parameter, using the F-distributed model test statis- tic [equation 20 of R. A. Bennett, W. Rodi, R. E. Reilinger J. Geophys. Res. 101, 21943 (1996)]. This test allows us to assess the level of complexity in the deformation model required to explain the baseline time series. 18. See C. H. Scholz, The Mechanics of Earthquakes and Faulting (Cambridge Univ. Press, Cambridge, 1990), chaps. 4 and 5, and references therein. 19. J. L. Davis, T. A. Herring, I. I. Shapiro, A. E. E. Rog- ers, G. Elgered, Radio Sci. 20, 1593 (1985). 20. If the error sources serendipitously resulted in the observed  2 per degree of freedom of slightly less than unity (12), the “true”  2 per degree of freedom would be significantly less than unity. 21. The average rate across the entire Basin and Range is 15 to 20 nstr/year [for example, T. H. Dixon, S. Robaudo, J. Lee, M. C. Reheis, Tectonics 14, 755 (1995); R. A. Bennett, B. P. Wernicke, J. L. Davis, Geophys. Res. Lett. 25, 563 (1998)]. Rates of 200 nstr/year are typical along the San Andreas fault [for example, W. Thatcher, U.S. Geol. Surv. Prof. Pap. 1515 (1990)], p. 189. 22. R. E. Wallace, J. Geophys. Res. 89, 5763 (1984); R. S. Stein, S. E. Barrientos, ibid. 90, 11355 (1985); M. N. Machette, S. F. Personius, A. R. Nelson, Ann. Tectonic. 6 (suppl.), 5 (1992). 23. T. Parsons and G. A. Thompson, Science 253, 1399 (1991). 24. J. R. Evans and M. Smith III, in Major Results of Geophysical Investigations at Yucca Mountain and Vicinity, Southern Nevada, H. W. Oliver, D. A. Ponce, W. Clay Hunter, Eds. [Open-File Report, U.S. Geo- logical Survey, OF-0074 (1995)], pp. 135 –156. 25. P. T. Delaney and A. E. Gartner, Geol. Soc. Am. Bull. 109, 1177 (1997). 26. R. E. Wallace, Bull. Seismol. Soc. Am. 77, 868 (1987). 27. E. I. Smith, D. L Feuerbach, T. R. Nauman, J. E. Faulds, Proceedings of the International Topical Meeting, High-Level Radioactive Waste Management (American Nuclear Society/American Society of Civil Engineers, Las Vegas, 1990), vol. 1, pp. 81–90. 28. We thank J. Savage and M. Lisowski for providing trilateration data and GPS data and results from their 1993 survey, and J. Savage for useful discussions. The University NAVSTAR Consortium provided equipment and field logistical support. This project was funded by Nuclear Regulatory Commission contracts NRC-04-92-071 and NRC-02-93-005, and National Science Foundation grant EAR-94- 18784. 29 October 1997; accepted 3 March 1998 Test of General Relativity and Measurement of the Lense-Thirring Effect with Two Earth Satellites Ignazio Ciufolini, Erricos Pavlis, Federico Chieppa, Eduardo Fernandes-Vieira, Juan Pe ´ rez-Mercader The Lense-Thirring effect, a tiny perturbation of the orbit of a particle caused by the spin of the attracting body, was accurately measured with the use of the data of two laser- ranged satellites, LAGEOS and LAGEOS II, and the Earth gravitational model EGM-96. The parameter , which measures the strength of the Lense-Thirring effect, was found to be 1.1  0.2; general relativity predicts  1. This result represents an accurate test and measurement of one of the fundamental predictions of general relativity, that the spin of a body changes the geometry of the universe by generating space-time curvature. Einstein’s general theory of relativity (1, 2) predicts the occurrence of peculiar phe- nomena in the vicinity of a spinning body, caused by its rotation, that have not yet been measured (3). When a clock that co- rotates very slowly around a spinning body returns to its starting point, it finds itself advanced relative to a clock kept there at “rest” (with respect to “distant stars”). In- deed, synchronization of clocks all around a closed path near a spinning body is not possible, and light co-rotating around a spinning body would take less time to re- turn to a fixed point than light rotating in the opposite direction (2). Similarly, the orbital period of a particle co-rotating around a spinning body would be longer than the orbital period of a particle counter-rotating on the same orbit. Further- more, an orbiting particle around a spinning body will have its orbital plane “dragged” around the spinning body in the same sense as the rotation of the body, and small gyro- scopes that determine the axes of a local, freely falling, inertial frame, where “locally” the gravitational field is “unobservable,” will rotate with respect to “distant stars” because of the rotation of the body. This phenomenon— called “dragging of inertial frames” or, more simply, “frame dragging,” as Einstein named it—is also known as the Lense-Thirring effect (1, 2, 4). In Einstein’s general theory of relativity, all of these phe- nomena are the result of the rotation of the central mass. Rotation, inertia, and the “fictitious” in- ertial forces arising in a rotating system have been central issues and problems of mechanics since the time of Galileo and Newton (5). Mach thought that the cen- trifugal forces were the result of rotation with respect to the masses in the universe, and Einstein’s development of the general theory of relativity was influenced by Mach’s ideas on the origin of inertia and inertial forces. Today, the level at which general relativity satisfies Mach’s ideas on inertia is still debated and discussed. How- ever general relativity satisfies at least a kind of “weak manifestation” of Mach’s ideas: the dragging of inertial frames (2). Indeed, in Einstein’s gravitational theory, the concept of an inertial frame has only a local meaning, and a local inertial frame is “rotationally dragged” by mass-energy cur- rents because moving masses influence and change the orientation of the axes of a local inertial frame (that is, the gyroscopes); thus, a current of mass such as the spinning Earth “drags” and changes the orientation of the gyroscopes with respect to the distant stars. To understand these phenomena of gen- eral relativity associated with the rotation of a mass, one may use a formal analogy with the classical theory of electromagne- tism. Newton’s law of gravitation has a formal counterpart in Coulomb’s law of electrostatics; however, Newton’s theory has no phenomenon formally analogous to magnetism. On the other hand, Einstein’s theory of gravitation predicts that the force generated by a current of electrical charge, described by Ampere’s law, should also have a formal counterpart “force” generated by a current of mass. The detection and mea- surement of this “gravitomagnetic” force is the subject of this report. The gravitomagnetic force causes a gy- roscope to precess with respect to an asymp- totic inertial frame with angular velocity ˙ =- 1 /2H = [-J + 3(Jx ˆ )x ˆ ]/x 3 , where H is the gravitomagnetic field, J is the angular momentum of the central object, and x is the gyroscope’s position vector. This formula quantifies the Lense-Thirring effect for a gyroscope (1, 2). The gravito- magnetic force also causes small changes in the orbit of a test particle (4). In particular, there is a secular rate of change of the longitude of the nodes (intersection be- tween the orbital plane of the test particle and the equatorial plane of the central object) given by ˙  Lense-Thirring = 2J/ [a 3 (1 - e 2 ) 3/2 ], where a is the semimajor axis of the test particle’s orbit and e is its orbital eccentricity. In addition, there is a secular rate of change of the longitude of the pericenter (2),  ˜ (determined by the Runge-Lenz vector):  ˜ Lense-Thirring = 2J[ J ˆ - ˙ I. Ciufolini, Istituto Fisica Spazio Interplanetario –Consiglio Nazionale delle Ricerche, and Dipartimento Aerospa- ziale, Universita ´ di Roma “La Sapienza,” via Eudossiana 16, 00184 Rome, Italy. E. Pavlis, Joint Center for Earth System Technology, Uni- versity of Maryland–Baltimore County, Baltimore, MD 21250, USA. F. Chieppa, Scuola Ingegneria Aerospaziale, Universita ´ di Roma “La Sapienza,” Rome, Italy. E. Fernandes-Vieira and J. Pe ´ rez-Mercader, Laboratorio de Astrofisica Espacial y Fisica Fundamental (INTA- CSIC), Madrid, Spain. SCIENCE  VOL. 279  27 MARCH 1998  www.sciencemag.org 2100