Simulations for LISA & GRACE-Follow-On: Satellite constellations at Lagrangian points for LISA-like missions & Interferometer simulations for the GRACE Follow-On mission

Abstract

This thesis is separated into two parts. The first part is about satellite orbits for space-based gravitational wave detectors. Gravitational waves are ripples in the four-dimensional spacetime and were firstly predicted by Albert Einstein. They can be caused by astrophysical events (e.g. merging black holes, stellar explosions) and manifest as length changes between objects, for example, satellites. The order of magnitude of the relative length changes corresponds approximately to the size of an atom over a measurement distance between Sun and Earth. However, even this tiny effect can be measured with laser light, interferometrically. In this thesis the construction of satellite constellations in the vicinity of the so-called Lagrangian points is investigated, which might be stable enough over the mission duration to allow interferometric measurements between the spacecrafts. Therefore, the fundamental dynamics of single objects in the proximity of Lagrangian points are studied, followed by attempts to construct constellations by combining different trajectories. Finally, numerical optimization techniques are applied to further improve the constellations. The second part of this thesis is concerned with an instrument for the GRACE Follow-On mission. This planned mission consists of two satellites in a low Earth orbit, which shall measure Earth’s gravity field. Therefore, the inter-satellite distance fluctuations need to be determined very precisely in the frequency range from 2 mHz to 100 mHz. For this purpose the Albert-Einstein-Institute develops in cooperation with industry and international partners a Laser Ranging Interferometer with a target precision better than 0.001 millimeter. An overview about the working principle of the instrument as well as the purpose of single components is presented. The contribution of various perturbations like spacecraft attitude jitter on the performance is computed. Finally, simulation results show how various misadjustments of components influence the measurements