An Introduction to Celestial MechanicsMacmillan, 1902 - 384 síður |
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Aðrar útgáfur - View all
Common terms and phrases
a₁ angle areal velocity axes B₁ becomes C₁ c₂ center of mass comet computed conic section constants of integration coördinates cos² curves derivatives determined differential equations direction distance disturbing acceleration dt dt earth eccentric anomaly eccentricity ecliptic elements ellipse ellipsoids equal expressed exterior particle finite bodies follows force varies function given homogeneous infinitesimal body inversely K₁ Kepler's equation line of apsides Lunar Theory m₁ major axis meteors method moon motion moves na² Newton nodes normal component orbit origin P₁ parabola perigee perihelion perturbations plane polar coördinates positive r₁ r₂ radius vector respect right member rotation sin² solution solved sphere Substituting Suppose surface t₁ t₂ tangential component theorem Three Bodies values variables variation velocity x-axis x₁ zero ак
Vinsælir kaflar
Síða 3 - 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.
Síða 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.
Síða 3 - Change of motion is proportional to the impressed force, and takes place in the direction of the straight line in which the force acts.
Síða 3 - III. To every action there is an equal and opposite reaction; or, the mutual actions of two bodies are always equal and oppositely directed.
Síða 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...
Síða 76 - Kepler's laws of planetary motion: 1. The orbit of each planet is an ellipse with the Sun at one of its foci.
Síða 213 - Conditions for Circular Orbits. The theorem of Lagrange that it is possible to start three finite bodies in such a manner that their orbits will be similar ellipses, all described in the same time, will be proved in this section. It will be established first for the special case in which the orbits are circles. It will be assumed that the three bodies are projected in the same plane. Take the origin at their center of mass and the f>7-plane as the plane of motion.
Síða 55 - The amount of heat generated is proportional to the product of the square of the velocity and the mass of the moving particle. Then, letting Q represent the number of calories, it follows that (44) Q = Cmv*.
Síða 109 - The attraction upon an interior particle is given by therefore X' = - -™- , agreeing with results previously obtained (Arts. 69, 70). XI. PROBLEMS. 1. Prove by the limiting process that the potential and components of attraction have finite, determinate, values, and that equations (11) hold when the particle is on the surface of the attracting mass. 2. Find the expression for the potential function for a particle exterior to the attracting body when the force varies inversely as the nth power of...
Síða 160 - The formulas will now be derived for determining the position referred to different systems of axes. The origin will first be kept fixed at the body with respect to which the motion of the second is given. Since most of the applications are in the solar system where the origin is at the center of the sun, the coordinates will be called heliocentric. Positions of bodies in the solar system are usually referred to one of two systems of coordinates, the ecliptic system, or the equatorial system. The...