When to do Oberth Maneuver and when not?

[Kerbal2023]

By Oberth maneuver (look that up if you don't know what I'm talking about) I am referring to "wasting" fuel slowing down to get closer to a gravity well (planet) in order to be able to accelerate more efficiently from that low periapsis. I understand for escape trajectories within Kerbin gravity, I always want to do Oberth maneuvers rather than to accelerat at a higher point, and exceptions where this is not the most fuel efficient really only start popping up for further away missions like Duna.

But when do I want to do Oberth maneuvers when it is not an escape? Say I just want to lift a circular satellite to a slightly higher orbit. Do I lower the periapsis first to then raise the orbit from the lower, more efficient point, or do I just burn at the high periapsis?

When are Oberth maneuvers the most efficient option and when are they not?

Edited November 18, 2023 by Kerbal2023

[Vanamonde]

I think you'd have to do some calculus to determine this, but one thing to keep in mind is that you can burn laterally to reduce the periapsis rather than braking to lower it, which may be a feul savings. 

Meanwhile, since what you're asking involves real world physics, you might get better answers from the Science subforum, so I will move your question there. 

[tomf]

What you are taking about is called a bi-eliptic transfer.

https://en.m.wikipedia.org/wiki/Bi-elliptic_transfer

As the article explains how f the ratio between the radius of the starting or it is less than 11 it is always better to do a hohmann transfer. If it is greater than 16 it is better to do a bi-eliptic transfer.

That is for coplanar orbits, if you are changing inclination then an intermediate orbit with a high AP can give good savings (the opposite of lowering PE to take advantage of Oberth)

[magnemoe]

1 hour ago, tomf said:

What you are taking about is called a bi-eliptic transfer.

https://en.m.wikipedia.org/wiki/Bi-elliptic_transfer

As the article explains how f the ratio between the radius of the starting or it is less than 11 it is always better to do a hohmann transfer. If it is greater than 16 it is better to do a bi-eliptic transfer.

That is for coplanar orbits, if you are changing inclination then an intermediate orbit with a high AP can give good savings (the opposite of lowering PE to take advantage of Oberth)

Then why is the hohmann example an much larger orbit change than the bi-eliptic one in the example? something more like LEO to GTO sounds more like an bi-eliptic one

[Superfluous J]

16 minutes ago, magnemoe said:

Then why is the hohmann example an much larger orbit change than the bi-eliptic one in the example? something more like LEO to GTO sounds more like an bi-eliptic one

I expect they're just showing you what they look like, not when you should do one.

[magnemoe]

46 minutes ago, Superfluous J said:

I expect they're just showing you what they look like, not when you should do one.

Probably, but it make the examples just confusing  
Now it was some geniuses who had an GSO satellite with an bad circulation burn using an moon flyby to correct their orbit, making it the first commercial lunar flyby even it was just to exploit the moons gravity  

[darthgently]

58 minutes ago, magnemoe said:

Now it was some geniuses who had an GSO satellite with an bad circulation burn using an moon flyby to correct their orbit, making it the first commercial lunar flyby even it was just to exploit the moons gravity  

Wait, did this actually happen?  Sounds like a good story.  Now I'm googlin'...

[sevenperforce]

15 hours ago, darthgently said:

16 hours ago, magnemoe said:

Now it was some geniuses who had an GSO satellite with an bad circulation burn using an moon flyby to correct their orbit, making it the first commercial lunar flyby even it was just to exploit the moons gravity  

Wait, did this actually happen?  Sounds like a good story.  Now I'm googlin'...

Yep, this was PAS-22, launched in 1997. It was launched on Proton but the final Block-DM stage failed, which left it in a useless orbit. The satellite didn't have enough propellant to correct its orbit, but after the insurance companies declared it a total loss a subsequent team figured out how to do repeated Oberth apogee-raising maneuvers to reach a lunar flyby. They ended up doing two different lunar flybys to correct both inclination and perigee -- essentially using lunar gravity as the "burn" of a bi-elliptic transfer -- and then used onboard propellant to lower the apogee to geostationary orbit:

The maneuvers burned through a lot of the onboard propellant, which cut the operable lifespan of the satellite in half, but that was much better than losing the satellite entirely.

This is a good illustration of another value in bi-elliptic transfers: inclination corrections. It is MUCH more inexpensive to change inclination at apogee than at perigee, and the higher the apogee the better. Most GTO launches today actually place the comsat's apogee well above geostationary altitudes so that the satellite will expend less onboard propellant to correct inclination and raise perigee. 

[Kerbal2023]

19 hours ago, tomf said:

What you are taking about is called a bi-eliptic transfer.

https://en.m.wikipedia.org/wiki/Bi-elliptic_transfer

As the article explains how f the ratio between the radius of the starting or it is less than 11 it is always better to do a hohmann transfer. If it is greater than 16 it is better to do a bi-eliptic transfer.

That is for coplanar orbits, if you are changing inclination then an intermediate orbit with a high AP can give good savings (the opposite of lowering PE to take advantage of Oberth)

Yes, that. This is getting complicated.

[GluttonyReaper]

29 minutes ago, Kerbal2023 said:

Yes, that. This is getting complicated.

The good news is that KSP lets you plan manoeuvres before you commit to them - you can always try out different transfers with the manoeuvre tool before going for an actual burn, usually with pretty low time commitment

[Kerbal2023]

Quote

some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial semi-major axis is 11.94 or greater, depending on the intermediate semi-major axis chosen.

A ratio of 11 would would be a transfer to the mun from below a 1000km orbit. Then a Bi-elliptic would save fuel compared to a Hohmann.

[darthgently]

2 hours ago, sevenperforce said:

It is MUCH more inexpensive to change inclination at apogee than at perigee, and the higher the apogee the better. Most GTO launches today actually place the comsat's apogee well above geostationary altitudes so that the satellite will expend less onboard propellant to correct inclination and raise perigee. 

There is a great write up, I think in the ksp-kos reddit, that shows that any relative inclination change greater that 45 deg or so and it will be more efficient to first jack the AP to just under the SOI radius, do the inclination change at the furthest AN/DN (relative, equatorial depending, near AP ideally), then circularize at PE.  Works  a charm in KSP for highly elliptical capture followed by matching a rendezvous orbit for example.

[Kerbal2023]

I suppose an Oberth maneuver is like a gravity assist where I burn at the periapsis. Sometimes it pays to use fuel to get to a place where you can do that.

[darthgently]

17 hours ago, darthgently said:

Works  a charm in KSP for highly elliptical capture followed by matching a rendezvous orbit for example.

Just to add to this for those interested, you want your initial PE to ideally be at a relative ascending or descending node (AN/DN) of the eventual target rendezvous orbit.  This will put your elliptical AP near the opposite node.  This can be tricky to set up when not yet in the SOI

 

Edited November 21, 2023 by darthgently

[Kerbal2023]

So does the same ratio of 11 apply to an Oberth (lowering the periapssi to raise the apoapsis) as to a bi-elliptic transfer (going to higher apoapsis to raise the periapsis)?

Edited November 21, 2023 by Kerbal2023

[Superfluous J]

You know you can test this in KSP, and it's ridiculously easy?

1. Make 1 maneuver node to transfer to the other planet. Write down how much m/s it costs.
2. Make 1 maneuver node to lower your Pe near the planet you're orbiting. Make another maneuver node to eject to the other planet. Write down how much each costs and add them together.

Pro tip: You don't even need to ENCOUNTER the other planet, just eject from your current planet's SOI efficiently (i.e. prograde for outer planets, retrograde for inner planets) and make your ship's trajectory get about to the target planet's orbit. You're not making these burns, just drawing maneuver nodes to see how much stuff costs.

 

[darthgently]

1 hour ago, Superfluous J said:

Pro tip: You don't even need to ENCOUNTER the other planet, just eject from your current planet's SOI efficiently (i.e. prograde for outer planets, retrograde for inner planets) and make your ship's trajectory get about to the target planet's orbit. You're not making these burns, just drawing maneuver nodes to see how much stuff costs

For near circular orbits it doesn't matter if you get an encounter or not, it may otherwise

[Superfluous J]

10 minutes ago, darthgently said:

For near circular orbits it doesn't matter if you get an encounter or not, it may otherwise

True, but you also have to do the plan at the same time you'll be doing the transfer (or at least aim for the spot in the target planet's orbit that you'll be hitting) in that case.

And unless you're going from Moho to Eeloo, at least one of the orbits (target or source) will be pretty circular... at least in the Kerbolar system. And for most uses, Kerbin is always going to be either the source or target planet.

Also, it will affect both tests the same so if all you care about is the difference between them, either they'll be similar, or the one that would have obviously won will still be the one that obviously wins.

Edited November 22, 2023 by Superfluous J