A satellite is initially in circular orbit at radius R about a planet of mass M. We wish to transfer it to a new circular orbit at radius 2R, using an intermediate transfer orbit which is an ellipse with perigee R and apogee 2R. We make a brief rocket burn in the longitudinal direction to switch from circle to ellipse at r = R, and another burn at r = 2R to exit the ellipse and start the larger circle. What are the two velocity changes required? What is the eccentricity of the transfer ellipse? How long does the transfer take?