What would have to be the mass of this asteroid, in terms of the earth's mass MM , for the day to become 23.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.

The mass of this asteroid, in terms of the earth's mass m = 0.092 M.

Explanation:

The length of the day T = 2π rad / ω.

where ω = Earth's angular rotation rate

Conservation of angular momentum applied to collision between the Earth and the asteroid gives:

                    and

                    which gives

          and  

 The mass of this asteroid, in terms of the earth's mass m = 0.092 M.