A Commentary On Newtons Principia With a Supplementary volume volume 1
A Commentary On Newtons Principia With a Supplementary volume volume 1
J M F John Martin Frederick Wright
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Finite] altitude A S On A S describe a circle and an equal circle round the center S. From any point of descent C erect the ordinate C D, join S D. Make the sector O S K = the area A D S (O K = A D + D C) the body will fall from A to C in the time of describing O K about the center S Vet. J. N 194 A COMMENTARY ON [SECT. VII. uniformly, the force oc _ -. Also S K being given, the period in the circle may be found, (P =^/ . R . S K *), and the time through O O K = P . - ? . The time through O K i...s known. . -. The time circumference through A C is known. 248. Find the time in which a Planet would fall from any point in its orbit to the Sun. H circle S P Time of fall = time of describing ^ O K H, S O = g-, 5. period in the circle O K H _ period in the circle rad. S O _ S O g period in the ellipse " period in the circle rad. AC A C ^ . -. The time of fall = i . P . Be considered a circle , P = period of the planet. If the orbit AC and the time of fall 4 V 2 p . Vs = P. Nearly. = nearly. BOOK I.
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