A binary star system has two stars, each with the same mass as our sun, separated by 1.00×10¹² m. A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a straight line that passes through the midpoint between the two stars.

What is the comet's speed at the midpoint?

Model the two stars as spherical masses, and the comet as a point mass. This is an isolated system, so mechanical energy is conserved.

In the initial state, the comet is far away from the two stars and thus it has neither kinetic energy nor potential energy. In the final state, as the comet passes through the midpoint connecting the two stars, it possesses both kinetic energy and potential energy.

The conservation of energy equation is