# Light deflection and time delay in the solar gravitational field

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The second nonvanishing order of contribution to light deflection and time delay in the solar gravitational field is studied for a realistic solar model and for a wide range of metric theories of gravity. It is shown that the second-order effects arise at order (GM/c²R)² = ε⁴. To calculate these effects, every component of the solar metric must be known to order ε⁴. The parametrized post Newtonian (PPN) metric provides most of those components. However, some extension of the PPN metric is required. This extension leads to the parametrized post-linear (PPL) metric, which is used in all calculations. To study light deflection to order ε⁴ requires that the orbits of scattered photons be known to that order. These orbits are solved for, first in the equatorial plane and then in general, and are used to determine the deflection as measured by an observer at rest with respect to the sun. In the equatorial plane there is only a radial component to this deflection. In general, there is another component orthogonal to the radial plane, but knowledge of this component is not necessary to determine the total deflection to order ε⁴. The total second-order deflection can be as large as 300 μ arcsec (for deflection by Jupiter). Measurements of some second-order terms are within the astrometric capabilities of experiments proposed for the 1990's. The time delay in the round-trip travel time of a radar beam reflected from a planet is due to the variable coordinate speed of the light signal and to the bending of the beam path. The delay is calculated to order ε⁴ . It is shown that the beam-bending gives a second-order contribution as large as the present-day uncertainties in time delay experiments with the Viking spacecraft. Polarization changes in light waves propagating through the solar gravitational field are also studied to order ε⁴