1. The problem statement, all variables and given/known data A comet in a circular orbit around the Sun has speed v0 and radius r0 = aRE , where RE is the radius of the Earth’s orbit and α is a constant > 1. The comet has its velocity reduced by Δv in a collision that does not change its initial direction. Show that the minimum value of Δv required to move the comet into an orbit which intersects the Earth’s orbit is given by delta v min = vo[1- root(2/(1+a))] 2. Relevant equations 3. The attempt at a solution Not sure what the neatest way to proceed is? Im guessing we look at energy and angular momentum.. after the collision, total energy is 1/2 m(vo - delta v)^2 - PE (which is unchanged).. But when i put this into the Ellipse equation for energy i.e. E = 1/2m(dr/dt)^2 + J^2/... etc and set dr/dt = 0 and J = mRe(vo-deltav)..i get everything cancelling out and leaving vo^2 = GM/Re.. not sure what im meant to do basically!