I am an engineering student who is interested in orbital mechanics. I am doing some self study before taking some orbital mechanics courses next year. I was learning about various orbit types, elliptical, parabolic, hyperbolic, etc. and the effects of burning in various directions. I have found a lot of good information about about how to manipulate elliptical orbits (raising/lowering apo/periapsis, changing inclinations, etc.).

However, I haven't found a lot of information on manipulating a hyperbolic trajectory. I have found a lot of good information like this in calculating various parameters (impact parameter, turning angle, etc.) but little specifics on how to change one.

For example, say you were on a hyperbolic flyby like in this example. However, you wanted to lower your radius at periapsis by a couple hundred km for some reason (take some measurements, increase turning angle etc.). What would be the most efficient direction to burn? I could see doing it 2 different ways but unsure of which would be more efficient. You could burn retrograde lowering your velocity magnitude which would pull you closer to the planet. Or you could burn perpendicular to your current velocity vector in the direction of the planet changing your approach angle? Perhaps some combination of the 2??

Anyone know how to determine what would be the most optimal? Thanks.

I am an engineering student who is interested in orbital mechanics. I am doing some self study before taking some orbital mechanics courses next year. I was learning about various orbit types (elliptical, parabolic, hyperbolic, etc.) and the effects of burning in various directions. I have found a lot of good information about about how to manipulate elliptical orbits (raising/lowering apo/periapsis, changing inclinations, etc.).

However, I haven't found a lot of information on manipulating a hyperbolic trajectory. I have found a lot of good information like this in calculating various parameters (impact parameter, turning angle, etc.) but little specifics on how to change one.

For example, say you were on a hyperbolic flyby like in this example. However, you wanted to lower your radius at periapsis by a couple hundred km for some reason (take some measurements, increase turning angle etc.). What would be the most efficient direction to burn? I could see doing it 2 different ways but unsure of which would be more efficient. You could burn retrograde lowering your velocity magnitude which would pull you closer to the planet. Or you could burn perpendicular to your current velocity vector in the direction of the planet changing your approach angle? Perhaps some combination of the 2?

Anyone know how to determine what would be the most optimal?