If anyone can help me please get in touch. Here's the details:

TL;DR: Orbit changes depending on what true anomaly I choose to start with, which makes no sense to me. Tried changing various model options but no luck in resolving or explaining the problem. Includes some graphs for better explanation. See bottom of post for my thoughts.

Essentially I'm getting very confusing results from what should be a basic impulsive burn, and I can't figure out why. The setup is a satellite at 500km altitude, I want to perform a single impulsive transfer at periapsis so as to raise the altitude at apoapsis by 500m. Relevant points to note are that I took the tutorial's values for the gravity model (degree 10, order 10), and started at 0 degrees true anomaly.

Mission outline was:

1. Record current radius of apoapsis, calculate the new required radius of apoapsis

2. Propagate one orbit, then to periapsis

3. Target the new radius of apoapsis

- Vary the Delta-V

- Perform the burn

- Propagate to apoapsis

- Check that the RMAG is equal to the required radius of periapsis

(RMAG: magnitude of satellite's position vector, at apoapsis and periapsis should be equivalent to radius)

All looked well; the Delta-V value I got matched my hand calculations and the final orbit had it's RMAG in line with my new required radius of apoapsis. My first problem was however that before the burn occurred, the orbit looked entirely wrong. The RMAG never once hit the initial radius of apoapsis and the orbit had no clear periapsis.

Initial Results ^

**Change 1: Moved starting true anomaly to 180 degrees.**

After the change, The initial orbit looked perfect. However now, my Delta-V value was a whole order of magnitude lower than expected (\~0.00018 compared to \~0.002). Investigating further, changing true anomaly to 90 and 270 degrees produced even worse results with my targeting failing to converge.

*This makes zero sense to me as true anomaly should not change the characteristics of the orbit, merely the spacecraft's angle on it.*

Results after Change 1 ^

**Change 2: Reduced the gravity model order and degree.**

Starting with degree and order 0 (0,0), the starting true anomaly no longer had an effect on the result which was good progress. The Delta-V value was however still, in my opinion, incorrect. Increasing to (1,1) made no difference however as soon as the 2nd degree/order started to produce cyclic variations in the semi-major axis, the problem returned.

Results with JGM-2 (1,1) model

**Thoughts**

I wondered if the osculating elements are being used for the semi-major axis, and hence messing with the model somehow? Clearly something is not right but I am struggling to figure out where. In addition to the above I've tried lots of random changes to the mission model and the propagation model i.e reducing step size. No joy on that either.

Can anyone with more knowledge than me explain this? If anything, at least deciding which model is

*less incorrect*would allow me to move on to other models such as finite burns.

At the end of the day, I'm doing an analysis for a project with GMAT and I wanted to prove to myself that I was doing it properly. It would appear either I am not doing it properly, or, my model is not set up correctly but I'm totally stuck so any help or comments are more than welcome!