Position of Ascending and Descending Nodes

[TheHarvesteR]

Hi again.

I'm trying to determine the position of an orbit's ascending and descending nodes here. I already have the Longitude of the ascending node, and a unit vector that points to it, so what I now need is a way to find out the actual distance of the node from the central body.

More specifically, I'm trying to find some way to determine what my "altitude" would be at the ascending and descending nodes. Or, the point at which the line of nodes intersects the orbit.

So far I haven't had much luck with this one, all I can find are directions for calculating the longitude of the ascendind node, but nothing about it's actual distance from the central body.

The reason I'm trying to find these points is that I'm building an orbital visualization system here, and I'm placing icons over the more important points of the orbit, like periapsis, apoapsis, object position, and ascending and descending nodes. All other points are accounted for, but I'm missing that one bit of information to correctly place AN and DN.

Any help would be greatly appreciated.

Thanks in advance,

Cheers

 

[BobG]

How did you find a vector that pointed towards the ascending node?

The normal way is to take the cross product of unit vector k (which lies on the geocentric Z axis) and your angular momentum vector, which means you have the angular momentum vector and can calculate its magnitude.

How did you find a vector that points towards perigee?

The normal way is to create an eccentricity vector that's derived from the LaPlace vector.

You can use the dot product of the eccentricity vector and your line of nodes to find the cosine of true anomaly. The easier way would probably be to subtract your argument of perigee from 360 to actually find your true anomaly at the ascending node. Once you have your true anomaly, you can use the following version of the trajectory equation to find the magnitude of your radius at the ascending node.

$$r = \frac{h^2/\mu}{1 + e cos(\nu)}$$

with h being the magnitude of your angular momentum vector
mu being your geocentric gravitational constant
e being the magnitude of your eccentricity vector (or just your eccentricity if you're getting your info from elsets)

And your angular momentum vector is the cross product of the position vector and the velocity vector. Since it remains constant, you can calculate it anywhere in your orbit. It's easiest to calculate at perigee or apogee since the velocity vector is perpendicular to the position vector at those two points. In other words, at perigee and apogee, the magnitude of your angular momentum is just your radius times your velocity (with both measured in either meters & meters/sec or km and km/sec, depending on the units you want your final answer to be in).

 

[TheHarvesteR]

The easier way would probably be to subtract your argument of perigee from 360 to actually find your true anomaly at the ascending node.

This just might work :)

I already have functions set up to get a position given a true anomaly angle, so if I can find the true anomaly of the nodes, I pretty much aready have their positions.

I'll give this a try now. I'll let you know how this goes.

Thanks! (BTW, I'm loving these forums )

Cheers

 

[TheHarvesteR]

Worked perfect! So simple and elegant!

Thanks a million!

Cheers