PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two identical spherical asteroids, each of mass 2.0×1012kg, are initially held at rest with their centers separated by an unknown distance r. At this instant, the gravitational potential energy of the asteroid–asteroid system (taking the zero of potential energy at infinite separation) is measured to be −1.5×105J.
After release, the asteroids accelerate toward each other solely under their mutual gravitational attraction. Neglect all other forces. Use G=6.67×10−11Nm2kg−2.
(a) Determine the initial separation distance r between the centers of the two asteroids.
(b) When the separation has decreased to 21r, calculate the total kinetic energy of the two-asteroid system at that instant.
(c) Under the same conditions as in part (b), find the speed of each asteroid relative to the center of mass of the system.
(d) Explain qualitatively how your answers to parts (b) and (c) would change, if at all, if the asteroids had unequal masses while the initial potential energy remained the same magnitude.