On the minimum flexing of LISA's arms

The joint ESA-NASA mission LISA relies crucially on the stability of that three spacecraft constellation. All three spacecraft are on heliocentric and weakly eccentric orbits forming a nearly stable triangle. It has been shown that for certain spacecraft orbits, the arms keep constant distances to the first order in eccenticities. However, exact orbitography exhibits the so-called 'breathing modes' resulting in slow variations of the armlengths on the timescale of one year. In this paper, we analyse the breathing modes (flexing of the arms) with the help of the geodesic deviation equation up to the octupole order, which is shown to be equivalent to higher order Clohessy-Wiltshire equations. We analytically show that the flexing of the arms can be reduced to a peak-to-peak variation of about 50 000 km, and the corresponding peak-to-peak variation in the Doppler laser frequency shift to about 8 m s-1. This is achieved by slightly changing the well-known tilt of 600. We further show that it is the minimum within the assumption of equivalent spacecraft orbits, where the orbit of each spacecraft is rotated by 1200 from the preceding one