# LISA Pathfinder Platform Stability and Drag-free Performance

## TL;DR

This paper evaluates the stability and drag-free performance of the LISA Pathfinder spacecraft across all degrees of freedom, using a comprehensive model that aligns well with flight data to identify noise sources and physical phenomena affecting stability.

## Contribution

It provides a detailed, quantitative analysis of spacecraft stability in all degrees of freedom, extending beyond the optical axis focus, with a validated model matching flight data.

## Key findings

- Spacecraft stability near 1 mHz is about 5.0×10⁻¹⁵ m/s²/√Hz for X-axis.
- Y and Z axes stability are approximately 4.0×10⁻¹⁴ m/s²/√Hz.
- Angular stability is around 3×10⁻¹² rad/s²/√Hz for pitch and 3×10⁻¹³ rad/s²/√Hz for yaw and roll.

## Abstract

The science operations of the LISA Pathfinder mission has demonstrated the feasibility of sub-femto-g free-fall of macroscopic test masses necessary to build a LISA-like gravitational wave observatory in space. While the main focus of interest, i.e. the optical axis or the $x$-axis, has been extensively studied, it is also of interest to evaluate the stability of the spacecraft with respect to all the other degrees of freedom. The current paper is dedicated to such a study, with a focus set on an exhaustive and quantitative evaluation of the imperfections and dynamical effects that impact the stability with respect to its local geodesic. A model of the complete closed-loop system provides a comprehensive understanding of each part of the in-loop coordinates spectra. As will be presented, this model gives very good agreements with LISA Pathfinder flight data. It allows one to identify the physical noise source at the origin and the physical phenomena underlying the couplings. From this, the performances of the stability of the spacecraft, with respect to its geodesic, are extracted as a function of frequency. Close to $1 mHz$, the stability of the spacecraft on the $X_{SC}$, $Y_{SC}$ and $Z_{SC}$ degrees of freedom is shown to be of the order of $5.0\ 10^{-15} m\ s^{-2}/\sqrt{Hz}$ for X and $4.0 \ 10^{-14} m\ s^{-2}/\sqrt{Hz}$ for Y and Z. For the angular degrees of freedom, the values are of the order $3\ 10^{-12} rad\ s^{-2}/\sqrt{Hz}$ for $\Theta_{SC}$ and $3\ 10^{-13} rad\ s^{-2}/\sqrt{Hz}$ for $H_{SC}$ and $\Phi_{SC}$.