Origin of Longitude

[Tristavius]

Hi All,

I've been spending the last few days trying to teach myself a lot of the maths/science that goes into KSP. I think I now have a handle on most things that effect the game (starting with ISP, TWR etc and working my way up) and I'm now happy what each of the six orbital elements that make up an orbit are and how they relate to each other.

I am however struggling to get my head around part of the Longitude of the Ascending Node which is the use of an Origin of Longitude. I understand what the LAN shows, but not how to acquire the Origin of Longitude itself.

A lot refers to the First Point of Aries, but I believe this is no longer a relevant terminology. Further reading show it has to do with the Spring/Vernal Equinox and where the Sun (or Kerbol) would be at the spring Equinox. In the sun's case this seems to be round about Mexico? That only makes things more confusing though... does Kerbin actually have an Equinox as it has a non-eccentric, non-inclined orbit?! This also wouldn't account for how it's measured on, say, Dres.

In short, I suspect I'm missing something big here; something isn't clicking into place. Have read the articles available from the most obvious places and I'm still banging my head off the desk.

Can anyone offer me more or an explanation (both real world and KSP)?

Much appreciated.

[Nuke]

for lan i think we just use an arbitrary point in space (ive heard first point in ares too, which i guess is a particular star) to mark where the zero point is, and measure the angle from that.

[Tristavius]

Yeah that's the conclusion I'd come to. I think the First point of Ares refers to a particular star (or constellation) that used to be at a certain position during the Equinox. Over time of course the movement of stars will have changed so I think the term is now 'out of date'.

So if in the real world we have a fairly arbitrary direction, where is that direction in KSP and how can it be worked out for the various bodies?

[maltesh]

In Kerbal Space Program, the Reference Direction for Celestial Longitude is not marked by any significant object, last I checked. In the universe of KSP, a ray drawn from Kerbin to the Sun at the epoch UT = 0.0 points about 0.09° east of the Reference Direction.

An Orbit whose Longitude of the Ascending Node is 180.0°, and whose Argument of Periapsis is 0.0° (abbreviated as LPE in KSP) will have an apoapsis that points in the Reference Direction. Through save file editing, you could add an object with a highly-eccentric elliptical orbit and a 90-degree orbital inclination around the sun to use its orbit as a pointer toward the Reference direction.

Edit:

In the above image, screenshotted a few minutes after UT=0.0, the apoapsis of the Reference Director spacecraft points in the Reference Direction for KSP Celestial Longitude.

Edited November 23, 2013 by maltesh

[Tristavius]

Okay, I think that's everything clicked into place.

So for any individual body, it's 0° Longitude of the Ascending Node was the point of the body facing in the (lets call it 'A' for arbitrary') direction at UT 0. Makes sense.

Now I just need to work out the maths for how people are working it out at specific point in time; my next challenge!

[AdamMil]

Sorry to revive an old thread, but for the sake of helping other people who may be wondering the same thing, in KSP the reference direction points down the X axis of the XYZ coordinate system used internally to represent position and velocity vectors. (The Z axis points upwards, and is parallel to the polar axis of all celestial objects, since no celestial object has axial tilt.) I know this holds true for the orbits of all of the planets relative to Kerbol. For the orbits of moons relative to planets or ships relative to other bodies, I believe the local reference direction is parallel to the global reference direction (i.e. parallel to the global X axis), and the local (parent-relative) XYZ coordinate system is simply translated but not rotated, so the local reference direction points down the X axis of the local coordinate system.

The reason the reference direction is about 0.09 degrees away from the opposite side of Kerbin's orbit at UT 0 is because Kerbin is in a circular, non-inclined orbit with a longitude of ascending node of 0 radians and a mean anomaly at epoch of 3.14 radians (taken from http://wiki.kerbalspaceprogram.com/wiki/Kerbin). This represents a total rotation of 0 + 3.14 radians away from the reference direction, or 179.91 degrees, which is 0.09 degrees away from the opposite side.

Edited January 19, 2016 by AdamMil