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Jumping off an asteroid is no big deal as its gravitational pull would be small. But in the absence of any other heavenly bodies your combined center of mass would continue to accelerate earthwards, so in order not to participate in the extinction event, you would have to jump away from the earth at or above escape speed. Whilst this would exonerate you from the evolution of mankind in your own mind, it would however bring forward the date of extinction by accelerating the asteroid earthwards, and incur the wrath of treehuggers.
While a good fantasy, it isn't really true.The asteroid must arrive at earth's orbit around the sun at the precise date and time.