A detection of the Lense-Thirring effect, or the "dragging of inertial frames", would provide a fifth test of general relativity. Here, we present a study of the Lense-Thirring general relativistic time delay on electromagnetic signals in the Sun's gravitational field and in a binary system of pulsars. These tests would involve an investigation of the Lense-Thirring effect on local light cones or the propagation of photons, and would be distinct from the Gravity Probe-B experiment that is investigating the Lense-Thirring effect on the motion of massive bodies.; We use an approximation method to derive an analytical expression for the delay of light due to the Lense-Thirring effect in the solar system and to investigate the possibility of its detection using orbiting spacecraft in heliocentric cruise. The corrupting effect of the solar corona is considered and a method for removing it is suggested. Finally, we evaluate the delay of light caused by the Lense-Thirring effect in binary systems of pulsars similar to PSR J0737-3039 and discuss the use of pulse time of arrival measurements to detect the general relativistic effect in such systems. We conclude that, though attempts at detection of the Lense-Thirring effect on photon propagation using these methods would be challenging, it is not beyond present-day technological means.
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