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Obviously, the question as posed in the title is very incomplete. Allow me to rephrase it in more specific terms:

What are the minimum possible "combined parameters" (velocity, mass, angle of impact,?) for an asteroid be able to "significantly" (I agree that this is ambiguous too) alter Earth's orbit after impact?

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closed as off-topic by ACuriousMind, Jon Custer, heather, Gert, user36790 Sep 27 '16 at 4:40

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    $\begingroup$ Hi Matemáticos, no offense intended, but it's not that difficult to work out, it's basically two rocks hitting each other. take say one of the 1,000 NEO asteroids such as this one that NASA is going to: bbc.com/news/science-environment-37309903 500m wide $\endgroup$ – user108787 Sep 11 '16 at 19:36
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    $\begingroup$ this page contains all the answers you need ( there is a link to a document ). Bonus : you can test any crazy scenario $\endgroup$ – user46925 Sep 11 '16 at 23:01
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Any asteroid no matter the size that comes close to the Earth will change the orbit by gravitational forces a little. The change may be so minuet its not measurable by instruments but is measurable by math. https://en.wikipedia.org/wiki/List_of_Earth-crossing_minor_planets enter image description here

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