Solid Tides influenced by body's gravity?

Orekit usage
1

I am propagating a satellite for 12 hours using Earth Gravity and Solid Tides, then comparing the norms of a reference final 3D vector with my propagation’s final position.

However, I get different results when including the Moon and Sun as celestial bodies.

Force Model Position Difference (km)
Solid Tides SUN + Gravitational Forces -3.0430546961724758 × 10⁻⁵
ONLY Gravitational Forces -5.945321079343557 × 10⁻⁵
Solid Tides MOON + Gravitational Forces -3.8074825890362266 × 10⁻⁵
ALL (Solid Tides (Sun + Moon) + Gravitational) -2.566743642091751 × 10⁻⁷

I ran these different tests because I wasn’t sure how the Moon and Sun would impact the results when passed to the SolidTides function.

Could anybody please explain me deeper how moon and sun affects the Solid Tides? These variations are related to the gravity of these bodies?

Here is my code implementation:

// Perturbations
            // 1. Gravitational Perturbations (Spherical Harmonics JGM-3 4x4)
            NormalizedSphericalHarmonicsProvider gravityProvider = GravityFieldFactory.getNormalizedProvider(4,4);
            ForceModel earthGravity = new HolmesFeatherstoneAttractionModel(earthFrame, gravityProvider);
            propagator.addForceModel(earthGravity);

            //2. Solid Tides
             // Add Gravity Model with Solid Tides (using IERS conventions)
            
            double ae = 6402000.0;           // Earth's equatorial radius
            TideSystem tideSystem = TideSystem.TIDE_FREE;                  // Tidal system
            IERSConventions conventions = IERSConventions.IERS_2010;      // IERS conventions
            UT1Scale ut1 = TimeScalesFactory.getUT1(conventions, true);   // UT1 time scale

            CelestialBody sun = CelestialBodyFactory.getSun();
            CelestialBody moon = CelestialBodyFactory.getMoon();
            

            SolidTides solidTides = new SolidTides(
                earthFrame,        // Central body frame
                ae,                // Earth's equatorial radius
                mu,                // Gravitational parameter
                tideSystem,        // Tidal system
                conventions,       // IERS conventions
                ut1,               // UT1 time scale
                moon, sun
            );

            propagator.addForceModel(solidTides);
2

Hi @rodreras,

Yes, the tides are due to the third body/ies. Just like the oceanic tides are due to the Moon (and the Sun) and depend on the position of these bodies with respect to Earth; the solid tides are the deformations of the Earth’s crust due to the influence of (mostly) the Moon and the Sun.
Here’s a Navipedia short reference, and a more developed one from IERS.

Hope this helps,
Maxime

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3

Once again, thank you for the response @MaximeJ !

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4

I am revisiting this thread as I am back to the propagation with the external forces influences.

Maxime, I understand the concepts, but I still did not fully understand how SolidTide works.

If I run SolidTides without 3rd bodies force, I get a value.

When I run with Moon and Sun, either separated or together, it got different values.

  • What is the difference when I use moon and sun as point masses instead of forces within the SolidTide function?
  • Why do I get different values?

I ran another batch of examples, and once again, got distinct values.

Case A - 3rd Bodies as Points

//Third bodies: Sun and Moon

CelestialBody sun = CelestialBodyFactory.getSun();
CelestialBody moon = CelestialBodyFactory.getMoon();


propagator.addForceModel(new ThirdBodyAttraction(sun));
propagator.addForceModel(new ThirdBodyAttraction(moon));

Result Test Case A - 3rd Bodies as Points

Position Difference (km):6.181731605902314E-4
Velocity Difference (km):-3.5333510186319474E-7

Case B - 3rd Bodies in SolidTides

SolidTides solidTides = new SolidTides(
                earthFrame,        // Central body frame
                ae,                // Earth's equatorial radius
                mu,                // Gravitational parameter
                tideSystem,        // Tidal system
                conventions,       // IERS conventions
                ut1,               // UT1 time scale
                moon, sun
            );

Result Test Case B - 3rd Bodies in Solid Tides

Position Difference (km):-2.5667063891887666E-7
Velocity Difference (km):1.1625352271948941E-9

5

Hi @rodreras,

Solid tides and third bodies’ gravity are different perturbations:

  • 3rd body perturbation is the direct gravitational effect of the 3rd body (Moon or Sun)
  • Solid tides model the deformation of the Earth’s crust due to the 3rd body, and then this deformation itself influences the path of the satellite.

Hope this helps,
Maxime

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