The Oberth Effect and Stuff

[Chickstick]

I have read quite a few forum posts and wiki entries on the oberth effect and would like to ask you guys if my observation are correct:

Reasons for the Oberth Effect:

1) Work = Force (your Engine) times distance (distance covered while thrusting)

2) When firing at periapsis, you loose mass that you then don't have to carry up to apoapsis again, so the remaining ship can go higher

Questions:

1)Does this also apply to slowing down?

2)Will your spacecraft accelerate faster if the planet you are orbiting is at periaps, too?

Thanks, looking forward to your answers!

[Ravenchant]

1) Yep, but AFAIK the effect is only useful when your orbital path is leaving the bodies sphere of influence

2) KSP doesn't model n-body interactions, so... I guess no?

[Ralathon]

I have read quite a few forum posts and wiki entries on the oberth effect and would like to ask you guys if my observation are correct:

Reasons for the Oberth Effect:

1) Work = Force (your Engine) times distance (distance covered while thrusting)

2) When firing at periapsis, you loose mass that you then don't have to carry up to apoapsis again, so the remaining ship can go higher

Both valid ways of looking at it yea. You could also look at it from an energy PoV: Energy increases quadratically with velocity, so a constant increase in velocity results in more energy gain if the starting velocity was higher.

Questions:

1)Does this also apply to slowing down?

Yes, it does. It is most efficient to do a capture maneuver at periapsis.

2)Will your spacecraft accelerate faster if the planet you are orbiting is at periaps, too?

Thanks, looking forward to your answers!

It will gain energy faster relative to the sun, but not relative to the planet. Think about it as running in a train that's stationary vs running in a train that's moving. In both cases you move the same speed relative to the train but you move faster relative to the ground in the latter case. Same thing goes for the Oberth effect, it'll work better when you try to do an escape burn from a body at periapsis because you benefit more from the solar oberth effect at that point. But in practice you don't have to worry too much about this. It is a miniscule effect for planets as in KSP or Real Life with their almost circular orbits. Unless you try to escape an orbit around a comet I wouldn't worry.

[K^2]

Obereth effect is a 2-body phenomenon, so n-body effects have to be accounted for separetely.

Basically, ship's total energy is conserved in barycentric coordinates. (Position with respect to center of mass of the 2-body system.) Because of that, Obereth effect is reduced to an energy optimization problem, and you get most energy per unit of fuel consumed when you are at the periapsis.

Generally, if you consider a problem of escaping planet into interstellar space, it's more complicated. But if your starting orbit is close enough to the planet so that you can ignore the Sun, the way KSP handles it, then you can break it up into two parts, and Obereth effect will apply to each separately. You'll have most energy if you perform the burn at periapsis around the planet, while the planet is at its own periapsis. This would be relevant for something like return from Moho.

[TonboIV]

2) When firing at periapsis, you loose mass that you then don't have to carry up to apoapsis again, so the remaining ship can go higher

Actually no. The spacecraft will always reach the same height, regardless of its mass. It's like Galileo's thought experiment in reverse.

[J.Random]

Actually no. The spacecraft will always reach the same height, regardless of its mass. It's like Galileo's thought experiment in reverse.

This. I don't know exact reason for Oberth effect, but I would guess energy conservation. The lower you are, the faster you go, the more kinetic energy you will get by spending the same dV (because kinetic energy is proportional to velocity squared), and the more of it may be converted into potential energy, giving you the increase in AP height.

[UH60guy]

The Wikipedia page has two paragraphs that sum it up quite nicely:

[snip]

Rocket engines produce the same force regardless of their velocity. A rocket acting on a fixed object, as in a static firing, does no useful work at all; the rocket's stored energy is entirely expended on accelerating its propellant to hypersonic speed. But when the rocket moves, its thrust acts through the distance it moves. Force acting through a distance is the definition of mechanical energy or work. So the farther the rocket and payload move during the burn, (i.e. the faster they move), the greater the kinetic energy imparted to the rocket and its payload and the less to its exhaust.

...

It may seem that the rocket is getting energy for free, which would violate conservation of energy. However, any gain to the rocket's energy is balanced by an equal decrease in the energy the exhaust is left with. When expended lower in the gravitational field, even if the exhaust is left with more kinetic energy, it is left with less total energy. The effect would be even stronger if the exhaust speed could be made equal to the speed of the rocket, then the exhaust would be left without kinetic energy, so the total energy of the exhaust would be as low as its potential energy. Contrast this to the situation of static firing: as the speed of the engine is zero its specific energy does not increase at all, with all chemical energy of the fuel being converted to the exhaust's kinetic energy.

[Chickstick]

Actually no. The spacecraft will always reach the same height, regardless of its mass. It's like Galileo's thought experiment in reverse.

What? If i accelerate at periaps (but at any point, really) my orbit will in most situations change so that my spacecraft will reach different altitudes than before.

[Evans310]

What? If i accelerate at periaps (but at any point, really) my orbit will in most situations change so that my spacecraft will reach different altitudes than before.

Yes, but the change in altitude is a result of the change in velocity, not the change in mass. Look at it this way: Your 5 tonne spacecraft orbits Kerbin at 2500m/s at 77km altitude. (numbers out my arse, for example only) If you want to dock a 3 ton spacecraft with it, you'll need to bring it up to 77km altitude as well, and match velocity with the target at 2500m/s. Height of the orbit is a function of velocity. Mass doesn't matter (at least not in a mathematically significant way).