# Hohmann Transfer - Adaptive Guidance Law

Is there an equivalent adaptive guidance law for the Hohmann transfer as there is with the initial ascent profile for a rocket launch (e.g. Powered Explicit Guidance)?

This is for a personal project - I have a simulator written and my goal is to add guidance. I want to recompute the desired transfer orbit based on the parking orbit realised during the initial ascent phase (incurring dispersion, but will target the highest possible orbit with fuel available in second stage).

I tried adapting the PEG to produce a steering law to produce a steering profile to move from first circular orbit to transfer, with a basic optimiser used to select position/velocity of the vehicle at the end of the first burn - but quickly realised that because the steering law as described in the original NASA TN (linked below) corrects for gravitational and centripetal accelerations, this produces a non-Hohmann steering profile (indeed in the nominal case the 'Hohmann' steering is such that the vehicle always points in the direction of travel?).

Thanks for any advice - I will provide more details if necessary.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Commented Nov 10, 2022 at 17:39
• @user49768 What kind of simulator? please expand on this. Commented Nov 10, 2022 at 17:39
• Equations of motion integrator. 6DOF with variable mass/variable centre of mass. Implemented in Simulink. I have full control over any implemented math - for both dynamic model or guidance law(s). Commented Nov 10, 2022 at 18:21
• You should look into using a Lambert solver rather than a Hohmann transfer. At a very low rate, you run the Lambert solver multiple times to find the propellant-optimal initiation and arrival times. At a moderate rate, you run the Lambert solver (once) using that previously solved-for arrival time. At a high rate, you correct the vehicle's orientation based on the direction from the moderate rate Lambert solver. At some point, you'll stop the burn because you're close enough. (You do not want to burn constantly.) You don't need PEG once the vehicle is on orbit. Commented Nov 12, 2022 at 13:14
• Thank you @DavidHammen - this seems to be exactly what I’m looking for. Commented Nov 14, 2022 at 8:12