# The Oberth effect and multiple orbits

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• razidan
In summary, the conversation discusses the SpaceIL lunar lander and its fuel-efficient approach to reach the moon through multiple orbits around Earth with small impulses at the perigee. The group also considers the efficiency of one strong impulse versus multiple smaller impulses in terms of fuel usage. It is concluded that multiple small burns are more efficient due to limited thrust. The conversation also touches on the use of the Oberth effect and the time frame for changing from LEO to an elliptical orbit to reach the moon.
razidan
Hi all,

I've been following the launch of the first commercial lunar lander, SpaceIL.
Because of its small size, there is not enough fuel for a more direct approach to the moon, so the path they are taking is multiple orbits around the Earth with impulses at the perigee, at each orbit.
As I understand it, they are using the oberth effect to gain better fuel efficiency.

Here is my question - I've been wondering if one impulse that provides a lot of ## \Delta v## will be as efficient as many smaller impulses that build up to the same ## \Delta v##, say, in terms of mass of fuel used.

My guess is that many smaller impulses are better, because each time the engine fires, the speed is a bit faster (from the previous burn) so the oberth effect tells us the burn will be more efficient. But, I want to prove it to myself, also, I'm not sure I'm correct. I have no experience with astrodynamics or orbital mechanics

Thanks!

https://www.space.com/spaceil-beresheet.html

Multiple small burns are more efficient, but it happens mostly because of limited thrust. With single burn, you need to fire engine for longer for same orbital transfer, and therefore some of thrusting occurs far from perigee.
As i understand, SpaceIL lander re-use Moon landing engine for Earth-Moon tranfer, having initial acceleration below 0.1g, which require ~1 hour single burn for Earth-Moon transfer - impossible to make in one burn before leaving perigee part of orbit.

razidan said:
Here is my question - I've been wondering if one impulse that provides a lot of ΔvΔv \Delta v will be as efficient as many smaller impulses that build up to the same ΔvΔv \Delta v, say, in terms of mass of fuel used.
With this style of orbit change, you can only use the impulse at the lowest point in the orbit and each orbit will take a very long time (almost one month at maximum). How long do you have in which to change from LEO to an elliptical orbit to reach the Moon?
The Oberth effect saves around half of the fuel that you would need to reach a full Moon orbit, I believe.

## 1. What is the Oberth effect?

The Oberth effect is a phenomenon in orbital mechanics where the use of a rocket engine at high speeds near a gravitational body results in a greater change in velocity than at lower speeds. This is due to the conversion of potential energy into kinetic energy, resulting in a more efficient use of fuel.

## 2. How does the Oberth effect relate to multiple orbits?

The Oberth effect can be utilized in multiple orbits to maximize the efficiency of a spacecraft's propulsion. By performing a burn at the periapsis (closest point) of each orbit, the spacecraft can gain a larger change in velocity compared to performing the burn at the apoapsis (farthest point).

## 3. Can the Oberth effect be applied to any type of orbit?

Yes, the Oberth effect can be applied to any type of orbit, including elliptical, circular, and hyperbolic orbits. However, it is most effective in highly elliptical orbits where the spacecraft is traveling at high speeds near the periapsis.

## 4. Are there any limitations to the Oberth effect?

One limitation of the Oberth effect is that it requires a significant amount of propellant to be burned at high speeds, which may not be feasible for all spacecraft. Additionally, the effect is less pronounced in lower gravity environments, such as in outer space, compared to on Earth.

## 5. How is the Oberth effect used in space missions?

The Oberth effect is commonly used in space missions to maximize the efficiency of a spacecraft's propulsion. It is often utilized in maneuvers such as orbital insertion, planetary flybys, and trajectory corrections. By taking advantage of the Oberth effect, spacecraft can conserve fuel and reach their destinations more efficiently.

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