Modeling coupled constellation dynamics for TianQin under self-gravity

TL;DR

The paper develops a comprehensive $9$-body coupled dynamics framework for TianQin that propagates the full interdependence of three satellites and six TMs under inter-satellite pointing and drag-free controls, including satellite self-gravity. It demonstrates that a geocentric two-TM pointing scheme remains feasible and provides design guidelines to minimize common self-gravity along the flight direction while keeping differential self-gravity around $10^{-10}$ m s$^{-2}$. High-precision quadruple-precision orbit propagation (via TQPOP) paired with the coupled dynamics solver (TQDYN) yields sub-pm/Hz$^{1/2}$ precision for the long-range light path, and the results support decoupling closed-loop dynamics from high-precision orbit propagation for computational efficiency. The study offers actionable guidance for self-gravity design, validates the decoupling approach, and establishes a framework applicable to future orbit-attitude coupled GW missions and TTL-noise analyses.

Abstract

TianQin is a dedicated geocentric mission for space-based gravitational wave (GW) detection. Among its core technologies, the drag-free and pointing control subsystem (DFPCS) - consisting of suspension, drag-free and pointing controls - keeps the two test masses (TMs) centered and aligned within their housings while maintaining drag-free conditions and precise telescope pointing along the laser-arm directions. This results in orbit-attitude coupled dynamics for the constellation. The coupling is made more prominent due to satellite self-gravity, which requires compensation from DFPCS and generally makes the satellites deviate from pure free-fall orbits. Previous studies assumed that the orbit and attitude dynamics could be decoupled in numerical simulation, neglecting the back-action from the closed-loop control to orbit propagation. To address this, we develop a comprehensive model that can propagate the full 9-body (6 TMs + 3 satellites, orbits and attitudes) dynamics inter-dependently under the inter-satellite pointing and drag-free conditions. This paper is threefold. First, we reassess the applicability of the two TMs and telescope pointing scheme to TianQin using the new model, and confirm the previous conclusion. Second, to meet the constellation stability requirements, it is found that the DC common self-gravity in the flight direction should be minimized, or kept close for the three satellites. Finally, we simulate the long-range light path between two TMs/satellites with a precision of sub-pm/Hz$^{1/2}$, and the results support the decoupling of the closed-loop dynamics and high-precision orbit for computational efficiency. The method is instrumental to other future missions where the orbit-attitude coupling needs careful consideration.

Figures (11)

• Figure 1: Illustrative diagram of the long-range light path in split measurement. The satellite attitude at the current global time $t_0$ is determined by the light signal transmitted from the remote satellite at the previous time $t_0 - \tau$, where $\tau$ represents the light travel time between two distant TMs' nominal positions (i.e., the housing center). The propagation path of the light through space is depicted by the dark purple vector.
• Figure 2: Schematic description of the drag-free control designed to enable free-fall of the two TMs along the sensitive axes in each satellite. The red vectors indicate the electrostatic controls applied to the TMs, allowing the satellite to simultaneously follow both of them as the purple vector indicated.
• Figure 3: Demonstration diagram of the satellite architecture. The red vectors $\vec{g}_{TM_1}$ and $\vec{g}_{TM_2}$ are the differential accelerations of each TM relative to the satellite (including celestial gravity acceleration, inertial acceleration, and DC self-gravity acceleration).
• Figure 4: Sketch of the attitude determination with global (solid line) and local (dashed line) constellation plane. The black dots represent the real-time satellite position and the blank dots represent the last-time satellite position where they transmitted the light to the current local satellite.
• Figure 5: Comparison of different strategies for calculating satellite pointing. In the case of TianQin, the global constellation method will introduce a pointing error of $10^{-6}$ rad (upper plot), while the approximation method for pointing calculation shows accuracy errors on the order of $10^{-11}$ rad (lower plot).