Right ascension of the ascending node and geographic longitude

1

Hello everyone.
How to convert the right ascension of the ascending node into geographic longitude?Conversion to epoch time. Does Orekit provide this functionality?
Thanks!

2

Hi!

What I recommend is to use the full orbit and not only the RAAN.

Giving an Orbit and the BodyShape representing your central body, you can have the geographic longitude with

bodyShape.transform(orbit.getPVCoordinates().getPosition(), orbit.getFrame(), orbit.getDate()).getLongitude();

Now, if you want the longitude in terms of equinoctial elements you can obtain with


longitudeEquinoctial = perigeeArgument + RAAN + anomaly

Depending if the anomaly is mean or true you will have a mean or true longitude.

Bryan

3

Hello @newWL,

I would like to suggest another solution to complete @bcazabonne’s answer which only use the RAAN and epoch as inputs. It is from a purely geometrical point of view :

package org.example;

import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.orekit.data.DataContext;
import org.orekit.data.DataProvider;
import org.orekit.data.DirectoryCrawler;
import org.orekit.frames.Frame;
import org.orekit.frames.FramesFactory;
import org.orekit.frames.Transform;
import org.orekit.time.AbsoluteDate;
import org.orekit.utils.IERSConventions;

import java.awt.*;
import java.io.File;

public class RAANToLon {

    private static void loadOrekitData() {
        final File rootFile   = new File(System.getProperty("user.home"));
        final File         orekitFile = new File(rootFile, "orekit-data");
        final DataProvider dirCrawler = new DirectoryCrawler(orekitFile);
        DataContext.getDefault().getDataProvidersManager().addProvider(dirCrawler);
    }

    public static void main(String[] args) {

        // Load Orekit data
        loadOrekitData();

        // Inputs
        final double raan = FastMath.toRadians(30.);
        final AbsoluteDate epoch = new AbsoluteDate();

        // Convert to longitude
        final Frame eme2000 = FramesFactory.getEME2000();
        final Frame itrf = FramesFactory.getITRF(IERSConventions.IERS_2010, false);

        final Transform eme2000ToITRF = eme2000.getTransformTo(itrf, epoch);

        final Vector3D dirInEME2000 = new Vector3D(FastMath.cos(raan), FastMath.sin(raan),0.);
        final Vector3D dirInITRF = eme2000ToITRF.transformVector(dirInEME2000);

        final double lon = FastMath.acos(dirInITRF.dotProduct(Vector3D.PLUS_I) / dirInITRF.getNorm());

        System.out.format("Epoch : %s\n",epoch);
        System.out.format("Raan : %4.2f°\n",FastMath.toDegrees(raan));
        System.out.format("Longitude: %4.2f°",FastMath.toDegrees(lon));
    }
}

Cheers,
Vincent

4

Thank you so much for your help. I really appreciate it.

5

Thank you so much for your help. I really appreciate it. Your support means a lot to me and I am grateful for your kindness.

6

Thank you for your help. The result I converted with your method does not match STK. What is the reason?

7

Hi @newWL,

Could you provide me with your test case and expected results so i can investigate it on my end ?

Cheers,
Vincent

8

Thank you for your help. I apologize for any inconvenience caused.

Inputs

raan = FastMath.toRadians(120.0)
epoch = AbsoluteDate(2020, 6, 10, 12, 00, 00.000, TimeScalesFactory.getUTC())
#Output
40.95907874323129
The above is the result of running your code.
The orbit built to obtain LLA is -137.61578912644933.

9

Hi @newWL and sorry for answering late,

I have yet to see the flaw in my logic. Could you provide me the full orbit so i can compare with Bryan’s code ?

Cheers,
Vincent

10

Hello @newWL the result you obtain for the geographic longitude corresponding to the given right ascension using @Vincent code is correct.

All the best

11

Thanks! What is the geographic longitude you obtained?