# Annals of the Astronomical Observatory of Harvard College Volume 61-62

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 edition. Excerpt: ...nearly opposite to the aphelion of the comet, and we will further assume that its distance from the Sun is 400 units, that is to say the distance of the assumed planet Q. The calculation involves a solution of Kepler's problem, and therefore a general equation for it cannot be given, but an approximate value is readily obtained which will be quite accurate enough for our present purposes. with a uniform velocity in traversing each of these ten sections of its orbit. The distances of the middle points of these sections from the perihelion is given in the sixth column. The distances in the fifth column are each equal to r+1. Subtracting 1 and taking the reciprocals gives us the numbers in Let us assume a comet whose aphelion distance is 399 units, and its 199 perihelion unity. Its eccentricity therefore =----= 0.995. Its velocity v in any portion of its orbit is given by the formula for elliptic motion u2 = U% n where U is the parabolic velocity, and is therefore a constant for all ellipses having the same perihelion distance. When this distance is unity and the mass equal to that of the Sun, U = 42.10 km. per sec. In the above formula n is the mass of the Sun, r the radius vector of the comet, and s its aphelion distance. A comet moving in an orbit whose semi-major axis is 200 units has a period of 2,828 years. In the first column of Table XLIV the semi-period is divided into ten equal parts starting from the aphelion, and the year given at which it reaches each of the eleven dividing points of its orbit. The second and third columns give the corresponding mean and eccentric anomalies, the latter being taken directly from Astrand's tables. The fourth column gives the natural cosines of the eccentric anomalies, and the fifth, obtained by...