Orbit design for the Laser Interferometer Space Antenna (LISA)

Abstract

The Laser Interferometer Space Antenna (LISA) is a joint ESA-NASA mission for detecting low-frequency gravitational waves in the frequency range from 0.1 mHz to 1 Hz, by using accurate laser interferometry between three spacecrafts, which will be launched around 2018 and one year later reach their operational orbits around the Sun. In order to operate successfully, it is crucial for the constellation of the three spacecrafts to have extremely high stability. Based on the study of operational orbits for a 2015 launch, we design the operational orbits of beginning epoch on 2019-03-01, and introduce the method of orbit design and optimization. We design the orbits of the transfer from Earth to the operational orbits, including launch phase and separation phase; furthermore, the relationship between energy requirement and flight time of these two orbit phases is investigated. Finally, an example of the whole orbit design is presented. co-orbital restricted problem, orbit design, orbit optimization, launch energyThe Laser Interferometer Space Antenna (LISA) is a joint ESA-NASA mission for detecting low-frequency gravitational waves in the frequency range from 0.1 mHz to 1 Hz. Three spacecrafts will be launched around 2018, and reach their operational orbits around the Sun after 14 months. Observation will last 5 to 10 years.As shown in Figure 1, the three spacecrafts form an equilateral triangle with an arm-length (side length) of around 5×10 6 km. The center of the constellation moves on an Earth-like orbit around the sun, trailing 20° behind the Earth. The angle between the direction from the constellation center to the Sun and the constellation plane is about 60°. Distance variations between the spacecraft will be measured by laser interferometry to detect gravitational waves. In order to avoid additional complications in the challenging interferometry, in order for LISA to operate successfully, it is crucial that the constellation of the three spacecrafts has extremely high stability. More stable constellation makes simplifications in the hardware realizationDue to the combined effect of the eccentricity of the spacecraft orbit and the gravity of the other bodies in the solar system including the Earth, all of the arm length, l, the internal angles of the constellation, β and the trailing angle behind the Earth, θ vary continuously, causing relative velocities between the spacecraft, v r , as an indicator of the Figure 1 LISA constellation moving around the Sun.

Optimizing orbits for TianQin

“…In regard to orbit stability and optimization for other space GW detection missions, the well-known heliocentric LISA design [5][6][7] has been extensively studied with analytic and numerical methods [8][9][10][11][12][13][14][15][16][17]. Particularly, the cost-function method based on carefully chosen performance measures has proved effective in numerical optimization [12][13][14][15][16].…”

Optimizing the Earth–LISA ‘rendezvous’

“…The required amount of this variation can be determined by minimizing the cost function σ 2 ( 1 , 2 , 3 , δ 1 ) defined in (12). However, the analytic expression for σ 2 is sufficiently cumbersome to impose a numerical minimization: this, on the other hand, allows us to use the exact equations of motion…”

“…In this section, we describe the fully numeric evaluation and minimization of the cost function (12) by solving the exact equations of motion and taking into account the perturbing effect of the Sun, Venus, Earth, Moon, Mars and Jupiter. Their real trajectories R (t ), R ⊕ (t ), R (t ), R (t ), R (t ), R (t ) in the solar system barycenter (SSB), are provided by the JPL HORIZON ephemerides [15], with the following characteristics:…”

Optimizing the Earth-LISA "rendez-vous"

“…However, other strategies can be devised that provide better performance of the constellation. An appreciable reduction of the flexing due to the Earth tidal field is in any case possible, over a limited time span, by suitable tuning of all orbital parameters [8,9,10]. In our analytical approach, in order to keep things simple, we still use three identical orbits (apart for relative phase shifts, see (3)) for the 3 S/Cs of the constellation and, Table 1: Change of the relevant orbit indicators (arm length, breathing, Doppler modulation) for the three S/C's, for both IRT and ET configurations, in the standard δ 1 = 0 and modified δ 1 = 5/8 inclination.…”