Empirical Solar Radiation Pressure Models for GLONASS Satellites

These models had been investigated for the IGS processing, but they were discarded because the use of the ROCK model in combination with the sine and cosine empirical accelerations proved to be equivalent. IGEX gave a second chance for the use of this implementation.

The parametrization of the model describes the forces on each of the reference frame axes as a function of the selected argument A as:

where K is a factor that can be 1 or a scaling including the variation in solar radiation pressure with satellite-sun distance and an estimable global scale factor.

Several arguments and reference frames have been tested.

The most interesting arguments are:

• The solar angle (see figure). It is used in the ROCK models. Useful for spacecraft with orientation accordingly with the Sun direction.
• The solar anomaly. It is the orbital angle for which the origin is the point in the orbit closest to the Sun.
• True anomaly: for spacecraft in elliptic orbits.
• Argument of latitude: spacecraft in near circular orbits.

Tested reference frames are:

• The ROCK model frame. Body fixed defined by the Sun and Earth directions.
• Solar frame. Defined by the Sun and the Earth and rotating in satellite fixed axes around the solar panel axis.
• Orbital frame. Defined by the position and velocity.

After several tests the selected argument is the solar anomaly, and the frame the solar one. Sine and cosine terms are only estimated in the z axis. Terms in 2A are not estimated.

Resulting in a 5 estimated coefficients model: constant terms in x, y and z directions and sine and cosine terms in the z direction. The x, y, z directions are defined as:

• x: antisolar
• z: contained in the plane of the satellite c.o.m., the geocenter and the sun and pointing towards the semiplane including the earth.
• y: completing a right-handed system.

The coefficients of the solar radiation pressure model are plotted for several days of the campaign.

If this model is used for the GPS satellites it produces a fit similar to the ROCK model plus four estimated parameters (scale, y-bias, two radial cyclical accelerations).

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