Rocket Physics and Relativity

[Bluejayek]

To begin, when I say relativity, what I mean is 'Physics must be the same in all inertial reference frames' not the special/general theory of relativity dealing with the speed of light and gravitation.

Now, what I am discussing is the kinetic energy of ships at high velocity. The kinetic energy scales as velocity squared, so you require a lot more energy to accelerate the same amount when at high velocity. (exempli gratia: 0 to 10m/s for 2 kg object is 10^2 - 0^2 = 100J, 1000-1010m/s for a 2kg object is 1010^2 - 1000^2 = 20,100J)

A rocket that spits out rocket fuel gains momentum equal to the momentum of the rocket fuel relative to the ship. Say the exhaust velocity is 1000m/s and you spit out 0.1kg of fuel from a ship that is 1kg at the end, the rocket will gain 100 kg m/s of momentum or 100m/s of velocity.

Assume the ship is originally travelling at 1000m/s. An observer following alongside at 1000m/s sees the ship accelerate from 0m/s (relative) to 100m/s, gaining 5000J of kinetic energy, and he sees the fuel accelerate from 0m/s to -1000m/s, gaining 50,000J of kinetic energy. He therefore sees a net increase of 55,000J of energy from the fuel being ejected; this would be from the chemical explosion, or ion propulsion or whatsoever device propelled the fuel.

A second observor who is stationary sees the ship originally travelling at 1000m/s. It accelerates from 1000 to 1100m/s gaining 105,000J of kinetic energy. The fuel decelerations from 1000m/s to 0m/s loosing 50,000J of kinetic energy. The net kinetic energy change is an increase 55,000J, the same as above.

This means that your ship is gaining a heck of a lot more kinetic energy when you burn at high velocity then low. Does this have any ramifications for how orbital manoeuvres should be done? Like, should you only do burns when at highest velocity possible (periapsis) in order to have best fuel use?

[togfox]

This means that your ship is gaining a heck of a lot more kinetic energy when you burn at high velocity then low. Does this have any ramifications for how orbital manoeuvres should be done? Like, should you only do burns when at highest velocity possible (periapsis) in order to have best fuel use?

I\'m not sure what all the above means - but - the answer is \'yes\'. Pe or AP are your best burn points.

[vexx32]

Ahahaha... If I recall correctly, it is in fact the opposite. Look up the Oberth Effect.

[togfox]

Hang on - you talking about plane changes or changes in orbital height/altitude?

[Bluejayek]

I was just talking in general. It appears that you get a more kinetic energy per fuel at higher speeds, so then all manoeuvring should be done at as high a speed as possible...

[RangerDanger75]

Ahahaha... If I recall correctly, it is in fact the opposite. Look up the Oberth Effect.

On the contrary, Oberth Effect states that rockets can do work more efficiently at higher velocities. This is why some satellites/rockets will do burns through gravity slingshots around planets/moons.

[semininja]

Burning at periapsis changes your apoapsis far more than burning at apoapsis changes your periapsis.

[Bluejayek]

Burning at periapsis changes your apoapsis far more than burning at apoapsis changes your periapsis.

Your avatar is epic.

[Coupon]

If they ever do interstellar with ships travelling close to light speed, then they will need to account for that.

[vexx32]

On the contrary, Oberth Effect states that rockets can do work more efficiently at higher velocities. This is why some satellites/rockets will do burns through gravity slingshots around planets/moons.

Burning at periapsis changes your apoapsis far more than burning at apoapsis changes your periapsis.

Ah, right. Never mind, then. I had it wrong. I was misreading -- I thought he was asking if higher altitude would produce this effect. I contradicted, since as can be seen, in any orbit, the lowest point will have the ship moving fastest. My mistake :3

If they ever do interstellar with ships travelling close to light speed, then they will need to account for that.

As far as I know, the effect is a direct result of the physics involved... so I don\'t think they\'ll need to worry about it. Besides, there\'s no such thing as light being a speed limit in the Kerbalverse... unless they decide to make it one.