Document Type : Original Article

**Author**

Department of Civil Engineering, Imam Hossein University (IHU), Tehran, Iran

**Abstract**

In this paper, an advanced version of the Lagrange method, F and G series, is proposed for the many

applications in the celestial mechanics and space science such as initial orbit determination and satellite

orbit propagation. In this development, the Lagrange coefficients were developed from a gravitational

field of an inhomogeneous attractive body to all the perturbing accelerations acting on an orbiter. The

efficiency of the method is tested for the satellite orbit propagation. This assessment is based on the

comparison between the Lagrange solution and the analytical one for Keplerian motion and numerically

integrated orbit for non-Keplerian motion. The discrepancy at centimeter and sub-centimeter accuracy

shows the performance of the developed algorithm for MEO and LEO satellites orbit propagation. The

results of computational time showed that the Lagrange method is as time-consuming as the multi-step

methods where it is faster than the single-step methods. Besides the CPU-time, the stability test of the

Lagrange method shows that it is as stable as the single-step and is more stable than the multi-step

methods at the equivalent orders. Therefore, the Lagrange method offers the advantages of the single- and

multi-step methods.

applications in the celestial mechanics and space science such as initial orbit determination and satellite

orbit propagation. In this development, the Lagrange coefficients were developed from a gravitational

field of an inhomogeneous attractive body to all the perturbing accelerations acting on an orbiter. The

efficiency of the method is tested for the satellite orbit propagation. This assessment is based on the

comparison between the Lagrange solution and the analytical one for Keplerian motion and numerically

integrated orbit for non-Keplerian motion. The discrepancy at centimeter and sub-centimeter accuracy

shows the performance of the developed algorithm for MEO and LEO satellites orbit propagation. The

results of computational time showed that the Lagrange method is as time-consuming as the multi-step

methods where it is faster than the single-step methods. Besides the CPU-time, the stability test of the

Lagrange method shows that it is as stable as the single-step and is more stable than the multi-step

methods at the equivalent orders. Therefore, the Lagrange method offers the advantages of the single- and

multi-step methods.

**Keywords**

**Main Subjects**

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