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What is the bare minimum of deviating a planet's orbit?

Since earth's and Sun's gravitational force is balanced by earth's centrifugal force. Also as not much is given, I think you can take the value just above or equal to Gravitational force btw sun and earth, this should work in my understanding.

Edit: quick Google search says it's 3.57 × 10 22 N, so Class Z LS. Nothing is given about how much it deviated but I'd say it wouldn't be as negligible, so take around earth's radius of half of it and multiply with 3.57 × 10²² N, to get energy.
 
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