How to change a 0 degree heading to a 90 degree heading?

[gdscei]

I am currently in orbit around Kerbin at 175km circularized, but I am going at a 0 degree heading (upwards you could say, polar?). I want to go equatorial (90 degree heading) eastward. How do I this? I know I have to burn in some angle, but I am not sure which, I've tried some stuff but that only seems to change my Pe and Ap. I need to actually change my orbital heading.

[pebble_garden]

This case is the most extreme example of a plane-change maneuver. You want to tip your orbital plane a whole 90 degrees.

In a polar orbit, only two points lie along the equatorial plane. Those two points will be where you do all your thrusting, spread over several orbits.

Some terminology:

Prograde: the direction of your orbital path.

Retrograde: the opposite direction from your orbital path.

Normal: 90 degrees counter-clockwise to the plane of your orbit. Make a circular shape with your right hand to represent an easterly orbit. Your thumb will point up along the normal.

Antinormal: 180 degrees opposite the normal.

I recommend this approach:

1. As you cross the equator going North, turn toward the normal, in this case a heading of prograde (90 degrees, East) and thrust. Time your burn so it's a minute before and a minute after, but not much more than that. You'll see the plane of your orbit begin to tilt east at the top, with your burn point forming the pivot point.

2. After your burn, your prograde marker will be offset from a 0 heading by a few degrees. Make a note of this offset.

3. When you're passing the equator on the other (downward) side of your orbit, burn 90 (+ the offset) from step 2 for the same amount of time. This will continue to tilt your orbital plane clockwise.

3. Burn each time you cross the equator. As your orbit tilts, always thrust at along the normal and watch the growing offset in your prograde and retrograde markers.

4. Repeat as necessary until your orbit is aligned with the equator. It might take several orbits, and a lot of fuel.

I hope that helps!

Edited August 4, 2012 by pebble_garden

[Kosmo-not]

When you cross the equator, burn in the 135° direction until you come back to your orbital speed. You should then be heading 090°.

[Zephram Kerman]

For a very large plane change like this, it's helpful to first boost into a higher orbit, do the turn at the new apoapsis, and then reduce it again. Changing plane at the higher apoapsis is so much more efficient that it pays for the boost and retro burns, and then some.

Unfortunately, I don't know the higher math to determine when this method is more efficient than doing the plane change directly. It's certainly worthwhile for a 90° change, but not for 15°.

Edited August 5, 2012 by Zephram Kerman

[pebble_garden]

For a very large plane change like this, it's helpful to first boost into a higher orbit, do the turn at the new apoapsis, and then reduce it again. Changing plane at the higher apoapsis is so much more efficient that it pays for the boost and retro burns, and then some.

Oh, that's very clever, Zephram. I shall have to try that. It makes perfect sense.

In the case of a rendezvous with another orbiting object, you'd want to place your apoapsis right at a crossing node for the two orbits, I assume.

Though the best strategy is to launch with the proper inclination at the outset.