Theoretical Astronomy Relating to the Motions of the Heavenly Bodies Revolving Around the Sun in Accordance with the Law of Universal Gravitation, Embracing a Systematic Derivation of the Formulæ for the Calculation of the Geocentric and Heliocentric Places, for the Determination of the Orbits of Planets and Comets, for the Correction of Approximate Elements, and for the Computation of Special Perturbations; Together with the Theory of the Combination of Observations and the Method of Least Squares. With Numerical Examples and Auxiliary TablesJ.B. Lippincott & Company, 1885 - 662 síður |
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Common terms and phrases
according accuracy action adopted already angle anomaly appears applied approximate argument ascension assumed auxiliary becomes body calculation centre co-ordinates comet complete computed condition consider constant corrections corresponding denote derived determined Diff differences differential coefficients Direct directly distance disturbing dt dt earth ecliptic effected elements equal equations error expressed final force formula function fundamental furnish further geocentric given gives heliocentric hence integration interval introduce known latitude limits longitude manner mass means method motion multiply necessary neglected observed obtain orbit parabolic perihelion perturbations plane positive probable reduced referred regard remains respect Retrograde Substituting successive Table taken third tions true unit unknown quantities values variation weight
Vinsælir kaflar
Síða 6 - ... also such practical directions as might guide the inexperienced computer, might add very materially to the progress of the science by attracting the attention of a greater number of competent computers. Having carefully read the works of the great masters, my plan was to prepare a complete work on this subject, commencing with the fundamental principles of dynamics, and systematically treating, from one point of view, all the problems presented.
Síða 538 - ... the most probable values of the corrections to be applied to the assumed position of the solar apex.
Síða 26 - If (x, y, z) be the coordinates of the centre of gravity of the body d2x we have, by Art.
Síða 378 - A system of linear equations has a definite number of solutions, (i.) When the number of equations is the same as the number of unknown numbers.
Síða 81 - Si, is the angular distance of this point from the vernal equinox. The line of intersection of the plane of the orbit with the fundamental plane is called the line of nodes. The angle which the plane of the orbit makes with the plane of the ecliptic, which we will denote by i, is called the inclination of the orbit. It will readily be seen that, if we suppose the plane of the orbit to revolve about the line of nodes, when the angle i exceeds 180°...
Síða 86 - ... case of Mercury, this intermediate date is mean noon of the day immediately following; in the case of Venus, Mars, Jupiter, and Saturn, it is mean noon of the second day following; and in the case of Uranus and Neptune, mean noon of the fourth day following. Pages 264 — 271 contain the rectangular co-ordinates of the centre of the sun, referred to the centre of the earth as the origin, and to the true equator and equinox of each date as the circle and point of reference. Each co-ordinate is...
Síða 324 - ... billions of units of heat. The effect produced by the rays of the sun on the surface of the earth in one minute is therefore 5-5 cubic miles of heat. Let us imagine the sun to be surrounded by a hollow sphere whose radius is equal to the mean distance of the earth from the sun, or 20,589,000 geographical miles ; the surface of this sphere would be equal to 5326 billions of square miles.
Síða 43 - ... of the primary. The Integrals of these equations introduce six arbitrary constants of integration, which, when known, will completely determine the undisturbed motion of m relative to the sun. If we multiply the first of these equations by y, and the second by x, and subtract the last product from the first, we shall find, by integrating the result, xdy — ydx _ ~dt~ = 0> c being an arbitrary constant.
Síða 556 - ... and in a sense contrary to that of the motion. The amount of the resistance will depend chiefly on the density of the ethereal fluid and on the velocity of the body. In accordance with what takes place within the limits of our observation, we may assume that the resistance, in a medium of constant density, is proportional to the square of the velocity. The density of the fluid may be assumed to diminish as the distance from the sun increases, and hence it may be expressed as a function of the...
Síða 38 - F, since the square root of this quantity appears frequently in the formulae which will be derived. If we take arbitrarily the mass of the sun as the unit of mass, the unit of time must be determined. Let t denote the number of mean solar days which must be taken for the unit of time when the unit of mass is the mass of the sun. The space which the force due to this mass, acting constantly on a material point at a distance equal to the mean distance of the earth from the sun, would cause the point...