Orbit Collision

[me9900]

1. The problem statement, all variables and given/known data
If Halley's comet hits the earth head on and after the collision the earth continues to move in its initial direction but with 12% greater speed, find the new semi-major and semi-minor axes on the new earth orbit in terms of the earth-sun distance (R) for the present circular orbit of the earth.


2. Relevant equations
F=ma
F=GMm/r^2


3. The attempt at a solution

[HalfThere]

Remember that the earth's angular momentum is conserved through its orbit.
L = mvr

And consider that, since the earth's new velocity is in the same direction as before, it would go back to R for its semi-minor axis, due to the fact that the new velocity is in a single coordinate only, and it therefore has no force pushing it tangentially from its original path - it only moves tangential relative to it's old path as it diverges from it due to higher speed.

[me9900]

I don't necessarily agree with R remaining as the semi-minor axis because the origin of orbit(now an ellipse) isn't at the previous focus (being the sun). However, could R be given by a-c=R or (semi-major axis)-(distance from origin to focus)=R ?