Abstract
IN the Annuaire du Bureau des Longitudes for 1889 occurs an interesting article by M. Tisserand on the methods employed in the measurement of the masses of the heavenly bodies. The writer begins with an explanation of the elementary principles leading to the law of Newton that all bodies attract one another with a force which is proportional to their masses and inversely as the square of the distance between them. He proves, in a popular manner, that this force is equal to the product of mass into acceleration; and therefore, speaking theoretically, to compare the masses of two bodies it is only necessary to apply directly to each of them the same force and to measure the acceleration produced; or, if a body be placed in succession at the same distance from the sun and the earth it will be attracted towards each with a force which is proportional to their masses. Hence, since the space traversed by a body is directly proportional to the acceleration, if during the first second the body fell 330 metres towards the sun, and 1 millimetre towards the earth, it would be obvious that the sun had a mass 330,000 times greater than the earth. Similarly, by applying the law of inverse squares, the relative masses of the sun and earth might be found when the distance of the body from each was not the same. We find that the earth falls towards the sun 10˙60 metres in a minute, and that our moon falls towards the earth 4˙90 metres in the same time. But the earth is 386 times nearer the moon than it is to the sun, so correcting for difference of distance we get 4˙9/(386)2 = 0˙0000328 metre as the fall of the moon towards the earth in a minute. Therefore the sun's mass is to the earth's mass as 10˙6 is to 0˙0000328—that is, 1/323,000. This method is, however, dependent on our knowledge of the distance of the sun and moon. The same calculation may be employed, without modification, to find the mass of a planet having a satellite. Kepler's third law is used for expressing the mass m of a planet in terms of the sun's mass M. The formula being:—
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GREGORY, R. On the Determination of Masses in Astronomy. . Nature 40, 80–82 (1889). https://doi.org/10.1038/040080a0
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DOI: https://doi.org/10.1038/040080a0