In an elliptical orbit, where should a rocket fire its engines for maximum efficiency?
If a rocket ship with limited fuel has fallen into a decades-long elliptical orbit around the Sun, where in the orbit should it fire its engines in order to achieve escape velocity with a minimum of fuel? Likewise, where would the most efficient place in the orbit be to fire the engines in order to stay in-system but with a shorter orbital period?
This post was sourced from https://worldbuilding.stackexchange.com/q/76272. It is licensed under CC BY-SA 3.0.
1 answer
Fire the engines closer to the Sun for maximum efficiency. This is due to the Oberth effect.
Assume the spacecraft undergoes a burn when it is farther away from the Sun. The expelled propellant will have a certain amount of kinetic and potential energy, $E_p$. If an energy of $\Delta E$ is released during the burn, the spacecraft gains an energy of $\Delta E-E_p$.
Now, if the burn is done when the spacecraft is close to the Sun, $E_p$ is lower because the propellant has a lower potential energy. Therefore, the quantity $\Delta E-E_p$ is higher, and the spacecraft has more energy. This makes it a lot more efficient maneuver for transferring to a variety of orbits - or, in this case, leaving the Solar System entirely.
As SF. pointed out, the Oberth effect holds for all massive bodies. It therefore makes sense that you can use other planets, not just the Sun, to reach a higher orbit or escape velocity.
0 comment threads
0 comment threads