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It does, but because the Earth is so much more massive than a person, the movement is extremely small, far too small to be measured.

Action and reaction are equal and opposite, and momentum is conserved when you jump - the sum of your momentum and the Earth's.

Supposing you have a mass of 70 kg and you apply a jumping force of 140 kg or 1372 Newtons for 0.1 seconds, an impulse of 137.2 Newton-seconds. Impulse equals change of momentum so your momentum is Mv = Ft or in this case 70 x v = 137.2 and your upward speed is initially 1.96 metres per second. For the Earth the same applies and Mv = Ft tells us the the Earth's downward speed initially is given by 6E21 x v = 137.2 so that the Earth's inital speed is 2.3E-20 metres per second - assuming that the Earth is totally rigid! That is a displacement that is far too small to be detected.

NB the notation 6E21 is an alternative that means six times ten to the power 21 on web sites that fail to provide the normal subscripted notation.

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