As in electromagnetism, the characteristic impedance of free space plays a central role in all radiation problems, such as in a comparison of the radiation resistance of gravity-wave antennas to the value of this impedance in order to estimate the coupling efficiency of these antennas to free space.
The numerical value of this impedance is extremely small, but the impedance of all material objects must be “impedance matched” to this extremely small quantity before significant power can be transferred efficiently from gravitational waves to these detectors.
The gravitational characteristic impedance of free space may be connected with other constants:
In the 80-ties Maxwell-like equations were considered in the Wald book of general relativity.  In the 90-ties Kraus  first introduced the gravitational characteristic impedance of free space, which was detailed later by Kiefer , and now by Raymond Y. Chiao, 
who is developing the ways of experimental determination of the gravitational waves.
Typical gravitational impedance at the megascopic scale
In the general case only planets (with their sattelites) and stars could be considered "as free, as possible" to be used as some "antenna" to the gravitational waves detection. Spherical megascopic bodies have the folloving characteristic impedance:
↑ O. Heaviside, Electromagnetic Theory (”The Electrician” Printing and Publishing Co., London, 1894) pp. 455-465.
W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955), p. 168, 166.
↑R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
↑J. D. Kraus, IEEE Antennas and Propagation. Magazine 33, 21 (1991).
↑C. Kiefer and C. Weber, Annalen der Physik (Leipzig) 14, 253 (2005).
↑ Raymond Y. Chiao. "Conceptual tensions between quantum mechanics and general relativity: Are there experimental consequences, e.g., superconducting transducers between electromagnetic and gravitational radiation?" arXiv:gr-qc/0208024v3 (2002). [PDF
↑R.Y. Chiao and W.J. Fitelson. Time and matter in the interaction between gravity and quantum fluids: are there macroscopic quantum transducers between gravitational and electromagnetic waves? In Proceedings of the “Time & Matter Conference” (2002 August 11-17; Venice, Italy), ed. I. Bigi and M. Faessler (Singapore: World Scientific, 2006), p. 85. arXiv: gr-qc/0303089. PDF
↑R.Y. Chiao. Conceptual tensions between quantum mechanics and general relativity: are there experimental consequences? In Science and Ultimate Reality, ed. J.D. Barrow, P.C.W. Davies, and C.L.Harper, Jr. (Cambridge:Cambridge University Press, 2004), p. 254. arXiv:gr-qc/0303100.
↑Raymond Y. Chiao. "New directions for gravitational wave physics via “Millikan oil drops” arXiv:gr-qc/0610146v16 (2009). PDF
↑Stephen Minter, Kirk Wegter-McNelly, and Raymond Chiao. Do Mirrors for Gravitational Waves Exist? arXiv:gr-qc/0903.0661v10 (2009). PDF
↑ 12.012.112.2Allen C.W.(1973). Astrophysical quantities. 3-d edition. University of London, The Athlone Press.