An Introduction to Celestial MechanicsMacmillan, 1902 - 384 pages |
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Common terms and phrases
a₁ acceleration angle areal velocity astronomical axes B₁ becomes c₁ c₂ center of mass central force comet components of attraction computed conic section coördinates cos² curve defined determined differential equations direction distance disturbing dt dt earth eccentric anomaly eccentricity ecliptic elements ellipse ellipsoid equal expressed exterior particle follows force varies function geocentric given infinitesimal body Kepler's equation line of apsides m₁ major axis meters method moon motion na² Newton node normal component observations orbit origin P₁ parabola perigee perihelion perturbations plane polar coördinates positive problem r₁ r₂ radius vector respect right member rotation shell sin² solution solved sphere spherical square Substituting Suppose surface t₁ T₂ tangential tangential component theorem theory true anomaly u₁ variables variation velocity x-axis x₁ zero
Popular passages
Page 77 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 4 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 3 - LAW I. Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Page 234 - They communicate this tendency to the whole earth so that the plane of the earth's equator turns in the retrograde " direction on the plane of the ecliptic. On the other hand, it follows ' from the symmetry of the figure with respect to the nodes of the orbits of the particles of the equatorial ring that there will be no change in the inclination of the plane of the equator to that of the ecliptic or the moon's orbit. The mass moved is so great, and the forces acting are so small, that this retrograde...
Page 42 - ... as the differences increase. Theoretically, in all gases the range of the values of the velocities is from zero to infinity, although the extreme cases occur at infinitely rare intervals compared to the others. Under constant pressure the velocities are directly proportional to the square root of the temperature, and inversely proportional to the square root of the molecular weight. Since in all gases all velocities exist, some of the molecules of the gaseous envelopes of the heavenly bodies...
Page 53 - The following may be taken for this purpose : — 1. The locus of the second foci of the paths of all projectiles leaving a given point, with a given velocity, in a vertical plane, is a circle. 2. The direction of projection for the greatest range on a given line, passing through the point of projection, bisects the angle between the vertical and the line. 3. Any other point on the line which can be reached at all, can be reached by two different paths, and the directions of projection for these...
Page 249 - made his head ache and kept him awake so often that he would think of it no more.
Page 55 - CALORIE is the amount of heat required to raise the temperature of one kilogram of water one degree centigrade.
Page 128 - Any two bodies attract each other with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Page 19 - The coordinates of the vector in the ox'y' system are (x',y') and, furthermore, as may be verified, x' = x cos 6 + y sin 6 y