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Updated: August 18, 2024
The two cases only differ in this, that the form of the orbit was not, like the form of the earth itself, deduced by ratiocination from facts which were marks of ellipticity, but was got at by boldly guessing that the path was an ellipse, and finding afterward, on examination, that the observations were in harmony with the hypothesis. According to Dr.
Now and then, at intervals of hundreds of thousands or millions of years, the orbit becomes very elliptical; then again for long periods it may in form approach a circle. When in the state of extreme ellipticity, the precession of the equinoxes will cause the hemispheres in turn each to have their winter and summer alternately near and far from the sun.
The moon, and it is this circumstance which renders the result of such inestimable value, ought to assign, and has in reality assigned the general ellipticity of the earth; in other words, it has indicated a sort of mean value of the various determinations obtained at enormous expense, and with infinite labour, as the result of long voyages undertaken by astronomers of all the countries of Europe.
If this result were correct, Leverrier would have no need of looking for intermercurial planets to account for the motion of the perihelion of Mercury; he would find a sufficient cause in the ellipticity of the sun.
The smallness of the outstanding uncertainty can be judged of by comparing J. B. Listing's with General Clarke's results, published in the same year . Listing stated the dimensions of the terrestrial spheroid as follows: Equatorial radius = 3,960 miles; polar radius = 3,947 miles; ellipticity = 1/288·5. Clarke's corresponding figures were: 3,963 and 3,950 miles, giving an ellipticity of 1/293·5.
My mind and my heart were much disposed to admire all, to respect all, that was connected with him who had discovered the cause of the secular equation of the moon, had found in the movement of this planet the means of calculating the ellipticity of the earth, had traced to the laws of attraction the long inequalities of Jupiter and of Saturn, &c. &c.
These, though they confirm the foregoing results, give a somewhat greater ellipticity to the earth than that found by the measurement of degrees. Pendulums vibrate more slowly the nearer they are to the equator. It follows, therefore, that they are there farther from the centre of the earth.
But, as a result of the rapid rotation of the great planet, and the ellipticity of its figure, the unfortunate visitor could find a perceptible relief from his troublesome weight by seeking the planet's equator, where the centrifugal tendency would remove about twenty pounds from every one hundred as compared with his weight at the poles.
So many took part in these singular experiments, which assumed rather the appearance of outdoor sports than of scientific demonstrations, that in a short time we had provided the asteroid with a very large number of little moons, or satellites, of gold, which revolved around it in orbits of various degrees of ellipticity, taking, on the average, about three-quarters of an hour to complete a circuit.
Many of the asteroids have very eccentric orbits, and their orbits are curiously intermixed, varying widely among themselves, both in ellipticity and in inclination to the common plane of the solar system.
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