Gravitational attraction of the moon might cause synodic month periodic variation in the ionosphere, but it has not been observed so far. On June 29, 2004, France launched an ionospheric satellite DEMETER (Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions), that was placed on a quasi Sun synchroneous circular orbit. In this paper, the data observed by the Langmuir probe of the DEMETER satellite are split into two groups： the data on the dayside and the data on the nightside. The two groups of data are re-sampled, with the missing data being padded, and the signals on the dayside and the signals on the nightside are generated. For the two groups of signals, the solar day periodic variations are filtered out, SNRs of a series of periods are calculated, and SNR-period curves are obtained. The synodic month periodic variations of electron density, ion density and electron temperature on the dayside are shown clearly, but those on the nightside are not observed. Why? The gravitational attraction of the moon can cause the lunar atmospheric tide. During day time, the photoionization causes vertical variations of electron density, ion density and electron temperature, and lunar atmospheric tide can be observed by DEMETER satellite that was placed at the same altitude. At night, the photoionization stops and does not cause vertical variations of electron density, ion density and electron temperature, and the lunar atmospheric tide can not be observed by DEMETER satellite.