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# Question for the rocket scientists about transfer orbits to other planets.

## Question

OK,

I was watching one of the youtube videos for SKP by Scott Manly http://youtu.be/jiB2ywSM6i0. He stated that the burns for transfer orbits were more efficient when starting from a low initial orbit. Is this correct, because it doesn't make sense to me? Any type of transfer orbit requires increasing your orbital velocity to a point where it escapes. The transfer part comes from timing that escape, correct? To go from a small orbit to a large orbit you need to increase your orbital velocity as well, and if you are making a symmetric orbit (2 burns) timing isn't a factor because you can still do your escape burn at any time on that new orbit. In other words your velocity increase to get a bigger orbit is put towards your escape burn and not wasted. The reason I am wondering is because when using nuclear motors, trying to escape from a low orbit and firing before the node to balance your burn you actually need to burn in towards the planet, which when it has an atmosphere can prevent an escape at all.

Am I missing something?

Edited by 2-Zons

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It's called the Oberth Efffect, I can't really explain it but http://en.wikipedia.org/wiki/Oberth_effect

And the burning towards the planet is because your burn time is so long. To reduce it you could do 2 or more burns.

Edited by Redjoker

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He's taking advantage of the Oberth effect, which states that a burn like a one tangent burn for a transfer is more efficient at higher velocities. Apollo took advantage of this with the low 187km Earth Parking Orbit and the even lower orbits on the later missions.

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I'm not certain but it could be because you add to your AP from your PE. If you Burn from your AP then all the fuel to raise your AP above your PE is wasted as you are using your PE as a starting point. So since your AP should be low your PE needs to be as well. You can't have a high PE then burn from the lower AP as this is the PE. You could raise a high AP and have a low PE which is EXACTLY where you need to make the burn to reach your target but in practise it never is. I'm not sure how clear this is but I can't think of a better way of putting it at the moment. Maybe I'll draw a picture

Here is the picture

You are right about long burns being inefficient in fact if your Trust to weight is too low it can be worse than having a more powerful less efficient engine.

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The above picture is not the only reason. To get captured at your target, you have to raise your Peri (although not longer visible from the new SOI) anyway to match the target's orbit.

It's easier: Kinetic energy is E=1/2 m vÃ‚Â². So, because of the square, the same amount of dV increases the orbital energy more if the current velocity is already high. If the velocity is low, more energy instead is lost with the rocket exhaust.

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OK, from what I read on the Wikipedia link I think I get it. It's kind of like when you slingshot past Mun, where you don't have escape velocity before passing but you do after. You are kind of starting the slingshot in a close orbit?

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A Slingshot takes energy from the Mun/Orbital body and transfers it to your ship. That has nothing to do with fuel.

Running your engines at lower altitudes is more efficient because you're moving faster, and have a higher kinetic energy. That means the fuel in your tanks also has a higher kinetic energy - and when you burn that fuel, some of that kinetic energy is transferred to your ship.

In other words, the faster you're going, the more of a "bonus" you get when burning fuel. I'm at a loss to explain it any simpler than that...

=Smidge=

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The only way I was convinced was by doing it myself. I still don't understand why it works.

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Found this thread on the science forum: The Oberth Effect and Stuff.

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I have noticed that as well. If you can get a direct capture from Kerbal orbit to another planet, the burn is much more efficient then launching to escape velocity and later doing the burn to capture.

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As a general rule, it's a good idea to take Scott Manley at his word when he talks about orbital mechanics. I seem to recall he even has a video explaining why the Oberth Effect works, so that might be worth looking up because he's pretty good at explaining things.

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A Slingshot takes energy from the Mun/Orbital body and transfers it to your ship. That has nothing to do with fuel.

Running your engines at lower altitudes is more efficient because you're moving faster, and have a higher kinetic energy. That means the fuel in your tanks also has a higher kinetic energy - and when you burn that fuel, some of that kinetic energy is transferred to your ship.

In other words, the faster you're going, the more of a "bonus" you get when burning fuel. I'm at a loss to explain it any simpler than that...

=Smidge=

This is really the simplest explanation. It can't be summed up any more than that. Although a powered slingshot can use the oberth effect.

At a lower orbit compared to a higher one, a rocket has a higher velocity, right? This means the rocket (and the fuel inside it) has more kinetic energy. When this fuel is burned, some of this kinetic energy is used to do mechanical work (propel the vessel). At a higher orbit, the vessel is moving slower, which means less kinetic energy which then means less work (less efficient propulsion).

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Here's a more down to earth example of the same effect.

If you got very strong legs, and you jump upwards with a velocity of 10 m/s you will reach 5 meters (assuming for simplicity's sake that G is 10 m/s).

If you climb a 5 meter ladder and then perform the same jump you will reach 10 meters.

If you instead double the velocity of the initial jump to 20 m/s you will reach 20 meters.

When you pass the 5 meter mark your velocity will not be 10 m/s, but 17.3 m/s

To experience this effect in a very big way in KSP, build a probe that can escape the Kerbol system. Burn straight from Kirbin and out and observe your velocity when you reach the orbit of Jool.

Now do it again, but this time raise the apoapsis to the orbit of Jool, and then lower your periapsis as close to Kerbol as possible.

Burn the rest of the fuel at the orbit of the sun and observe how you leave the Kerbol system at ludicrous speed.

https://dl.dropboxusercontent.com/u/22015656/ludicrousSpeed.png

Edited by maccollo

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The only way I was convinced was by doing it myself. I still don't understand why it works.
I'm 99% sure it's due to inertia since I'm contributing more energy to my speed and less towards movement of mass. Of course I could be wrong

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OK, I'm not saying it isn't true I am just trying to understand better. I don't see how your speed is faster in a lower orbit. It is a faster rotational speed around the planet but your actual speed, or orbital speed around the sun is slower in a lower orbit, it has to be because you increase your speed (fire rockets pro-grade) to get into a higher orbit. So how can your speed be faster in a lower orbit. Also when you are in a higher orbit you need to slow down (retro) to get into a lower orbit. This is the thing that's screwing with my brain.

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I have read zero literature on the Oberth Effect (that's going to be the name of my next metal band, by the way), but the way I understand it is this:

An orbit is just a free-fall, with a lateral velocity that allows the earth to fall away at least as quickly as the vessel falls toward it. When you pass your apoapsis, you begin falling into the planet's gravity well, with the acceleration due to gravity in a vacuum. When you pass your pereapsis, however, you begin fighting against the planet's gravity well and lose speed on the way up, until you hit the Ap again and begin "falling."

(Let me know if this is poorly-communicated, and I'll edit it to make more sense.)

You've seen people talk about "delta-v." What you need to know is that "delta" means change, and v = velocity. The delta-v of a burn is merely how much speed you have to add to reach a desired orbit. The farther you want to go, the more delta-v you need. The reason why it's more efficient to do this at your Pe is because you've already spent so much time falling in towards the planet, so your baseline velocity is higher, meaning less delta-v is required.

I'll try to explain with math, but I'm not that good with numbers. For those that are good with math, don't laugh at my ridiculously simplified explanation.

You want to reach a hypothetical orbit that requires a speed of 4,000 m/s. Your initial orbit is oblong. At your apoapsis, after fighting gravity for so long, your velocity is 800 m/s.

4000 - 800 = 3200 delta-v

At your periapsis, however, you've been falling freely for a while, so your velocity is 2,000 m/s.

4000 - 2000 = 2000 delta-v

On any given engine, lower delta-v required means less fuel burned.

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It is inefficient because you had to get to a higher parking orbit before you preform your transfer burn right? So by starting in a low parking orbit, you don't spend unnecessary fuel circularizing a high orbit.

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OK, I'm not saying it isn't true I am just trying to understand better. I don't see how your speed is faster in a lower orbit. It is a faster rotational speed around the planet but your actual speed, or orbital speed around the sun is slower in a lower orbit, it has to be because you increase your speed (fire rockets pro-grade) to get into a higher orbit. So how can your speed be faster in a lower orbit. Also when you are in a higher orbit you need to slow down (retro) to get into a lower orbit. This is the thing that's screwing with my brain.

That's one of the tricky things about orbits that sometimes is hard to grasp at first. But KSP is a wonderful tool to see how it all plays out. Next time you play, pay close attention to your ship's speed at various points of your flight. Watch what happens when you do a deorbit burn... your rocket impulse will initially make you slow down, but as you fall closer to the planet your speed increases. Meanwhile if you do a transfer burn up to the Mun (or any higher orbit, really), you gain speed upon firing your rocket, but slowly lose speed as you approach apoapsis.

For a more direct comparison you can also try putting two ships into orbit, one circularized at 100km and another at 500km. Then look at the orbital speeds of the two ships. You'll see that the one in the lower orbit is going faster than the one above it.

As for what you said about the sun, I don't really understand what you're getting at there. So long as you're in Kerbin's sphere of influence (or those of its moons), your average speed around the sun is just gonna be the same as Kerbin's. Doesn't matter how high or low you are relative to the planet.

Edited by FenrirWolf

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I think of it like this in terms of escape velocities (which is kind of a specific case of transfer orbits):

It doesn't really matter where you are when you make escape velocity, you just have to do it somewhere.

Your orbital speed is higher at periapsis than apoapsis.

Therefore, less acceleration is required to reach escape velocity at periapsis than at apoapsis.

Less acceleration means decreased fuel consuption means increased efficiency.

It's not a perfect explanation, but it's serviceable.

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OK, I'm not saying it isn't true I am just trying to understand better. I don't see how your speed is faster in a lower orbit. It is a faster rotational speed around the planet but your actual speed, or orbital speed around the sun is slower in a lower orbit, it has to be because you increase your speed (fire rockets pro-grade) to get into a higher orbit. So how can your speed be faster in a lower orbit. Also when you are in a higher orbit you need to slow down (retro) to get into a lower orbit. This is the thing that's screwing with my brain.

If you increase your speed your orbit becomes higher and vice versa, so on that part you've got things straight. Now the oberth is about how much bang (delta-v) you get for your buck (fuel). It turns out that unlike what you might intuitively think it does matter at what height you do your burn in a gravitational field.

There are different valid ways to approach the explanation on why this is case, this thread and the link I supplied earlier gives several, but the best way for me to understand it was to try it out in practice first and see for yourself and then going back to the theory.

What you'll see is that you use a lot more fuel if you first escape Kerbin and then go for a transfer burn to Duna while in an orbit around the sun in comparison to making a well timed transfer burn to Duna from low Kerbin orbit. It really saves a whopping amount of fuel. It's also important to realize that the developers did not need to add in anything extra into the game to make the oberth effect work, beyond the basic physics.

Maybe that's what makes it hard for people, including myself at some point, to wrap their head around it. The oberth effect works because of physics, and, unlike what the name might imply there isn't some spooky 'effect' going on at all which you can or should try to understand separately.

Hopes this helps.

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Thanks for all the responses from everyone.

A few replies resonated and I think I understand. When you fire pro-grade to increase your orbit you are actually pushing your orbit on the opposite side away from the planet. Another way of thinking about it is if you are at your periapsis (as was said above) you are at the bottom of falling towards the planet and are moving away from it due to your speed. When you fire pro grade you are increasing that speed on your ascent so you will get to a higher apoapsis. This combined with the fact that velocity increases as you get closer to the planet, for the same reason that an object on a string being spun around will increase in velocity as the string gets shorter wrapping around the object. I think I finally have wrapped my head around it.

So this brings up a new question.

When you are re entering an orbit from escape velocity. Is it more efficient to aim for a higher orbit and and retro. Actually as I type this I think I can answer, tell me if I'm correct. If you aim for a low orbit (high velocity) you have less velocity to lose. If you try and capture from a high altitude the orbit velocity is very low and you will have much more velocity to lose. So you should aim for a low orbit to get captured.

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It would be more efficient to aim for a higher orbit, yes. But in my experience, it has been more important that I do my retro burn as early as possible once I enter the new gravity well. Once you shift into the new gravity well, you begin falling towards the new "down" and begin gaining velocity.

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