Searches for planets via gravitational lensing have focused on cases in which the projected separation, a, between planet and star is comparable to the Einstein radius, RE . This paper considers smaller orbital separations and demonstrates that evidence of close-orbit planets can be found in the low-magnification portion of the light curves generated by the central star. We develop a protocol for discovering hot Jupiters as well as Neptune-mass and Earth-mass planets in the stellar habitable zone. When planets are not discovered, our method can be used to quantify the probability that the lens star does not have planets within specified ranges of the orbital separation and mass ratio. Nearby close-orbit planets discovered by lensing can be subject to follow-up observations to study the newly discovered planets or to discover other planets orbiting the same star. Careful study of the low-magnification portions of lensing light curves should produce, in addition to the discoveries of close-orbit planets, definite detections of wide-orbit planets through the discovery of "repeating" lensing events. We show that events exhibiting extremely high magnification can effectively be probed for planets in close, intermediate, and wide distance regimes simply by adding several-time-per-night monitoring in the low-magnification wings, possibly leading to gravitational lensing discoveries of multiple planets occupying a broad range of orbits, from close to wide, in a single planetary system.
