Love that you're using Spaceflight simulator to demonstrate your point. One very important factor which you're missing out on is the existence of other gravitational influences from other moons. and the parent star.

Another thing which you missed is the rotation of the planet. If an object approaches slowly enough and it's trajectory is approximately within the plane of rotation which is perpendicular to the axis of rotation of the planet, it's possible that the satellite might be captured, in return for an increase in the speed of rotation of the planet such that angular momentum is conserved, as well as a change in momentum of the satellite+planet system according to conservation of linear momentum.

Games like Spaceflight Simulator have inspired me to take engineering, but they are vastly oversimplified. They are just enough to get a cursory glance at the topic of orbital mechanics, which is a deep rabbit hole.