Hello awesome rocketeers, I hope that you are well!
I have been on a massive rabbit hole the past week where I discovered this game, discovered that it has a programming language and so I started to make myself an algorithm to get a rocket to a 100km circular orbit fully automated. The algorithm is completely calculating everything it needs to do so and there is almost no fixed user imput. I learned about orbital mechanichs and everything associated with it, really went into the physics with this one and wento also into vectors and whatever I found to be usefull. I managed to learn and do most of the things but now there is one more thing open which I can't solve and after 2 days of research and trying to figure out, I am writing this post to hopefully get an answer.
As I said, I made all the Delta V calculations and everything else so no need for help there.
My question is this:
-After takeoff, I burn through the 1st stage which brings me to about 37km.
-I start the 2nd stage to bring the apoapsis to 100km and then I shut the engine off. (the pitch function I use is simple and similar to a gravity turn so that means that when apoapsis hits 100km, my pitch hits 0 deg). At this moment in time the engines shut off and we are coasting towards apoapsis.
I have the following characteristics:
Altitude: 91.494 km
Time to apoapsis: 61 seconds
Orbital velocity: 2328.912 m/s
Surface velocity: 2182.02 m/s
Lateral velocity: 2153.88
Vertical velocity: 280.10 m/s
The orbital velocity needed to be in a 100km orbit around Juno is about 3402 m/s. Here(when the engines shut off and I start coasting) is where I make the calculation for the needed Delta V burn but I have an issue. The issue is that the orbital velocity is changing from 2328.912 m/s at the altitude of 91.494 km to 2297 m/s at the apoapsis of 10.003205 km. There is a deviation of ~32 m/s.
Because I make my initial calculation with the orbital velocity from the altitude of 91.494 km, the Delta V was not enough to get into a circular orbit as I didn't take into account the deviation.
My question is how to calculate the deviation (~32 m/s) from the first altitude of 91.494 km to the apoapsis at 10 km? I have tried Kepler's Laws but they either don't fit or I don't see it, I have tried with vector calculation(position/velocity of a projectile) but that also doesn't seem to fit.
For anyone having the patience to read this, I thank you very much! I hope that I made it clear enough. Please let me know if there are ambiguities. I will keep a tab open on this one.
Cheers!
Thank you! As you said and I mentioned, I know how to use the maneuver node. My request is bases on understanding the physics of the problem above as to make a program that makes it to orbit(and later more) fully automated.