PeriapsisPrograde
Wannabe addon dev
I have recently been interested in doing math by hand for my flights in Orbiter. However, there is one thing that I haven't been able to find: How do I align my ejection burn so that my final velocity is tangent to my path around the Sun?
For example, consider an ejection burn from Earth to Mars. The burn requires a velocity of 11307 m/s (at 6.68e6 m periapsis) to eject from Earth with 2926 m/s excess, which changes the orbit around the Sun to intersect with Mars at aphelion. Since circular orbital velocity at 6.68e6 m around Earth is 7723 m/s, the ejection requires 3584 m/s of dV. I understand the math to do those calculations.
My problem is determining beforehand what direction my velocity at infinity will be. How can I make it tangent to Earth's velocity around the Sun?
The equations relating angles in hyperbolic orbits seem to all use eccentricity, which I can't find a useful equation for in the case of hyperbolic orbits. Many sources say that e>1 for hyperbolic orbits, but don't give a formula.
Is there a way to predict the angle necessary to eject with all excess velocity tangent to a certain vector? Logically, the orbit is very nearly curved 90 degrees from periapsis to infinity of a barely hyperbolic orbit, but it curves less and less as velocity increases. I feel like this should have a relatively simple formula.
Thanks for helping.
For example, consider an ejection burn from Earth to Mars. The burn requires a velocity of 11307 m/s (at 6.68e6 m periapsis) to eject from Earth with 2926 m/s excess, which changes the orbit around the Sun to intersect with Mars at aphelion. Since circular orbital velocity at 6.68e6 m around Earth is 7723 m/s, the ejection requires 3584 m/s of dV. I understand the math to do those calculations.
My problem is determining beforehand what direction my velocity at infinity will be. How can I make it tangent to Earth's velocity around the Sun?
The equations relating angles in hyperbolic orbits seem to all use eccentricity, which I can't find a useful equation for in the case of hyperbolic orbits. Many sources say that e>1 for hyperbolic orbits, but don't give a formula.
Is there a way to predict the angle necessary to eject with all excess velocity tangent to a certain vector? Logically, the orbit is very nearly curved 90 degrees from periapsis to infinity of a barely hyperbolic orbit, but it curves less and less as velocity increases. I feel like this should have a relatively simple formula.
Thanks for helping.