A multi-dimensional nonlinear optimisation method for the TianQin constellation

Abstract

Abstract TianQin is a geocentric space-based gravitational wave detecting mission that relies on three drag-free spacecraft with a mean inter-spacecraft distance of approximately 1.7 × 105 km. Considering the efficiency requirement of orbit optimisation, we apply a gradient descent method based on variational gradient calculation and the damped Newton iterative method to find the most stable solution of the constellation near the given initial position and velocity of the spacecraft. The efficiency was improved and the number of orbital integrals required for gradient calculation was significantly reduced by over 83%. Based on this optimisation method, we analysed the influence of perturbation on the stability of the TianQin constellation, and Moon’s three-body perturbation was the main factor. In addition, the influence of the orbit elements on the optimisation results was studied. The influence of the initial mean anomaly can be ignored, and the stability of the optimised constellation decreases with an increase in the semi-major axis. Working in the ‘3 months on +3 months off’ observation scheme for 2 years, the optimisation result is the ideal direction when the normal direction of the orbital plane of the TianQin constellation points to RXJ0806.3 + 1527.