Randall D. Knight — Newton's Theory of Gravity: Problem 53

Two stationary \(5.0 \times 10^{18} \text{ kg}\) asteroids are \(500 \text{ km}\) apart, measured between their centers. A Federation spaceship tries to fly between the asteroids when, as luck would have it, the anti-matter reactor blows, releasing \(1.5 \times 10^{23} \text{ J}\) of energy. 2.0% of that energy goes to the asteroids, with each receiving an equal share, driving them apart. How far apart do they get before gravity pulls them back together?