Comments on: Two planets with identical mass are orbiting a distant star at the same speed. Planet X is twice as far from? http://www.ufo-watch.com/conspiracies-2/two-planets-with-identical-mass-are-orbiting-a-distant-star-at-the-same-speed-planet-x-is-twice-as-far-from.html UFO videos, images and reports from all over the world. Wed, 23 May 2012 20:04:39 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: not_publius http://www.ufo-watch.com/conspiracies-2/two-planets-with-identical-mass-are-orbiting-a-distant-star-at-the-same-speed-planet-x-is-twice-as-far-from.html#comment-5893 not_publius Mon, 17 Oct 2011 19:56:53 +0000 http://www.ufo-watch.com/conspiracies-2/two-planets-with-identical-mass-are-orbiting-a-distant-star-at-the-same-speed-planet-x-is-twice-as-far-from.html#comment-5893 The net force on each planet: F = mv^2/r v = sqrt(rF/m) For planet X: v = sqrt[(2r)(FX)/m] [1] For planet Y (mass and speed are the same as planet X): v = sqrt[(r)(FY)/m] [2] [1] = [2]: sqrt[(2r)(FX)/m] = sqrt[(r)(FY)/m] 2(FX) = (FY) Because this answer is inconsistent with the dynamics approach (inverse square law due to gravity), this problem describes an unrealistic scenario... Either the gravitational forces on these planets don't follow an inverse square law (to have the same speed under the other conditions given) or (more likely) the creator if this problem gave too much (erroneous) information in the problem (the planets won't have the same speed acting under gravity at the distances given). The net force on each planet:
F = mv^2/r
v = sqrt(rF/m)

For planet X:
v = sqrt[(2r)(FX)/m] [1]

For planet Y (mass and speed are the same as planet X):
v = sqrt[(r)(FY)/m] [2]

[1] = [2]:
sqrt[(2r)(FX)/m] = sqrt[(r)(FY)/m]
2(FX) = (FY)

Because this answer is inconsistent with the dynamics approach (inverse square law due to gravity), this problem describes an unrealistic scenario… Either the gravitational forces on these planets don’t follow an inverse square law (to have the same speed under the other conditions given) or (more likely) the creator if this problem gave too much (erroneous) information in the problem (the planets won’t have the same speed acting under gravity at the distances given).

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