiter to be the only two attracting bodies , it is easy to shew ...
... sole agency of a centripetal force , is more simple than that of their derangement according to the real circumstances that take place in nature . If we feign the Sun and Jupiter to be the only two attracting bodies , it is easy to shew ...
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Common terms and phrases
acceleration Apogee approximate arbitrary quantities argument attraction body's centripetal force Clairaut coefficient computed consequently correction cosines deduced determined differential equation diminution direction disturbing body disturbing force dv² Earth eccentricity elliptical equal Evection expound expression former formula Hence inclination inequality instance integration inverse Jupiter and Saturn Jupiter's Kepler's Laws Laplace latter longitude Lunar Apogee Lunar Theory mass mean distance mean motion method Moon Moon's nearly Newton nodes observation orbit parallax perihelion period perturbations Physical Astronomy planetary planets preceding Principia principles radius vector represent result retardation revolving satellite secular equation substitute Sun's supposed tangent terms involving terms that involve three bodies tion tricity Trig true longitude turbing variation Venus
Popular passages
Page lvi - For while comets move in very eccentric orbs in all manner of positions, blind fate could never make all the planets move one and the same way in orbs concentric, some inconsiderable irregularities excepted which may have risen from the mutual actions of comets and planets upon one another, and which will be apt to increase till this system wants a reformation.
Page xli - ... in the motions of p are very numerous. Lastly, that part of the disturbing force which acts in the direction of a line pm, fig. 13, at right angles to the plane of the orbit Npn, may be called the perpendicular force.
Page xliv - Their orbits are only nearly elliptical and their figures marly spherical. If we assume the former to be ellipses and the latter spheres, it is for the purpose of conveniently commencing our processes : of making, by such first steps, approximations towards remoter results. But it must not be supposed, from what has just been said, that the inequalities of motion of the revolving body caused by the oblateness of figure in the central are at all comparable", either for their magnitude or number, to...
Page xlv - It may be justly said," says H alley, a contemporary of Newton and one of the greatest men of that or of any age, " it may be justly said that so many and so valuable philosophical truths as are herein discovered and put past dispute, were never yet owing to the capacity and industry of any one man.
Page 366 - ... that the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, is always equal to two right angles.
Page lix - Ita extrication is due entirely to theory. The inequality is peculiar to the theory of Jupiter and Saturn : its special cause is to be sought for in the near commensurability of the mean motions of Jupiter and Saturn : which mean motions are nearly as 5 to 2. But we are thus referred rather to the mathematical cause than to any simple or palpable explanation of the phenomena. For, certainly, it is not easy to perceive any thing in the circumstance of the near commensurability of the mean motions...
Page xlvi - Clairaut, of which we have just spoken, were given in the Memoirs of the Academy of Sciences at Paris for the year 1743. And the Memoir was entitled ' De FOrbite de la Lune dans le Systeme Neuutonien.
Page xix - ... to any curve, whatever were the law of its description. From its application to an ellipse, it resulted that the law of force, tending to its focus, was inversely as the square of the distance : and it easily followed, by a converse process, that a body projected obliquely to a line joining it and the centre of force (the force varying inversely as the square of the distance) would describe an ellipse round that centre. This may be considered as the first instance of that law •which is frequently...
Page 125 - XLV.) the body's place may nearly be found in a moveable ellipse, when the orbit's eccentricity is very small; and the like equations and constructions obtain approximately for all other values of * It has been already remarked, (p. 122.) that some mathematicians, persuaded that Newton meant to find the progression of the Lunar Apogee by the method of the ninth Section, have pursued that method. Now in that Section there is no tangential disturbing force, and, besides, the expression for that part...
Page xl - ... peculiar relations among the periodic times of the planets, which do not compensate each other till after one, or even till after many revolutions of both bodies. A periodical inequality of this kind in the motions of Jupiter and Saturn, has a period of no less than 918 years. The radial force, or that part of the disturbing force which acts in the direction of the line joining the centres of the sun and disturbed planet, has no effect on the areas, but is the cause of periodical changes of small...