Quick Calculation Of The Disturbing Gravity And Its Placement Deviations

The effect of the disturbing gravitation on the long-range ballistic trajectory is can not be ignored. It can bring errors on the impact point. Sometimes the errors can reach hundreds of meters or even more. So in order to insure the precision of the missile, the disturbing gravitation is must be take into account when we calculating the ballistic trajectories. As a result, it will be necessary to find a way by which we can calculate the disturbing gravitation exactly and fast. In this paper, we not only analysed the different effects of the disturbing gravitation on the trajectories of different ranges, but also discussed shortcomeings of the spherical harmonics model by which the external gravitation potential of the earth is shown usually. When the model is applied directly to the calculation of the trajectory, since the recurrent calculation can not be avoided, an increase in orders of model will result on a decrease in the speed of calculation. In this paper, the transitional method of the spherical harmonics is applied and a new model is gained. The parameters of the new model are geocentric radius, range cross-deviation and polar is decided by different trajectories. With the recurrent calculation got rid of, the speed of calculation is increased. Practical calculations have shown that the new model not only have the high precision but also enables us to enhance the speed of calculation 6 or 7 times. So it is testified that the new model is superior to the spherical harmonics model.