this is my first question here; and a lot of what I've learnt so far has been pretty much self taught so I thought I best hear from professionals. :)
First let me set the scene as to what I am trying to achieve...
I am trying to calculate the fuel cost for a single stage to orbit spaceplane travelling from London Heathrow to Sydney Australia as part of my dissertation. For the purpose of avoiding supersonic overflight of populated areas (i.e. Europe), it is necessary to depart to the south-west in the climb to orbit. Since I am already facing that direction once I reach 7.84km/s at 100km above sea level, I thought I may as well just orbit in that direction (i.e between retrograde and polar) and follow a great circle that would take me over Sydney.
What I've calculated so far: is the change in net thrust, acceleration, mass, velocity, ect throughout the climb. What I've ended up with is a mass for my propellant and oxidiser used throughout the ascent under rocket thrust. Things like drag have been accounted for. I have assumed the atmosphere is under ISA conditions, with still and dry air. And I'm assuming a simplified circular orbit with a spherical earth.
Now, the point...
What I've NOT done, is take into account the direction I'm launching in. My calculations currently assume there's no spin at all. But I've read that a retrograde orbit is more costly to launch to than a prograde one. Is it a case of nothing more than increased drag? If so, are there altitudes at which this comes into effect? One would think that close to the surface (i.e. on a conventional airliner), the direction of the earths rotation is entirely negligible, so when is it not for spaceflight?
What I am assuming (just off the top of my head), that as acceleration due to gravity decreases in the ascent, the actual velocity of the aircraft in space and the velocity relative to the earths surface begins to differ, with the latter being the higher (if retrograde) and therefore with greater drag, if this is true than I suppose what I am asking is how to work it all out.
I understand that was a lot to read but I really appreciate your help! (Also, if my orbit passed over Sydney, is my inclination just the Latitude of Sydney? Thanks again!)