Abstract
In the differential equation system describes the motion of GLONASS satellites (rus. Globalnaya Navigazionnaya Sputnikovaya Sistema, or Global Navigation Satellite System ), the acceleration caused by the luni-solar traction is often taken as a constant during the period of the integration. In this work-study, we assume that the acceleration due to the luni-solar traction is not constant but varies linearly during the period of integration following this assumption; the linear functions in the three axes of the luni-solar acceleration are computed for an interval of 30 min and then implemented into the differential equations. The use of the numerical integration of Runge-Kutta fourth-order is recommended in the GLONASS-ICD (Interface Control Document) to solve for the differential equation system in order to get an orbit solution. The computation of the position and velocity of a GLONASS satellite in this study is performed by using the Runge-Kutta fourth-order method in forward and backward integration, with initial conditions provided in the broadcast ephemerides file.
Highlights
The use of the numerical integration of Runge-Kutta fourthorder is recommended in the GLONASS-ICD (Interface Control Document) to solve for the differential equation system in order to get an orbit solution
GLONASS stands for Globalnaya Navigazionnaya Sputnikovaya Sistema, or Global Navigation Satellite System was developed by the USSR (Union of Soviet Socialist Republics) in 1976 and is operated by Russia, with the first GLONASS satellite launched on 12 October, 1982, the full constellation was completed and put into operation at the beginning of 1996 (Guoet et al, 2020)
4.2 Results relative to 24 hours (23:45 to 23:45) Knowing the initial values of position, velocity and luni-solar acceleration at 48 different epochs (24 hours, 23:45 to 23:45) from the broadcast ephemerides of GLONASS SV 07 unregistered on February 09, 2020 we can compute the positions, velocities and luni-solar accelerations at (H: 00) and (H:30), where H is Hour
Summary
GLONASS stands for Globalnaya Navigazionnaya Sputnikovaya Sistema, or Global Navigation Satellite System was developed by the USSR (Union of Soviet Socialist Republics) in 1976 and is operated by Russia, with the first GLONASS satellite launched on 12 October, 1982, the full constellation was completed and put into operation at the beginning of 1996 (Guoet et al, 2020). Like GPS (Global Positioning System), GLONASS is used to provide positioning, velocity and precise time for marine, aerial, terrestrial, and space users (ICD, 2016). The space segment of GLONASS consists of 23 operational satellites and three backup satellites, which are evenly distributed over three orbital planes with an inclination of 64.8°. There are eight satellites separated by 45° in the argument of latitude, the altitude of a satellite above the terrestrial surface is 19100 km and its orbital period is 11 h 15 min 44 s (Guo et al, 2020). In September 2016, the number of operational satellites in orbit was increased to 27, 24 of which are GLONASS-M and GLONASS-K1 satellites with full operational capability. The GLONASS broadcast ephemerides are given in the PZ-90 (Parametry Zemli 1990 or Parameters of the Earth 1990) reference frame (ICD, 2016)
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