The gravitational attraction between two objects with masses m₁ and m₂, separated by distance x, is F = Gm₁m₂ /x², where G is the gravitational constant.
a. How much work is done by gravity when the separation changes from x₁ to x₂? Assume x₂ < x₁.
b. 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 × 10⁴ m/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.