Dependence of the detected signal on the kinematic parameters of the satellite in the S-LIGO-E2R space system

The changes of distances less than ~10–21 are registered during the gravitational wave experiment. This feature determines the minimum size of experimental installations and the frequency range of gravitational wave detectors. To expand the frequency range and increase the sensitivity of gravitational interference detectors, it is necessary to increase the linear dimensions of the detector significantly as big as Earth and even more. The Republic of Belarus has experience in the development, launch and operation of satellites, the use of which can significantly increase the linear dimensions of the gravitational space detector. The satellite systems as a space detector of gravitational waves S-LIGO-NxR-zy are considered. The S-LIGO-NxR-zy space gravitational wave detector is a system of laser interferometers consisting of x number of satellites with given z-type orbits, in orbit of planet N of the solar system. The interferometers in such systems are identical to interferometers with oscillating mirrors due to the complex satellite motion. The purpose of this work is to study the influence of the kinematic parameters of satellites on the detected signal in the S-LIGO-E2R-z2 system. The configuration of the space detector determines the set of satellite orbits, direction and initial phase of movement. The detector signals depend on the instantaneous distance between the satellites and can be described as periodic functions. There are obtained the equations that describe the periodic changes in the signal between satellites as a result of their relative motion, depending on the initial conditions for launching the satellites. The general case for arbitrary oriented orbits and two special cases for collinear and orthogonal circular orbits in space gravitational wave detectors S-LIGO-E2R-z2-p and S-LIGO-E2R-z2-o are considered in the paper. The graphs of the dependences of the detected signal on the kinematic parameters of the satellites of the detectors S-LIGO-E2R-z2-p and S-LIGO-E2R-z2-o are presented. It is shown that the detected signals contain sections of zero intensity, and the duration and frequency of sections of zero intensity are related to the kinematic parameters of satellites.

1. Abbot B.P., Abbot R., Abbot T.D. Observation of Gravitational Waves from a Binary Black Hole Merger Phys. Rev. Let. 2016;116 (iss. 6):061102. DOI: 10.1103/PhysRevLett.116.061102.

2. Weiss R. Electromagnetically coupled broadband gravitational antenna Quarterly Report of the Research Laboratory for Electronics. 1972;105:54-76.

3. Poincare H. Sur la dynamique de l'électron. Rend. Circ. Mat. Palermo. 1906;21(ser. 1):129-176.

4. Weber J. Gravitational-wave-detector events. Physical Review Letters. 1968;20(iss. 23):1307-1308.

5. Gertsenshtein M.E., Pustovoit V.I. On the detection of low frequency gravitational waves. JETP. 1962;43(2):605-607.

6. Aasi J., Abbot B.P. The LIGO Scientific Collaboration. Advanced LIGO. Class. Quantum Grav. 2015;32:074001. DOI: 10.1088/0264-9381/32/7/074001.

7. Somiya K. Detector configuration of KAGRA – the Japanese cryogenic gravitational-wave detector. Class. Quantum Grav. 2012;29:124007.

8. Unnikrishnan C.S. IndIGO and LIGO-India: scope and plans for gravitational wave research and precision metrology in India. Int J Mod Phys D. 2013;22:1341010.

9. Hild S., Abernathy M., Acernese F. Sensitivity studies for third-generation gravitational wave observatories. Class. Quantum Grav. 2011;28(9). DOI: 10.1088/0264-9381/28/9/094013.

10. Reitze D.R. Adhikari X., Ballmer S. Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO. Bulletin of the American Astronomical Society. 2019;51(iss. 7, id. 35).

11. Laser Interferometer Gravitational Wave Observatory. Instrument Science White Paper : LIGO-T1600119–v4: adopted 27.10.16. Cambridge: Technical Note: LIGO Scientific Collaboration, 2016: 116 p.

12. Kawamura S., Ando M., Nakamura T. The Japanese space gravitational wave antenna – DECIGO. J. Phys.: Conf. Ser. 2008;122. DOI: 10.1088/1742-6596/122/1/012006.

13. Yagi K., Seto N. Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries. Phys. Rev. D. 2011;83:20 p. DOI: 10.1103/PhysRevD.83.044011.

14. Danzmann K. Laser Interferometer Space Antenna: A proposal in response to the ESA call for L3 mission concepts. Hannover: Albert Einstein Institute; 2017.

15. Jenrich O., Binetruy P., Colpi M. NGO, Revealing a hidden Universe: opening a new chapter of discovery (New Gravitational wave Observatory): Assessment Study Report. Paris: European Space Agency; 2011; 153 p. № ESA/SRE (2011) 19.

16. Harry G.M., Fritschel P., Shaddock D.A., Folkner W., Phinney E.S. Laser interferometry for the Big Bang Observer. Class. Quantum Grav. 2006;23:4887-4894. DOI: 10.1088/0264-9381/23/15/008.