Photometric investigations on two totally eclipsing contact binaries: V342 UMa and V509 Cam

By analyzing two sets of complete $BVR_cI_c$ light curves of V342 UMa and three sets of complete $BVR_cI_c$ light curves of V509 Cam, we determined that the two systems are both W-subtype contact binaries and that V342 UMa shows a shallow contact configuration, while V509 Cam exhibits a medium contact configuration. Since both of them are totally eclipsing binaries, the physical parameters derived only by the photometric light curves are reliable.Meanwhile, the period changes of the two targets were analyzed based on all available eclipsing times. We discovered that V342 UMa shows long-term period decrease with a rate of $-1.02(\pm0.54)\times10^{-7}$ days/year and that V509 Cam exhibits long-term period increase with a rate of $3.96(\pm0.90)\times10^{-8}$ days/year. Both the conservative mass transfer and AML via magnetic stellar winds can interpret the long-term period decrease of V342 UMa. The long-term period increase of V509 Cam can be explained by mass transfer from the less massive star to the more massive one. The absolute parameters of the two binaries were estimated according to the Gaia distances and our derived photometric solution results. This method can be extended to other contact binaries without radial velocities but with reliable photometric solutions. The evolutionary states of them were discussed, we found that they reveal identical properties of other W-subtype contact systems.