Position of Ascending and Descending Nodes

In summary, the user is trying to determine the position of an orbit's ascending and descending nodes. They are also looking for a way to determine what their "altitude" would be at the ascending and descending nodes. They have been unsuccessful so far in finding a way to calculate this information. However, they have set up functions to get the position of a given true anomaly angle. This function worked perfectly, allowing them to determine the positions of the nodes.
  • #1
TheHarvesteR
14
0
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
 
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  • #2
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.

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

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).
 
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  • #3
BobG said:
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 :smile: )

Cheers
 
  • #4
Worked perfect! So simple and elegant!

Thanks a million!

Cheers
 
  • #5



Hello there,

To determine the position of an orbit's ascending and descending nodes, you will need to use some trigonometric calculations. The ascending and descending nodes are the points where the orbital plane intersects with the reference plane, which is usually the equatorial plane of the central body.

To find the actual distance of the node from the central body, you can use the following formula: r = a * (1 - e^2) / (1 + e * cos(θ)), where r is the distance from the central body, a is the semi-major axis of the orbit, e is the eccentricity of the orbit, and θ is the true anomaly at the ascending or descending node. This formula is derived from Kepler's second law, which states that the line connecting a planet to the sun sweeps out equal areas in equal times.

To determine the altitude at the ascending and descending nodes, you will need to use the formula: h = r - R, where h is the altitude, r is the distance from the central body, and R is the radius of the central body.

I hope this helps with your orbital visualization system. If you have any further questions, please don't hesitate to ask. Good luck with your project!

Best,
 

1. What is the Position of Ascending and Descending Nodes?

The position of ascending and descending nodes refers to the points in an orbit where a celestial body crosses the plane of reference, such as the ecliptic or the equator. These points mark the beginning and end of the orbital path of a celestial body in relation to the plane of reference.

2. How is the Position of Ascending and Descending Nodes determined?

The position of ascending and descending nodes is determined by the intersection of the orbital plane of a celestial body with the plane of reference. This can be calculated using orbital elements, such as the inclination and longitude of the ascending node, which describe the orientation of the orbital plane in space.

3. What are the implications of the Position of Ascending and Descending Nodes?

The position of ascending and descending nodes can affect the visibility and behavior of celestial bodies, such as planets or asteroids, as they pass through the plane of reference. It also plays a role in orbital mechanics and can impact the stability and evolution of an orbit.

4. How does the Position of Ascending and Descending Nodes relate to the Zodiac?

In the context of astrology, the position of ascending and descending nodes is sometimes referred to as the lunar nodes. These nodes are associated with the ecliptic and the zodiac, and their movement is believed to have an influence on human behavior and fate.

5. Can the Position of Ascending and Descending Nodes change?

Yes, the position of ascending and descending nodes can change over time due to perturbations from other celestial bodies or changes in the orientation of the orbital plane. It can also vary depending on the plane of reference used, as different coordinate systems may have different definitions of the ascending and descending nodes.

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