- Use a massive hydrogen balloon (inb4 Hindenburg) to raise your partially-fueled rocket with payload attached up to 50 km altitude (essentially the top of the atmosphere for our purposes).
- Before the balloon bursts from the low pressure, quickly condense and pump the hydrogen into one of the rocket fuel tanks. (or simply jettison the balloon?)
- Before you start to fall, ignite the rockets to compensate for the lost lift from the smaller balloon. Throttle up the engines as you deplete the balloon so you stay at constant altitude. Cut loose the balloon before it is empty (energy cost/benefit analysis?) & open the throttle.
- Since you are starting your rocket flight where there is little air and thus little atmospheric drag, you have tremendous gains in fuel efficiency over conventional launches. Get to the necessary speed and trajectory, then immediately cut engines. Use excess fuel to adjust orbit as necessary, and deploy the satellite(s). *Not for manned flight.
This actually seems doable. Just don't incinerate yourself up with the H2 if you try this.
massive hydrogen balloon capable of reaching 50 km
rocket capable of reaching LEO (160+ km) from 50 km
$$$$$, nav + fuel burn computers, earth coms, failsafes, light weight, lots of fuel and LOX engines
radiation and surge hardened computer + cameras + sensors + scientific instruments + antenas + heated batteries + solar panels + thrusters for orbit adjustments