Mean-motion Sentence Examples
Eight times the mean motion of Venus is so nearly equal to thirteen times that of the earth that the difference amounts to only the 2.
Instead of the period it is common in astronomical practice to use the mean angular speed, called the mean motion of the body.
It follows that putting n for the mean motion and T for the period of revolution we shall have in degrees nT=3600.
In these cases therefore the mean distance and mean motion are regarded as different elements, and the whole number of the latter is seven.
Putting a for the mean distance of the earth from the sun, and n for its mean motion in one second, we use the fundamental equation a3 n2 = Mo-1-M', Mo being the sun's mass, and M' the combined masses of the earth and moon, which are, however, too small to affect the result.Advertisement
For the mean motion of the earth in one second in circular measure, we have n 8149' l o g.
The moon's apparent mean motion in longitude seems also to indicate slow periodic changes in the earth's rotation; but these are not confirmed by transits of Mercury, which ought also to indicate them.
The motions of individual stars, it is true, vary widely, but if the mean motion of a number of stars is considered this tendency is always to be found.
Accordingly this mean motion of the stars relative to the sun has been more generally regarded from another point of view as a motion (in the opposite direction-towards the constellation Lyra) of the sun relatively to the stars.
Having determined the motions of the two drifts, and knowing also that the stars are nearly equally divided between them, it is evidently possible to determine the mean motion of the drifts combined.Advertisement
Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of ellipsoids; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.
In the following year his memoir on the secular acceleration of the moon's mean motion partially invalidated Laplace's famous explanation, which had held its place unchallenged for sixty years.
Assuming the mean motion of the moon to be known and the perigee to be fixed, three eclipses, observed in different points of the orbit, would give as many true longitudes of the moon, which longitudes could be employed to determine three unknown quantities - the mean longitude at a given epoch, the eccentricity, and the position of the perigee.
By taking three eclipses separated at short intervals, both the mean motion and the motion of the perigee would be known beforehand, from other data, with sufficient accuracy to reduce all the observations to the same epoch, and thus to leave only the three elements already mentioned unknown.
The mean motion of the moon round the earth is then invariable, the longitude containing no inequalities of longer period than that of the moon's node, 18.6 y.Advertisement
But Edmund Halley found, by a comparison of ancient eclipses with modern observations, that the mean motion had been accelerated.
Laplace first showed that modern observations of the rpoon indicated that its mean motion was really less during the second half of the 18th century than during the first half, and hence inferred the existence of an inequality having a period of more than a century.
It is shown in the article Astronomy (Celestial Mechanics) that the mean distance and mean motion or time of revolution of a planet are so related by Kepler's third law that, when one of these elements is given, the other can be found.
In an elaborate memoir 2 he showed that the ancient solar eclipses described by Herodotus, Thucydides, and others, which seemed to require an increased value of the secular acceleration of the moon's mean motion to bring them into line with modern results, might safely be neglected, the ambiguity of the accounts in each case rendering uncertain either the totality of the eclipse or the place from which it was visible.