An impact by a 10 kilometres asteroid on the Earth has historically caused an extinction-level event due to catastrophic damage to the biosphere. There is also the threat from comets coming into the inner Solar System. The impact speed of a long-period comet would likely be several times greater than that of a near-Earth asteroid, making its impact much more destructive...
Of course this is a paradoxical situation and question, but: suppose a perfectly spheric asteroid with radius of a few (hundred?) kilometers is on a collision course with the Earth.
If I were standing on its surface, could I deviate its direction just jumping on it in a direction perfectly perpendicular to the vector of velocity?
If it is possible, what is the angle of deflection, and the maximum size of an asteroid I could deviate?
The asteroid has velocity and momentum in the direction of motion. On the normal direction momentum is zero and we know that it takes negligible/non zero energy to change the direcion of motion. Can we consider the action on the perpendicular as if the asteroid were at rest and treat it like a collision, with conservation of momentum etc?
If the abovesaid is correct, how do we measure the angle of deflection? In what way the push/jump can be calibrate to obtain a desired oucome?