If half of the earth is blown away by the impact of a comet, what happens to the orbit of the moon?
Details and Assumptions:
- The mass of the earth is simply halved by the impact, without the fragments interacting with the moon of mass
- Before the impact, the moon's orbit is a perfect circle with radius
- so the moon can hardly affect the motion of the earth.
- Both the energy and the angular momentum of the moon are preserved, where is an arbitrary distance between the earth and moon after the impact.
- The gravitational potential energy of the earth and moon system reads where is the gravitational constant.