## An Elementary Treatise on Astronomy. ..., Volume 2Smith, 1818 - 487 pages |

### From inside the book

Page ii

Robert Woodhouse. CHAP . IV . Page The Elliptical Elements of a Planet's Orbit

Robert Woodhouse. CHAP . IV . Page The Elliptical Elements of a Planet's Orbit

**determined**: its Major Axis , Eccentricity , Longitude of the Perihelion , Inclination of its Plane , Longitude of the Node , Epoch of the Passage of the ... Page iv

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**determination**of the Lunar Apogee not removed by these Corrections . The deduction of Terms on which the Secular ...**determining**the Progression of the Apsides in the simplest Case of the Problem of the Three Bodies . Clairaut's ... Page v

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**determining**the Radius Vector : Expression for R : its development into a Series of Cosines of Multiple Arcs . Conditions on which the Convergency of such Series depends . Application of the Differential Equation to the Investigation of ... Page vi

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**determined**from the Epochs and Durations of their Eclipses ......... ....... 357 CHAP . XXI . Principle of the Method for**determining**the Variations of the Elements of a Planet's Orbit . The Elements viewed as the Arbitrary Quantities ... Page viii

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**determined**. The Methods for**determining**the Masses of Venus , Mars , & c . and , generally , of Planets that are without Satellites . The Masses of Satellites and of the Moon**determined**............. 466 PR E F A C E. IT must be in ...### Other editions - View all

### 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...