Heading and Inclination

[funkcanna]

Hi all, sorry if this has an obvious answer, but I'm wondering how the heading and final inclination relate. For example, what heading should I take off to get a given final orbital inclination? I know 90º heading relates to a 0º inclination - is it as simple as having a 80º heading equal a 10º inclination? Also as both 270º and 90º headings give a 0º inclination, what would the inclination be on a 80º or a 100º heading? 10º both ways? And is there a way to differentiate a 270º or 90º orbital inclination of 0º? Obviously they are going in opposite directions but is there a term for this?

Edited May 2, 2015 by funkcanna

[adinfinitum]

It's not an entirely obvious answer, it'll require a little bit of trigonometry to figure out precisely. Because Kerbin is rotating, you already have some eastward orbital velocity just sitting on the pad. If Kerbin didn't rotate, then if you took off at a heading of 45 degrees your orbit would have an inclination of 45 degrees.

Now, we can break the rotational velocity we get from Kerbins rotation into two parts, one is in the heading we want to go, and the other is perpendicular. Think of the velocity in the way we want to go just as free dV. The perpendicular stuff is either normal or anti-normal to our orbit, so it'll cause a plane rotation, and depending on whether you are heading east or west, rotate your orbit closer or farther from equatorial, respectively.

TLDR; if you take of at a heading of 45 degrees, your inclination will be closer to equatorial. If you take off at a heading of 315, your inclination will be closer to polar. Hope that helped somewhat, its late at night and I'm on my phone

[funkcanna]

Thank you, it does help!

[Shpaget]

If you take off in 270° and enter orbit in that direction your inclination will be 180°. It is called retrograde orbit.

The numerical difference between heading and inclination in all these examples comes from different references. Your heading is referenced to North of the body you are on or orbiting, while inclination is referenced to equatorial plane (the plane in which the planet rotates).

[funkcanna]

So does the inclination number go up from 0 as you head south? I.e. Take off at 180 heading gives 90 degree inclination and 0 heading gives 270?

[Reactordrone]

So does the inclination number go up from 0 as you head south? I.e. Take off at 180 heading gives 90 degree inclination and 0 heading gives 270?

0/360° gives a 90° inclination heading north (ignoring the planet's rotation vector).

270° heading gives a 0° inclination to the equator but retrograde, called 180°.

Edited May 1, 2015 by Reactordrone

[Shpaget]

Heading - Inclination

0° - 90°

45° - 45°

90° - 0°

135° - 45°

180° - 90°

225° - 135°

270° - 180°

315° - 135°

360° - 90° (Actually the same thing as the first line)

Edit:

Build yourself a simple rocket:

OKTO core

2x FL-T800 fuel tanks

4x AV-R8 Winglets

Swivel engine

It can easily reach low retrograde orbit. Play with it and see what results you get.

If you install Kerbal Engineer Redux mod, you can see all the pretty data as you go.

Edited May 1, 2015 by Shpaget

[Red Iron Crown]

Inclination can only be within the range of 0-180 degrees. If you launched directly north or south you would end up in an orbit with an inclination of 90 degrees either way, the longitude of ascending node would be very different, though. (See here for more info on orbital elements.)

Heading is a bit trickier for inclinations other than 0, 90 or 180 degrees, in that the desired heading changes as you move north or south from the equator. This happens because the spacecraft always follows a great circle route. Have a look at the ground track for an object in an orbit with about 45 degrees of inclination (yellow line):

You can see that the object's heading changes from about 45 degrees at the equator when moving north, then changing to 90 at the northernmost point, then 135 when crossing the equator moving south, then 90 again at the southernmost point.

[adinfinitum]

Okay, now that it's morning and I'm more awake, I did some of the math to help illustrate what happens. When you're sitting on the pad, you're moving about 174m/s directly east. Now you launch into a parking orbit of 75km, where your orbital velocity is 2,287 m/s. Assuming you keep your heading indicator right on 45 degrees heading and ignore your prograde marker, your orbit's inclination will be about 42 degrees. Under the same conditions, heading 90 degrees = inclination of 85.7 degrees, and heading 315 degrees = inclination of 48 degrees.

[funkcanna]

Thank you all for the replies, really appreciated!