So, a satellite launch takes a huge amount of fuel to launch a relatively small (compared to total rocket weight at takeoff) satellite into orbit. Obviously there is a lot of energy expended during the launch, but what percentage of the expended energy is actually needed to get the satellite itself up into orbit? I suppose it would just be a ratio of the amount of kinetic energy the satellite has at release in orbit compared to the potential energy of the fuel the rocket burns to get it there.
For a specific common scenario, consider a SpaceX Falcon9 launch of a max-weight satellite to LEO. Research on the SpaceX website indicates that its GTO capacity is 22,800kg. Other research indicates that the Falcon9 carries 136,900kg of RP-1 between its first two stages. However, I'm struggling to find out how to calculate the kinetic energy of such a satellite in LEO and the potential energy in the fuel.