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Fundamental Physics with the LAGEOS Satellites

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Gravity: Where Do We Stand?

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Abstract

The space(time) around Earth is a good environment in order to perform tests of gravitational theories. According to Einstein’s view of gravitational phenomena, it is curved, mainly by the Earth mass–energy content. This (relatively) quiet dynamical environment enables a good reconstruction of a satellite (test mass) orbit, provided high-quality tracking data are available. This is the case of the LAGEOS satellites, built and launched mainly for geodetic and geodynamical purposes, but equally good for fundamental physics studies.

In this chapter a review will be presented of these studies, focusing on data, models and analysis strategies. Several recent and less recent results will be presented. General relativity once more appears as a very precise and effective theory for the gravitational phenomena.

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Notes

  1. 1.

    For a review of this very general issue see the chapter Gravity: Newtonian, post-Newtonian and General Relativistic by Clifford Will in this book and [5].

  2. 2.

    The weak-field condition considers the space-time curvature so small that the metric can be written as \(g_{\mu \nu } = \eta_{\mu \nu } + h_{\mu \nu }\) (Minkowski metric plus a “small” perturbation, \(|h_{\mu \nu }| \ll 1\)). The slow-motion condition requires \(v \ll c\). Given the relative smallness of the masses at play, as well as that of their speed when compared with that of light, this approximation of the theory is sufficient for the purpose.

  3. 3.

    This effect appears due to the chosen geocentric non-inertial reference system.

  4. 4.

    In first-order perturbation theory, two kinds of behavior for a given element can arise. The first is a term \(\propto \sin t\) or \(\cos t\); this is called periodic. The second is a term \(\propto t\) (or higher powers); this is called secular , since it tends to accumulate over time.

  5. 5.

    In any case, the secular (systematic) character of the relativistic signal causes it to appear above the noise upon integration in a sufficiently longer time.

  6. 6.

    LAGEOS has an almost circular orbit, with an eccentricity \(e_{I} \simeq 0.004\), a semimajor axis \(a_{I} \simeq 12270\) km, and an inclination over the Earth’s equator \(i_{I} \simeq 109.8^{\circ }\). The LAGEOS II corresponding elements are: \(e_{II} \simeq 0.014\), \(a_{II} \simeq 12162\) km and \(i_{II} \simeq 52.66^{\circ }\).

  7. 7.

    For the LAGEOSs the bin size amounts to 120 s.

  8. 8.

    In order to obtain a good reference orbit for the considered period, it has been performed a preliminary data reduction of laser range data with a modeling setup slightly different from the nominal one of Table 3. In particular, the radiation coefficient \(C_\textrm{R}\) has been estimated, together with corrections to polar motion and length of day. Moreover, empirical acceleration components in the three Gauss directions have been added. The combined estimate led to the reported 1–2 cm level in range. Of course, this slight overestimation comes at the price of some aliasing: Therefore, the results of the analysis could not be directly used for the relativity signal recovery.

  9. 9.

    IERS is the international organization in charge of maintaining the reference frames used in astronomy, geodesy, and geophysics.

  10. 10.

    We use here the normalized coefficients \(\bar {C}_{l0}\) instead of the non-normalized \(C_{l0}\) or the \(J_l\). We remember that \(J_2 = -C_{20} = -\sqrt {5}\bar {C}_{20}\).

  11. 11.

    We consider only the quadrupolar part of this classical precession.

  12. 12.

    In [24] it is shown that the residuals obtained with their method are in fact rates.

  13. 13.

    In writing this equation, we neglect higher-degree multipoles and other sources of perturbation for the node. We can safely do that since we assume them sufficiently well-modeled in the orbit determination setup, in such a way that the neglected effects are small. How well this assumption holds is determined by the measurement error budget.

  14. 14.

    In fact, in the post-Newtonian framework \(\mu \,=\,(1\,+\,\gamma )/2\), with \(\gamma \) the PPN parameter quantifying how much space curvature is produced by unit rest mass; see [5].

  15. 15.

    In fact, this equals to admit no a priori knowledge on the amplitude of Lense–Thirring effect.

  16. 16.

    The reported value has been obtained fitting the combined residuals with a secular trend plus ten periodic terms.

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Acknowledgements

The author would like to thank David M. Lucchesi (Istituto di Astrofisica e Planetologia Spaziali, IAPS-INAF). He acknowledges the ILRS for providing high-quality laser ranging data of the two LAGEOS satellites.

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    Roberto Peron

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  1. Istituto di Astrofisica e Planetologia Spaziali, Istituto Nazionale di Astrofisica, Roma, Italy

    Roberto Peron

  2. Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano-Bicocca, Milano, Italy

    Monica Colpi

  3. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, Como, Italy

    Vittorio Gorini

  4. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, Como, Italy

    Ugo Moschella

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Peron, R. (2016). Fundamental Physics with the LAGEOS Satellites. In: Peron, R., Colpi, M., Gorini, V., Moschella, U. (eds) Gravity: Where Do We Stand?. Springer, Cham. https://doi.org/10.1007/978-3-319-20224-2_4

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