<p>You could convert the orbital elements into x,y,z and <span class="math-container">$ \dot{x}, \dot{y}, \dot{z}$</span> and then calculate a whole orbit. A source for converting orbital elements into cartesian coordinates is <a href="https://downloads.rene-schwarz.com/download/M001-Keplerian_Orbit_Elements_to_Cartesian_State_Vectors.pdf" rel="nofollow noreferrer">here</a>.</p>

CC BY-SA 4.0
2020-07-08T19:43:22.497Z
2020-07-08T19:43:22.497Z
Natsfan
<p>I'm trying to generate an 'overhead' view of the orbits of the moons of Neptune, similar to Figure 4 in <a href="https://iopscience.iop.org/article/10.1086/504799/pdf" rel="nofollow noreferrer">this paper</a>, using values given <a href="https://ssd.jpl.nasa.gov/?sat_elem#legend" rel="nofollow noreferrer">here</a>. I initially tried using both the Argument of Periapsis, and the Longitude of the Ascending Node separately but neither seems to give the correct results. After a bit more reading I now think I will need to combine both these values to derive the orientation of the major axis of the ellipse, but I can't find the formula anywhere. Am I correct? Could someone show me the correct calculation?</p>

CC BY-SA 4.0
2020-07-07T15:13:09.197Z
So how exactly did you try to do the projection and how does that not work? Show us what you did
planetmaker
CC BY-SA 4.0
2020-07-07T16:04:53.797Z
@planetmaker I drew the ellipses for each orbit orienting the major axes using the Argument of Periapsis, and then redrew them using the Longitude of the Ascending Node but neither of the results matched the diagram from the paper I referenced, so I am now assuming that I need to combine both the angles somehow, but I'm not sure how
codebox
CC BY-SA 4.0
2020-11-30T00:25:51.107Z
@jmh is right about working with x, y, and z coordinates, but I have also devised a script to draw the ellipse from any angle. I’m willing to share if you still need it.
Pierre Paquette
CC BY-SA 4.0
2020-11-30T10:03:54.747Z
That sounds useful @PierrePaquette if you could share it then that would be great
codebox
<orbit><orbital-elements><satellite>
How to calculate shape of orbit when projected onto the plane of the ecliptic
codebox
# How to calculate shape of orbit when projected onto the plane of the ecliptic

(Asked by: username_0 on 2020-07-07)

I'm trying to generate an 'overhead' view of the orbits of the moons of Neptune, similar to Figure 4 in [this paper](https://iopscience.iop.org/article/10.1086/504799/pdf), using values given [here](https://ssd.jpl.nasa.gov/?sat_elem#legend). I initially tried using both the Argument of Periapsis, and the Longitude of the Ascending Node separately but neither seems to give the correct results. After a bit more reading I now think I will need to combine both these values to derive the orientation of the major axis of the ellipse, but I can't find the formula anywhere. Am I correct? Could someone show me the correct calculation?

**Tags:** orbit, orbital-elements, satellite

> **Comments:**
> **username_1**: So how exactly did you try to do the projection and how does that not work? Show us what you did  
> **username_0**: @username_1 I drew the ellipses for each orbit orienting the major axes using the Argument of Periapsis, and then redrew them using the Longitude of the Ascending Node but neither of the results matched the diagram from the paper I referenced, so I am now assuming that I need to combine both the angles somehow, but I'm not sure how  
> **username_2**: @jmh is right about working with x, y, and z coordinates, but I have also devised a script to draw the ellipse from any angle. I’m willing to share if you still need it.  
> **username_0**: That sounds useful @PierrePaquette if you could share it then that would be great  

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## 1 answers

### Answer by username_3 on 2020-07-08. Score: 3 | Accepted answer

You could convert the orbital elements into x,y,z and $ \dot{x}, \dot{y}, \dot{z}$ and then calculate a whole orbit. A source for converting orbital elements into cartesian coordinates is [here](https://downloads.rene-schwarz.com/download/M001-Keplerian_Orbit_Elements_to_Cartesian_State_Vectors.pdf).


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