How do you flatten the orbit?

[CSI_d00d]

When you create an orbit around kerbin what do you have to do to make it at 0 degrees like the moons

[Vanamonde]

Fly toward east (90 on the navball) all the way to orbit, and you'll be on the ecliptic plane without having to correct later.

[Frederf]

Canceling inclination is best done by not having any in the first place. Direct launch azimuths to any desired inclination are pretty easy to calculate.

To answer the actual question though you want to cancel your out of plane velocity when your position is on the plane of the desired orbit. You can think of an inclined orbit as being two orbits happening at the same time. Your north-south wobble is an orbit around the center of mass. In any case the ring of your orbit intersects the equatorial plane at two points called the ascending node and descending node. At either one burn in the opposite direction of your ascension (south) or descent (north) until your inclination disappears.

Be aware that you can only fully cancel your north-south movement as you pass through such a node. If you cancel your north-south motion away from the equator you'll still have inclination because you're still north or south of the center of mass.

[KrazyKrl]

It's pretty simple, and already explained well enough. I personally use Kerbal Engineer for a decent readout during launch. It has way too much information to NOT use.

[PringleMan]

To answer the original question better, burn at a 90 degree angle to your current orbit. For example if the apoapsis is inclined towards the north pole, then at periapsis (which would itself then be inclined towards the south pole) you should burn north. Think of it this way, if looking at your orbit from the side, edge on, it is like a teeter-totter and you should apply a force in the direction you want to move that side of the orbit. Really you can fix this at pretty much any point in the orbit, though I believe either the AP or peri are going to be the most cost effective. Just plan a maneuver node

[rryy]

You should burn south at your ascending node and north at your descending node to change inclination, but not necessarily at apoapsis or periapsis. To show those nodes relative to the equator, you can set the Mun as target because it is also in an equatorial orbit.

[arq]

You can plan the burn with the purple markers on the maneuver node.

If you want to do a massive change of inclination, sometimes it is most efficient to raise the altitude of your ascending or descending node (make it the apoapsis) and do it out there. Inclination adjustments are more efficient at high orbits because you have lower speed at that point (so inclination burns are larger relative to your speed). As said above, you can only burn to change your inclination to be as small as your current latitude, so it's important to do this at the equator.

For large changes you can use moons to make inclination changes. If you get an intercept and pass close to a moon its gravity will change your orbit, including inclination. Use maneuver nodes to plan this. However, Mun is roughly 800dV away from LKO, so it will likely cost you around 1600dV to use it for a change and return to LKO. This is a lot, but changing from an equatorial to a polar orbit directly probably costs roughly 3000dV, so it can still be cheaper.

[Gus]

If you want to do a massive change of inclination, sometimes it is most efficient to raise the altitude of your ascending or descending node (make it the apoapsis) and do it out there. Inclination adjustments are more efficient at high orbits because you have lower speed at that point (so inclination burns are larger relative to your speed).

Ah, the magic of orbital mechanics. This is a lot easier to understand than the Oberth effect which describes how it is most efficient to do a retro or prograde burn when you are moving the fastest.

[arq]

If you want to do a massive change of inclination, sometimes it is most efficient to raise the altitude of your ascending or descending node (make it the apoapsis) and do it out there. Inclination adjustments are more efficient at high orbits because you have lower speed at that point (so inclination burns are larger relative to your speed). As said above, you can only burn to change your inclination to be as small as your current latitude, so it's important to do this at the equator.

Some quick numbers: For about 950dV you can get out to Minmus's orbit (with or without an intercept). On an elliptical 100km-50Mm orbit, your speed at apo is tiny, maybe 50m/s. That means that for 100dV out there, you can completely reverse your orbit (or go to any other orbit for slightly less). Then, with some aerobraking you can get back down almost for free. This means that for around 1100m/s you should be able to change from any LKO to any other.

Of course, there's no cheaper way than to simply launch in the orbit you want.

[-Velocity-]

Ah, the magic of orbital mechanics. This is a lot easier to understand than the Oberth effect which describes how it is most efficient to do a retro or prograde burn when you are moving the fastest.

I didn't know that had a name, but it's actually pretty simple- Work = Force X Distance. Since you are moving over more distance when you are moving faster, then your rocket engine does more work.

Another way to understand it is kinetic energy = 0.5*m*v^2. For any fixed delta V applied by your rocket engine, you get more benefit if you are moving faster- for example, say you go from 5 m/s to 10 m/s- then that's a change of (normalized) energy of 10^2 - 5^2 = 75. Now, apply that same delta V of 5 m/s to a vehicle that's already moving 10 m/s (so you start at 10 m/s and end at 15 m/s). Now, your change in kinetic energy is 15^2 - 10^2 = 125. A whole lot more than 75!