Deep impact

If half of the earth is blown away by the impact of a comet, what happens to the orbit of the moon?

During impact During impact After impact After impact

Details and Assumptions:

  • The mass of the earth MM is simply halved by the impact, without the fragments interacting with the moon of mass m.m.
  • Before the impact, the moon's orbit is a perfect circle with radius r0.r_0.
  • Mm,M \gg m, so the moon can hardly affect the motion of the earth.
  • Both the energy E=12mv2+V(r)E = \frac{1}{2} m v^2 + V(r) and the angular momentum L=mr2ϕ˙L = m r^2 \dot \phi of the moon are preserved, where rr is an arbitrary distance between the earth and moon after the impact.
  • The gravitational potential energy of the earth and moon system reads V(r)=GMmr,V(r) = - G \frac{M m}{r}, where GG is the gravitational constant.

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