Couple of questions on orbital mechanics

[dronkit]

Guys! I'm preparing a small course on gravitation, planets, satellites and stuff for my university and planning to use KSP for demonstrations (i know some physics is bogus, mostly spheres of influence but whatever) and I got some questions. I know some of you know this trade a lot since you've helped me a lot pre-forum crash.

1) Apollo shot free-return trajectories. Those trajectories look like an "8". The 8 is seen from what coordinate system? Was it truly an 8? Was the lunar orbit retrograde then?

2)oberth effect: does it work reversely? i.e.: If I have to retroburn, will it be most efficient at higher, lower speeds, or it's the same?

3)Why is the apoapsis the most efficient place to burn to lower periapsis and, reversely, the periapsis the best place to raise apoapsis? Oberth effect/reverse oberth effect? Does burning raise/lower every point but the current, but the opposite point raises/lower more? Why?

Thanks!

[OtherDalfite]

I'm afraid to answer the first question, as I don't quite understand it, but I can answer the last 2.

2) Yes, it does. It works at the highest point of your orbit to have the maximum effect on your periapsis. This is because you are going sideways relative to the planet and therefore not being effected by gravity. Basically, you are just adding or removing velocity, without having to fight gravity. You'll also notice this if, when in orbit, you go into your pod and look at the vertical speedometer. It will read 0. This is because you are only moving sideways relative to the source of gravity, and are not really being "pulled" by it.

3) The apoapsis and periapsis are the most efficient places to burn because, like above, you are not fighting against gravity. Burning at the periapsis is best for raising your orbit, while apoapsis burning is good for lowering your orbit. Anything before or after and you are fighting against gravity.

If this was at all confusing, please let me know and I'd be happy to try and explain it differently.

[magnemoe]

1) apollo was retrograde, for some reason it would make landings easier however I have no idea how. The point of free return is that you get an slight slingshot effect around the moon who will give you an landing or aerobrake path.

2) No, retroburn work best in low orbit, you want to get close for the burn. You might even want to first get into an very elliptical orbit then lowering the AP at the closest point.

3) two effects, one is that doing an small change far away will have larger impact, the other is the Oberth effect, its even more effective to adjust your PE before you reach the target SOI.

[Pursuedtank]

1) apollo was retrograde, for some reason it would make landings easier however I have no idea how.

Apparently it was easier because they could see the shadows of the rocks so they would know how close they were. It was also to land around the side facing earth so they would remain within communication range and tv range.

[rodion_herrera]

For Question 1, more detailed discussions here: http://forum.kerbalspaceprogram.com/showthread.php/30423-Anyone-do-this-kind-of-Mun-orbit

-RoDION

[tntristan12]

Guys! I'm preparing a small course on gravitation, planets, satellites and stuff for my university and planning to use KSP for demonstrations (i know some physics is bogus, mostly spheres of influence but whatever) and I got some questions. I know some of you know this trade a lot since you've helped me a lot pre-forum crash.

1) Apollo shot free-return trajectories. Those trajectories look like an "8". The 8 is seen from what coordinate system? Was it truly an 8? Was the lunar orbit retrograde then?

2)oberth effect: does it work reversely? i.e.: If I have to retroburn, will it be most efficient at higher, lower speeds, or it's the same?

3)Why is the apoapsis the most efficient place to burn to lower periapsis and, reversely, the periapsis the best place to raise apoapsis? Oberth effect/reverse oberth effect? Does burning raise/lower every point but the current, but the opposite point raises/lower more? Why?

Thanks!

1) The figure 8 is from the Earth's perspective. You can set up the same thing in KSP and see the figure 8 while you are still in Kerbin's SOI.

2) As far as I know Oberth works at higher speed for both acceleration and deceleration. This is because a small change in kinetic energy yields a larger change in velocity, ergo more for less.

3) At apoapsis you are moving slower and therefore don't need to lose as much velocity to lower periapsis. Try setting up a situation where you have a 100km by 1000km orbit, and then try lowering the opposite node to 50km. Obviously it's easier at apoapsis.

[Nibb31]

The "figure 8" is just an illustration as if the Moon wasn't moving. The Moon moves along it's own orbit, so the start of the "8" would point in front of the Moon, and the return would be somewhere else althogether, so depending on how long you loitered in lunar orbit, it wouldn't look like an 8 at all.

[karolus10]

Mun free return trajectory is truly looking similar to the "8" number (if we aim at moon position during our arrival), it require bit more ÃŽâ€V (~870) , so you pass right in front of mun path, but close enough to turn around and be slingshot back to kerbin (keep perigee not less than 20km or you can end up on collision course ,cause of SOI change error).

Also getting to mun using free-return trajectory is faster - less than 5 hours .

Edited May 23, 2013 by karolus10

[RoboRay]

Guys! I'm preparing a small course on gravitation, planets, satellites and stuff for my university and planning to use KSP for demonstrations (i know some physics is bogus, mostly spheres of influence but whatever) and I got some questions. I know some of you know this trade a lot since you've helped me a lot pre-forum crash.

1) Apollo shot free-return trajectories. Those trajectories look like an "8". The 8 is seen from what coordinate system? Was it truly an 8? Was the lunar orbit retrograde then?

Yes, the lunar orbit was retrograde. This is what makes the free-return possible. If you pass around the far side of the Moon in a prograde direction, the gravity assist would reduce your eccentricity, raising your perigee (Earth Pe) away from the Earth. By passing the far side retrograde (although you are still technically moving prograde in regards to the Earth at apogee, simply more slowly than the Moon is moving prograde), the Moon's gravity increases your eccentricity, dropping your perigee back down into the Earth's atmosphere... unless you make a burn at pericynthion (Moon Pe) to enter lunar orbit. This was simply insurance that if the engine didn't start, the crew would still get home.

They also timed the arrivals so that their landing zone would be just after dawn or just before sunset so the ground shadows would reveal surface features better.

2)oberth effect: does it work reversely? i.e.: If I have to retroburn, will it be most efficient at higher, lower speeds, or it's the same?

The Oberth effect derives from the kinetic energy of the fuel you're burning. When you burn it, the kinetic energy has to go somewhere, so it transfers to your ship. The faster you're moving, the more kinetic energy your fuel possesses, and the more free boost you get by burning it. Make your burns as close to Pe as possible to maximize it.

3)Why is the apoapsis the most efficient place to burn to lower periapsis and, reversely, the periapsis the best place to raise apoapsis? Oberth effect/reverse oberth effect? Does burning raise/lower every point but the current, but the opposite point raises/lower more? Why?

When you throw a ball several times, throwing harder each time, does the low-point of the trajectory rise, or the high point?

Orbital mechanics is really just an extension of those everyday effects you deal with on the ground. When you apply force to an object, the force doesn't alter the object's starting point, it merely changes where the object is going. If you could throw a ball hard enough that its high point (the apoapsis) would be on the opposite side of the planet (we'll pretend there is no air to slow it down), the ball would circle around and come right back to you. Throw it harder, and the Ap just keeps getting higher and higher, while the Pe (where you are standing) stays the same. If you wanted to change the Pe, where you're throwing the ball from, you'd have to find a way to apply force to the ball somehow after you've thrown it, when it's not at the Pe.

Burning prograde or retrograde raises or lowers every point of your orbit except the actual point of the burn. So, the opposite side of your orbit sees the most increase.

Edited May 23, 2013 by RoboRay

[Vanamonde]

Just to clarify, the Oberth effect has to do with the speed of the vehicle, not the altitude. It works out that low passes work better for it because your ship is moving faster there, but there's nothing magical about the altitude itself.

[CalculusWarrior]

While we're talking about the Oberth effect, is it the reason behind it being easier to return from the Mun than it is to get there, or is it simply taking advantage of the lower speeds up there and allowing yourself to fall back to Kerbin?

[AlexanderB]

They also timed the arrivals so that their landing zone would be just after dawn or just before sunset so the ground shadows would reveal surface features better.

A "night" on the moon would last 2 weeks, so they arrived just after dawn so they could see the shadows, and stayed (initially) a few days, later 2 weeks, lifting off before dusk.

[Frederf]

While we're talking about the Oberth effect, is it the reason behind it being easier to return from the Mun than it is to get there, or is it simply taking advantage of the lower speeds up there and allowing yourself to fall back to Kerbin?

The ease of return has to do with the asymmetry of the atmosphere fighting you during liftoff and helping you on landing as well as your ascent being a jillion times lighter which you can get away with since you don't need to do a powered descent. Without atmosphere you'd use the the fuel landing in any gravity well than you would taking off from it. As long as you did the same path there's a tremendous symmetry in flying any mission backward or forward. Mass changes are of course not symmetrical.

Oberth effect is perhaps best understood by comparing how much 1 delta-v buys you in terms of orbital energy at various speeds. Changing from 0 m/s to 1 m/s increases your kinetic energy by m/2 since it is 1/2m1^2 - 1/2m0^2. Call m/2 one "unit" of energy. Compare the energy change from 1000 m/s to 1001 m/s. This is (in m/2 units) equal to 1001^2 - 1000^2 which is 2001. By spending your delta-v at the faster speed you got two thousand times the orbital energy from it. The efficiency of your burn (work per fuel) is proportional to the speed you're going when you do it.