The LISA Pathfinder (LPF) mission objective is to verify that a test mass onboard the spacecraft can be kept 'free-floating', subject to unwanted accelerations of less than 3×10^-14 m s^-2. Practically, free-floating means that the test mass inside the spacecraft must not be subject to forces originating from mechanical contact and must only be subject to electrical, magnetic, thermal and internal gravitational forces leading to accelerations of less than 3×10^-14 m s^-2.

The dominant external force in the LPF orbital environment is a solar pressure (the force due to photons exchanging momentum with the spacecraft solar array) of roughly 19 micronewton. Such a force applied to a spacecraft with a mass of 500 kg would lead to an acceleration of 19×10^-6 / 500 = 3×10^-8 m s^-2 - well above the required 3×10^-14 m s^-2. Therefore, the spacecraft, while following the test mass, must shield it from the solar pressure. This is the first objective of the drag-free attitude control system: to counteract the disturbing forces and torques applied on the spacecraft, to maintain the free-floating conditions for the test mass.

The forces and torques acting on the spacecraft are not directly measurable, but their consequences can be measured. The position and rotation of the test mass with respect to its housing is measured by the inertial sensor electronics. The control laws running on the spacecraft on-board computer periodically use these measurements to compute the necessary forces and torques to apply to the spacecraft to maintain a steady position and orientation of the test mass within its housing. These forces and torques are periodically applied by the Field Emission Electric Propulsion (FEEP) thrusters that move the spacecraft around the test mass. The dynamics of the system and the conceptual representation of the control system are illustrated by the figures below.

Figure 1. Forces and torques acting on the spacecraft and test mass

Figure 2. Conceptual view of the drag-free control loop

The control law computes force and torque commands that null the test mass motion relative to the spacecraft by compensating for the environmental forces. The test mass relative motion would be due to the difference of forces applied on the test mass and forces applied on the spacecraft. Therefore, the control action corresponds to the force applied on the test mass minus the force applied on the spacecraft and consequently the spacecraft follows the test mass with the same acceleration.

In order to measure the test mass absolute acceleration, an external measurement of the spacecraft absolute position, e.g. by ground radio-tracking, with unachievable accuracy would be needed. The assessment of the acceleration of the test mass is therefore performed by means of a second test mass. The distance between the two tests masses is measured by an optical heterodyne interferometer and used to derive the differential acceleration.

Ideally the second test mass should also be free-floating but this is impossible. The spacecraft cannot follow simultaneously both test masses, consequently the second test mass is maintained centred in its housing using forces and torques applied by an electrostatic suspension system. The differential forces or accelerations between the tests masses are then derived by correcting the interferometer measurements taking into account this suspension control law.

Another important contribution to the disturbances of the free fall conditions is the parasitic coupling of the test masses to their housing. This coupling is called stiffness (by extension from the mechanical stiffness that a spring opposes to a force applied). As there is no mechanical contact between the masses and the housing, there is no mechanical stiffness, but the electrostatic, magnetic and gravitational stiffness have to be minimised in order not to disturb the measurements or the stability of the control laws. This is achieved by design, for example, by having large gaps between the test masses and the electrostatic suspension, by fine positioning (during final assembly) of the gravitational compensation masses, and by on-flight calibration of the 'zero' position of the test masses inside their housing.

Drag-Free Propulsion System