Longitude and period mean-square deviation computing after series of corrections completion near geostationary orbit

Dynamics, ballistics, movement control of flying vehicles


Agishev A. R.

Moscow Institute of Physics and Technology, 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia

e-mail: artur.agishev@phystech.edu


Putting a spacecraft into assigned longitude of geostationary orbit state and transfer to a new longitude state is performed on pre-calculated plans, containing information on values and time of fulfilling all orbit corrections. The result of these maneuvering contains random errors caused by measuring errors of the orbit parameters and errors of correction performing. Check measurements and extra corrections, which should be foreseen in advance, are necessary to ensure the required maneuver performing accuracy. In this case, calculation of static characteristics of random deviations, occurring as a result of performed planned corrections, is effective.

The initial data for the calculation are the plan of transversal and binormal corrections, as well as mean-square deviation of the period measuring error and mean-square deviation of correction performing error.

In the calculation, all mistakes are considered as independent random variables with a zero expectation. The main feature of method is account for the effect of each mistake on the longitude deviation. The total deviation of orbit period and longitude of the geostationary spacecraft are the period measuring error effect, as well as transversal corrections’ performing error and transversal components of binormal corrections. While calculation, all errors are assumed as independent random values with mathematical expectation equal to zero. The main peculiarity of the computation method is an accounting for longitude evolution, which is the consequence of each error, occurring while maneuvering process.

Verification of the calculation correctness was performed by the software simulation of the correcting flight of the spacecraft in geostationary orbit. Characteristic quantities of measuring and corrections performing errors were accounted for. Simulation results confirm the calculations correctness. Computed mean-square deviations correspond to its confidence interval with 0.99 probability, found from a sample of 50 realizations. Mean-square longitude deviation for a spacecraft correction was 0.9%.

The proposed method of calculation can be applied in control measurements planning and final corrections to ensure accuracy of the spacecraft transfer into geostationary orbit.


geostationary orbit, multiple-revolution maneuvers, low-thrust maneuvers, longitude deflections, measuring errors, correction errors


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