On the minimum flexing of LISA's arms

Abstract

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 60°. We further show that it is the minimum within the assumption of equivalent spacecraft orbits, where the orbit of each spacecraft is rotated by 120° from the preceding one.

Optimizing the Earth–LISA ‘rendezvous’

“…Finally, we choose x 0 = +h/2 to be consistent with the notations of [9,6] and the zeroth-order orbits turn out to be…”

“…the inclination of the triangle with respect to the ecliptic. Introducing a parameter δ 1 [6] such that,…”

“…It can be shown [6] that, due to the small eccentricity and inclination of the orbits, the solution given by the above zeroth-and first-order terms differs from the exact Keplerian solution by less than 0.03% making the method of analytical series expansion a useful basis for an analytical model of the motions of LISA/NGO. Choosing δ 1 = 5/8, the first-order (Keplerian) flexing is minimized in both ET and IRT configurations, giving, with arm lengths of order 1 Gm, an extra angle of respectively 7 and 4 .…”

“…ET and IRT (both with = 1 Gm) are the two configurations presently considered by the NGO Science Team for the mission reformulation: we conform to this choice. 6 The 'New LISA' or 'NGO' mission is presently (December 2011) considered for a two years lifetime. This is, however, a recent result that has emerged during the refereeing process.…”

Coorbital Restricted Problem and Its Application in the Design of the Orbits of the Lisa Spacecraft

“…The inclined ellipse is the osculating orbit of the spacecraft SC1 at the initial epoch. Assuming φ is the inclination between the constellation plane, on which the spacecraft move, and the ecliptic plane, the important relationship 16 between the eccentricity e of the spacecraft orbit, the inclination I to the ecliptic plane, the arm-length l of the constellation, and the angle φ is shown as Fig. 4.…”