I am confused about the concept of work in relation to conservative and non-conservative forces.
When transferring a satellite from a lower orbit into a higher orbit via a Hohmann transfer, my understanding is that work is initially done to increase the satellite's kinetic energy instantaneously to move it into an elliptical orbit, and then gravity does negative work in converting the satellite's kinetic energy to potential energy (this is simplified and disregards changes in energy in correcting the satellite's orbit into a circular shape).
I learnt that the work done was equal to the change in energy, or you could sum up the work done by the individual forces. I also learnt that work done by conservative forces is equal to change in kinetic energy, whereas work done by non-conservative forces is equal to change in total energy. However in this scenario, both gravity and the non-conservative force used to convert fuel to kinetic energy do work, but if you sum it up it does not equal to the total change in energy which is very confusing.
I'm very lost, please help!