An artificial earth satellite is initially orbiting the earth in a circular orbit of radius r0. at a certain instant, its rocket fires for a negligibly short period of time. this firing accelerates the satellite in the direction of motion and increases its velocity by a factor of α. the change of satellite mass due to the burning of fuel can be considered negligible. 1. let e0 and e denote the total energy of the satellite before and after the firing of the rocket. find e solely in terms of e0 and α. 2. for α > αes the satellite will escape from earth. what is αes? 3. for α < αes the orbit will be elliptical. for this case, find the maximum distance between the satellite and the center of the earth, rmax, in terms of r0 and α.