Optimizing the Earth–LISA ‘rendezvous’

The increasing precision of spacecraft radiometric tracking data experienced in the last number of years, coupled with the huge amount of data collected and the long baselines of the available datasets, has made the direct observation of Solar System dynamics possible, and in particular relativistic effects, through the measurement of some key parameters as the post-Newtonian parameters, the Nordtvedt parameter η and the graviton mass. In this work we investigate the potentialities of the datasets provided by the most promising past, present and future interplanetary missions to draw a realistic picture of the knowledge that can be reached in the next 10-15 years. To this aim, we update the semi-analytical model originally developed for the BepiColombo mission, to take into account planet-planet relativistic interactions and eccentricity-induced effects and validate it against well-established numerical models to assess the precision of the retrieval of the parameters of interest. Before the analysis of the results we give a review of some of the hypotheses and constrained analysis schemes that have been proposed until now to overcome geometrical weaknessess and model degeneracies, proving that these strategies introduce model inconsistencies. Finally we apply our semi-analytical model to perform a covariance analysis on three samples of interplanetary missions: 1) those for which data are available now (e.g. Cassini, MESSENGER, MRO, Juno), 2) in the next years (BepiColombo) and 3) still to be launched as JUICE and VERITAS (this latter is waiting for the approval).

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“…All terms into Eqs. (12), (13), (16), (20) and (28) can be written using Eq. (6) and the following formulas (where n = 0)…”

Section: Appendix A: First Order Corrections For Eccentricitymentioning

confidence: 99%

Testing general relativity in the solar system: present and future perspectives

Marchi

Cascioli

2020

Class. Quantum Grav.

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“…It has been shown that by adjusting the angle φ around ±π/3 at e 1 order, the variations of all the kinematic indicators of Taiji triangle are minimized, respectively, which is compatible to that of LISA in Refs. [7,14]. Further, all the optimized expressions of these kinematic indicators of Taiji triangle are presented in this paper.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The orbits of SC2 and SC3 are obtained, respectively, by rotating that of SC1 by 2π/3, 4π/3 about the z axis, where their phases also need to be adjusted correspondingly [6,7], i.e. r 2 , r 3 satisfy 6) and the eccentric anomalies ψ 2 , ψ 3 of SC2, SC3 satisfy [7], respectively, 14) and with it, Eq.…”

Section: A the Unperturbed Keplerian Orbits Of Scsmentioning

confidence: 99%

Analytical analysis on the orbits of Taiji spacecrafts

Huang

Qiao

2019

Phys. Rev. D

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The unperturbed Keplerian orbits of Taiji spacecrafts are expanded to e 3 order in the heliocentric coordinate system, where e is their orbital eccentricity. The three arm-lengths of Taiji triangle and their rates of change are also expanded to e 3 order, while the three vertex angles are expanded to e 2 order. These kinematic indicators of Taiji triangle are, further, minimized, respectively, by adjusting the tilt angle of Taiji plane relative to the ecliptic plane around ±π/3, and thus, their corresponding optimized expressions are presented. Then, under the case that the nominal trailing angle of Taiji constellation following the Earth is set to be χ(≈ ±π/9) from the viewpoint of the Sun, the influence of the Earth perturbation on three spacecrafts is calculated according to the equations of motion in the problem of three bodies, and the perturbative solutions of the leading order and the next leading order are derived. With the perturbative solutions, the leading-order corrections to the above kinematic indicators of Taiji triangle and the expression of the above trailing angle to the order of e 3 are provided.

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“…SEP has the advantage of a more efficient use of propellant mass and thus a higher dry mass fraction compared to chemical propulsion. Previous trajectory analyses for LISA [6][7][8][9][10][11][12] have mainly focussed on the optimal cartwheel orbit design and less on the transfer. Moreover, the interdependency between the transfer and the optimal cartwheel orbit has not been treated before.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Design for the ESA LISA Mission

Martens

Joffre

2021

J Astronaut Sci

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The three Laser Interferometer Space Antenna (LISA) spacecraft are going to be placed in a triangular formation in an Earth-trailing or Earth-leading orbit. They will be launched together on a single rocket and transferred to that science orbit using Solar Electric Propulsion. Since the transfer Δv depends on the chosen science orbit, both transfer and science orbit have been optimised together. For a thrust level of 90 mN, an allocation of 1092 m/s per spacecraft is sufficient for an all-year launch in 2034. For every launch month a dedicated science orbit is designed with a corner angle variation of 60° ± 1.0° and an arm length rate of maximum 10 m/s. Moreover, a detailed navigation analysis of the science orbit insertion and the impact on insertion errors on the constellation stability has been conducted. The analysis shows that Range/Doppler measurements together with a series of correction manoeuvres at the beginning of the science orbit phase can reduce insertion dispersions to a level where corner angle variations remain at about 60° ± 1.1° at 99% C.L. However, the situation can become significantly worse if the self-gravity accelerations acting during the science orbit phase are not sufficiently characterised prior to science orbit insertion.

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Optimizing the Earth–LISA ‘rendezvous’

Cited by 12 publications

References 13 publications

Testing general relativity in the solar system: present and future perspectives

Testing general relativity in the solar system: present and future perspectives

Analytical analysis on the orbits of Taiji spacecrafts

Trajectory Design for the ESA LISA Mission

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