Randall D. Knight — Dynamics II: Motion in a Plane: Problem 4

A \( 3.5 \times 10^{10} \text{ kg} \) asteroid is heading directly toward the center of the earth at a steady speed of \( 18 \text{ km/s} \). To save the planet, astronauts strap a giant rocket that generates \( 4.0 \times 10^9 \text{ N} \) of thrust. The rocket is fired when the asteroid is \( 3 \times 10^6 \text{ km} \) away from the earth. You can ignore the earth’s gravitational force on the asteroid and their rotation about the sun. a. If the mission fails, how many hours is it until the asteroid impacts the earth? b. The radius of the earth is \( 6400 \text{ km} \). By what minimum angle must the asteroid be deflected to just miss the earth? c. What is the actual angle of deflection if the rocket fires at full thrust for \( 300 \text{ s} \) before running out of fuel?