The Oberth effect and multiple orbits

[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!

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

 

[trurle]

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.

 

[sophiecentaur]

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.