in the two fields of view.

Because the parallactic displacement (parallax factor) of a given source is proportional to sin θ, where θ is the angle between the star and the Sun, the parallax factors of stars inside a given field of view are nearly identical, suggesting only relative parallaxes could be measured.

However, although scanning space astrometry makes purely differential measurements, absolute parallaxes can be obtained because the relative parallactic displacements can be measured between stars that are separated on the sky by a large angle (the basic angle) and, hence, have a substantially different parallax factor.

To illustrate this further, consider an observer at one astronomical unit from the Sun.

The apparent shift of a star owing to its parallax ϖ then equals ϖ sin θ and is directed along the great circle from the star towards the Sun.

As shown in Fig. 2 (left panel), the measurable, along-scan parallax shift of a star at position F (for following field of view) equals ϖF sin θ sin ψ = ϖF sin ξ sin Γ, where ξ is the angle between the Sun and the spin axis (the solar-aspect angle).

At the same time, the measurable, along-scan parallax shift of a star at position P (for preceding field of view) equals zero.

The along-scan measurement of F relative to P therefore depends on ϖF but not on ϖP, while the reverse is true at a different time (right panel).

So, scanning space astrometry delivers absolute parallaxes.

The sensitivity of Gaia to parallax, which means the measurable, along-scan effect, is proportional to sin ξ sin Γ.

This has the following implications:
Finally, the selected spin rate of Gaia, nominally 60′′ s−1 (actual, in-flight value: 59′′.9605 s−1), is a complex compromise involving arguments on mission duration and these arguments: revisit frequency, attitude-induced point spread function blurring during detector integration, signal-to-noise ratio considerations, focal plane layout and detector characteristics, and telemetry rate.
3.2.

Service module The mechanical service module comprises all mechanical, structural, and thermal elements supporting the instrument and the spacecraft electronics.

The service module physically accommodates several electronic boxes including the video processing units (Sect. 3.3.8), payload data-handling unit (Sect. 3.3.9), and clock distribution unit (Sect. 3.3.10), which functionally belong to the payload module but are housed elsewhere in view of the maintenance of the thermal stability of the payload.

The service module also includes the chemical and micro-propulsion systems, deployable-sunshield assembly, payload thermal tent, solar-array panels, and electrical harness.

The electrical services also support functions to the payload and spacecraft for attitude
– Ideally, Γ equals 90◦.

However, when scanning more or less along a great circle (as during a day or so), the accuracy with which the one-dimensional positions of stars along the great circle can be derived, as carried out in the one-day iterative solution (ODAS) as part of continuous payload health monitoring (Sect. 6.3), is poor when Γ = 360◦× m/n for small integer values of m and n (Lindegren & Bastian 2011); this can be understood in terms of the connectivity of stars Article number, page 6 of 36 subsystem (AOCS)