Class. Quantum Grav. 16 (1999) 1487–1502. Printed in the UK PII: S0264-9381(99)98791-9 Doppler measurement of the solar gravitational deflection Luciano Iess†, Giacomo Giampieri‡, John D Anderson§ and Bruno Bertottik † Dipartimento Aerospaziale, Universit` a di Roma ‘La Sapienza’, 00184 Rome, Italy ‡ Astronomy Unit, Queen Mary and Westfield College, London E1 4NS, UK § Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA k Dipartimento di Fisica Nucleare e Teorica, Universit` a di Pavia, 27100 Pavia, Italy Received 28 October 1998 Abstract. Testing alternative metric theories of gravity with an accuracy much better than the present level has recently drawn great attention, in particular in relation to the search for a very weak scalar field, a possible remnant of an early inflationary cosmology. The gravitational deflection of electromagnetic waves is controlled by the dimensionless post-Newtonian parameter γ , which takes a value of unity in general relativity. In this work we claim that the accuracy in the measurement of γ can be substantially improved by measuring the Doppler frequency shift of a microwave beam transponded back to the ground by an interplanetary spacecraft near solar conjunction. In this kind of experiment, the dispersion due to the plasma in the solar corona is the crucial difficulty, which, however, can be essentially overcome using skilful combinations of carriers with different frequencies. The spacecraft Cassini, launched in 1997, adopts a sophisticated radio system, including a Ka-band link at 32–34 GHz, which makes this possible. We discuss the noise budget for two experiments to be carried out with Cassini in 2002 and 2003. In particular, we consider the contribution of the solar corona, the non-gravitational accelerations, and thermal noise due to solar radio emission. We estimate that an accuracy in γ of about 10 -5 is achievable. PACS numbers: 0480C, 0450, 9555S, 9660P, 8440V 1. Introduction Metric theories of gravity, including general relativity, predict that photons passing near the Sun are deflected by an angle θ gr (b) = 2(1+ γ )GM  bc 2 ’ 8 × 10 -6  1+ γ 2  R  b  , (1) where b is the impact parameter of the ray, GM  /c 2 = 1.48 km is the gravitational radius of the Sun and R  is its radius. The bending effect is thus controlled by the parameter γ , whose value is unity in general relativity. Its present empirical value is [1] γ = 1.000 ± 0.001, (2) where the quoted uncertainty is a rough estimate of the results of different measurements. The parametrization of the gravitational deflection with the dimensionless parameter γ belongs to the ‘parametrized post-Newtonian’ (PPN) formalism, with which a wide class of metric theories of gravitation and their experimental consequences are described in a multi- dimensional parameter space. In the simplest case this space has two dimensions, γ and β , with general relativity at (1, 1). Different experiments are governed by different combinations of these two parameters: for example, for the secular advance of the periastron we have 0264-9381/99/051487+16$19.50 © 1999 IOP Publishing Ltd 1487