 | Henry William Watson, Edward John Routh - 1860 - 240 pages
...that point remaining the same, the periodic time will be unaltered, and the sum of the new axes is to their difference as the sum of the old axes to the distance between the foci. (vel.)2 at B = — = //a2, where a = semi-diameter parallel to the a major axis of the old orbit ;... | |
 | Harvey Goodwin - 1862 - 174 pages
...remaining the same at that point, the periodic time will be unaltered, and the sum of the new axes is to their difference as the sum of the old axes to the distance between the foci. 11. A perfectly elastic particle describing a parabola about the focus and moving towards the vertex,... | |
 | Sir Isaac Newton - 1863 - 316 pages
...force suddenly becomes repulsive ; determine the nature, position, and dimensions of the new orbit. 18. A particle is describing an ellipse under the action...of the old axes to the distance between the foci. 19. An ellipse and its auxiliary circle are described by two bodies in the same periodic time under... | |
 | Edward John Routh - 1898 - 435 pages
...point remaining the same. Prove that the periodic time is unaltered and that the sum of the new axes is to their difference as the sum of the old axes to the distance between the foci. [Math. Tripos, I860.] By Art. 325 the new orbit is an ellipse having the centre of force S in the centre.... | |
 | Edward John Routh - 1898 - 440 pages
...point remaining the same. Prove that the periodic time is unaltered and that the sum of the new axes is to their difference as the sum of the old axes to the distance between the foot [Math. Tripos, I860.] By Art. 325 the new orbit is an ellipse having the centre of force S in... | |
 | Isaac Newton - 1900 - 320 pages
...the parabola; shew that the planet will move through about 76° 22' of longitude, while the cornet passes from one extremity of the latus rectum to the...of S, prove that the new orbit may be a parabola if « > -J, and that, in this case, SP passes through the intersection of the two circles, one described... | |
 | Charles Ernest Weatherburn - 1921 - 218 pages
...point remaining the same, show that the periodic time is unaltered, and that the sum of the new axes is to their difference as the sum of the old axes to the distance between the foci. 15. A particle describes an ellipse with one focus S as the centre of force. When the particle is at... | |
 | Edward John Routh - 1960 - 440 pages
...point remaining the same. Prove that the periodic time is unaltered and that the sum of the new axes is to their difference as the sum of the old axes to the distance between the foci. [Math. Tripos, I860.] By Art. 325 the new orbit is an ellipse having the centre of force t~S in the... | |
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A particle is describing an ellipse under the action of a force tending to the focus ; if, on arriving at the extremity of the minor axis, the force has its law changed, so that it varies as the distance, the magnitude at that point remaining... 