Thanks. I guess my "solution" to the problem of landing the 1st stage back on the ground has gradually converged towards the SpaceX solution, which is no doubt close to optimal.....but I was wondering how @BrianJ managed to get the autopilot so incredible accurate (I mean it is doing the same burns at the same time as the original)? Did you just reverse-engineer the original SpaceX one from videos, or did you have some better source?
Since SpaceX have not been forthcoming with much hard info about the specs and functions of the Falcon9, I have relied on estimated data from Spaceflight101 (which concurs with most other websites) and comments dropped at press conferences etc., as well as watching the launch videos.
Apart from that, this old 1962 Ministry of Aviation paper "Minimum Energy Ballistic Trajectories Over A Non-Rotating Earth", was a help figuring the boostback flight vector.
The rest of it is put together from whatever I still remember from High School maths and physics :-D
Watching the SAOCOM launch video, I note the 1st stage came down a bit slower than the add-on, and the upper stage burned a bit longer, but otherwise the timings are pretty close. Which is nice
Cheers,
BrianJ

