oberth effect and parking orbits

[kahlzun]

hi guys,

i was just reading about the Oberth Effect (faster speed gives 'bonus' efficiency), and I started to think:

does this mean that starting from a -lower- orbit (where you travel faster) will net you extra fuel savings for going interplanetary,

as opposed to starting from a higher- and therefore slower orbit?

[phoenix_ca]

In short, no. You still need to expend roughly the same amount of delta-v to get up to the height of the parking orbit. What you'd be cutting-out is a circularization burn for the higher altitude, but then you end-up replacing it with a circularization burn for the lower orbit, which will necessarily require more delta-v.

[kahlzun]

but if you refuel-intercept in the lower orbit...

[phoenix_ca]

The amount of delta-v spent in total would still be roughly the same. Actually, more because you'd have refueled and thus be carrying more fuel when you escape orbit.

[Double Timan]

kahlzun you are absolutely correct and this is the whole reason that gravity assists from other planets can also help with reducing the total delta-v of a mission in the real world. On the later Apollo Missions one of the ways they could reach the sites they wanted to on the moon with the addition of the lunar rover was launching into a lower parking orbit. The orbit was actually low enough that it would have decayed very fast however the time from insertion to trans-lunar injection was short enough that the drag penalty was well worth the delta v reduction.

The simplest way to understand the effect is to look at the definition of work which is a force multiplied by a distance. The force generated by a rocket is constant and related to a given expenditure of fuel in a given time. The work done by a rocket in a given period of time (dictated perhaps by how much fuel is on board) is given by the distance travelled in that time multiplied by the force exerted by the rocket. Distance travelled in a unit of time is speed and so you can say that work done in a unit of time is given by the speed multiplied by the thrust which has the interesting result of yielding more energy from the same burn if you burn while travelling the fastest. Highest velocities in any trajectory are on closest approach to a massive body due to the exchange of potential energy for mechanical energy. This means that you should always plan your burns at as low an altitude as is practical. The energy gained however is not free it is the result of the kinetic energy of the fuel as well as an exchange of energy with the body being interacted with gravitationally. Since the object is huge the inverse effect is not measurable.

The effect holds in KSP and is very useful for minimizing rocket size.