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Please note that "fastest" can be interpreted two ways: the actual speed a planet is traveling around the sun, or the actual time required for a given planet to complete it's orbit around the sun. In the first case, the larger a planet is, the greater it's mass and therefore the higher it's speed. One of the gas giants like Jupiter or Saturn being hundreds of times times larger than the inner planets like earth is traveling at immense speed. In the second case, the closer a planet is to the sun the shorter it's orbit will be and generally the faster it's trip will be. The planet closest to the sun and having the shortest obit around it is Mercury.

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