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
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