1. The problem statement, all variables and given/known data A asteroid is hurtling towards Earth and humankind has decided to fire a nuclear warhead at it in order to avert disaster. In order be most effective the rocket carrying the warhead has to impact the asteroid at 40km/s. The rocket itself travels at 12km/s. What remains is to calculate the speed of the asteroid. During its elliptical orbit, the asteroid's greatest distance from the sun is 2.8 astronomical units (AU) and its smallest 1.00 AU. Its average distance from the sun is then 1.9 AU. 2. Relevant equations 1 x AU = 1.4960 * 1011m The formula provided for calculating the speed of the asteroid is: V2 = G * M * ((2/r) - (1/a)) where G *M = 1.327 * 1020 (gravitational constant times solar mass), r is the asteroid's distance from the sun (the book doesn't specify whether it is the greatest distance or the smallest) and a is its average distance from the sun. 2.8 * 1.4960 * 1011 = 4.1888 * 1011 = r 1.9 * 1.4960 * 1011 = 2.8424 * 1011 = a 3. The attempt at a solution Plugging the relevant values into the equation thus: V2 = 1.327 * 1020 * ((2/4.1888 * 1011) - (1/2.8424 * 1011)) gives 1.668 * 108 Taking the square root of both sides gives: sqrt(V2) = sqrt(1.668 * 108) ⇔ V = 12915.1 Assuming my answer is correct, I've no idea what the given units are. Whether metres per second, or kilometres per hour, the value still seems incredibly high, given how fast asteroids actually travel. Have I gone wrong somewhere?