Chapter 9, Problem 53EAP

53. The gravitational attraction between two objects with masses m₁and m₂, separated by distance x, is F = Gm₁m₂/x², where G is the gravitational constant.

1. How much work is done by gravity when the separation changes from x₁to x₂? Assume x₂< x₁.

If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a 1.5 × 10¹³ kg comet is passing the orbit of Mars, heading straight for the sun at a speed of 3.5 × 10⁴m/s. what will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and G = 6.67 × 10-11 N m²/kg²