If half of the earth is blown away by the impact of a comet, what happens to the orbit of the moon?
During impact
After impact
Details and Assumptions:
- The mass of the earth M is simply halved by the impact, without the fragments interacting with the moon of mass m.
- Before the impact, the moon's orbit is a perfect circle with radius r0.
- M≫m, so the moon can hardly affect the motion of the earth.
- Both the energy E=21mv2+V(r) and the angular momentum L=mr2ϕ˙ of the moon are preserved, where r 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)=−GrMm, where G is the gravitational constant.