Analytical Trajectory of Solar Sail With Fixed Pitch Angle From Elliptical Orbits

In this article, the two-dimensional trajectory of a solar sail with a fixed pitch angle from a heliocentric elliptical orbit is analytically approximated using the linear perturbation theory. The lightness number is defined as the perturbation coefficient and the analytical solution is expressed as a function of the propulsive acceleration and the orbital elements. Different from the assumption of small eccentricity in some other methods, the proposed method is applicable to solar sails flying away from a general heliocentric elliptical orbit. Additionally, in the long-period mission scenario, in order to reduce the approximation error caused by the change of the osculating orbit elements, rectification steps for all relevant elements are added to the trajectory approximation process. The trajectory obtained by numerical integration is used to compare the approximate accuracy of the analytical trajectory and the modified analytical approximations. Moreover, the comparative analytical trajectory derived by referring to another method is used to verify the superiority of the proposed analytical trajectories. For the propelled trajectory of 20 revolutions corresponding to a solar sail with characteristic acceleration of 0.01 mm/s2, the relative error of the modified analytical trajectory compared with the numerically integrated trajectory can be as low as 10-6. The analytical solution and its rectification proposed in this article can be used for the preliminary design and mission evaluation of interplanetary exploration missions, especially for long-term mission scenarios.