Ive been trying to come up with a program for a rocket to start to conduct a smooth gravity turn at 5000m to reach a 100km orbit. Ive been trying to find some sort of mathematical formula relating the time elapsed to the pitch angle of the rocket. I feel like the secret lies within the logarithmic or square root function, but what are your thoughts?
I looked for the same thing, and it turned out to be pretty complex. Here's what I found:
https://tinyurl.com/wp4xhyf