Draw a generalized orbit ellipse

CesiumJS
1

1. A concise explanation of the problem you’re experiencing.

I’m trying to draw the path of a orbit around Earth given the semi major axis, along with the point of perigee and apogee. Also, I’d like to incline the orbit, longitude of the ascending node and argument of periapsis. Basically everything that defines an orbit without having to say where the object is along the orbit.

I tried using a EllipseGeometry, but that didn’t work since it kept being attached to the surface of the Earth or curved with the surface when I added height.

2. A minimal code example. If you’ve found a bug, this helps us reproduce and repair it.

I can sort of get what I want using a polyline for a circular orbit:

var meo_orbit = 20000000;

var inclination = 30;

var meoline = viewer.entities.add({

name : ‘Blue dashed line’,

polyline : {

positions : Cesium.Cartesian3.fromDegreesArrayHeights(

[0, 0, meo_orbit,

90, inclination, meo_orbit,

180, 0, meo_orbit,

270,inclination * -1 , meo_orbit,

0, 0, meo_orbit

]),

width : 1,

material : new Cesium.PolylineDashMaterialProperty({

color: Cesium.Color.GRAY

})

}

});

The issue I’m having is generalizing the calculation of the 4 vertex points. I’m assuming there is a way I can calculate those with the given inputs but I want to make sure this is the best/proper approach as I’m just starting to learn space, orbits and such.

3. Context. Why do you need to do this? We might know a better way to accomplish your goal.

My goal is to create a simply panel for quickly visualizing different orbits (LEO, HEO, MEO, etc) paths without having to propagate a satellite or object around to get it. I want to visualize how the orbits change as different parameters are adjusted.

4. The Cesium version you’re using, your operating system and browser.

1.44. Linux. Firefox.

Thank you for help.

2

I have more complete code example:
var inclination = 30;

var parogee = 1000000;

var appogee = 20000000;

var loan = 30;

var e = 1 - 2 / ( (appogee / parogee) + 1);

// altitude for minor vertix

var h1 = appogee * Math.sqrt(1 - Math.pow(e, 2));

console.log(h1);

var meoline = viewer.entities.add({

name : ‘Blue dashed line’,

polyline : {

positions : Cesium.Cartesian3.fromDegreesArrayHeights(

[loan, 0, h1,

loan+90, inclination, appogee,

loan+180, 0, h1,

loan+270,inclination*-1 , parogee,

loan, 0, h1,

]),

width : 1,

material : new Cesium.PolylineDashMaterialProperty({

color: Cesium.Color.GRAY

})

}

});

As you can see in the attached screenshot, I’m not getting the ellipse I was hoping for. Any suggestions for a better way to accomplish this would be appreciated.

-Aaron

Screen Shot 2018-04-24 at 10.22.27 PM.png
Screen Shot 2018-04-24 at 10.22.27 PM.png1012×785 553 KB

3

Hi Aaron,

AGI, the company that founded Cesium is an aerospace company, so we often visualize satellite trajectories and use polylines to do so.

Your code looks correct, I;m guessing this may just be an issue with math and converting between Cartographic and Cartesian coordinates. Here is an example I put in a previous thread.

Hope that helps!

Gabby

4

That definitely helped. I did have a math issue.

I have just about everything working expect for the Argument of Perigee.

How do I get a transform so I can rotate around the orbit plane’s Z axis and not Earth’s? How to use the transform, and which one to use, properly is confusing me.

Example:

var inclination = 30;

var parogee = 1000000;

var appogee = 5000000;

var loan = 0;

var argument_of_periapsis = 45;

var semi_major = parogee + appogee / 2;

var e = 1 - 2 / ( (appogee / parogee) + 1);

// altitude for minor vertix

var semi_minor = semi_major * Math.sqrt(1 - Math.pow(e, 2));

var inclination_m = Cesium.Matrix3.fromRotationY(-1 * Cesium.Math.toRadians(inclination));

var raan_m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(loan));

var aop_m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(argument_of_periapsis));

var positions = ;

for ( var i = -180; i <= 180; i+=1) {

//r = a(1-e^2)/ 1+e\cos \theta}

var radius = semi_major * (1- Math.pow(e, 2)) / (1 + e * Math.cos(Cesium.Math.toRadians(i)));

//create point

var p = new Cesium.Cartesian3.fromDegrees(i-90, 0, radius);

//rotate around earth Y axis to apply inclination

var rotated = Cesium.Matrix3.multiplyByVector(inclination_m, p, new Cesium.Cartesian3());

//rotate around earth Z to apply RAAN

var raan = Cesium.Matrix3.multiplyByVector(raan_m, rotated, new Cesium.Cartesian3());

//rotate around orbit plane Z to apply AOP

//transform to local orbit plane

//???

var final = Cesium.Matrix3.multiplyByVector(aop_m, raan, new Cesium.Cartesian3());

positions.push(final);

}

5

I’m not all that familiar with the calculations here (maybe someone on the forum here may know, otherwise asking a more math-related or orbit-related forum might help), but I see you do have the correct way of applying rotations using the Cesium API:

// Rotate a point 45 degrees counterclockwise around the x-axis.
var p = new Cesium.Cartesian3(5, 6, 7);
var m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());

Thanks,

Gabby