  Mars' thin, CO$_2$-rich atmosphere poses a unique puzzle involving
composition, climate history, and habitability. This work explores the
intrincate relationship between Mars' atmospheric variations and dynamic solar
activity patterns. We focus on periodic oscillations in H$_2$O vapor and the
Pectinton solar flux index in the $\lambda$ = 10.7 cm radio band, around the
characteristic 11-year solar cycle. Periodic Mars activity was studied using
data from Mars Express' SPICAM instrument spanning 2004-2018. The Lomb-Scargle
Periodogram method was applied to analyze the power spectra of both signals
around this period, calibrated using peaks associated with the seasonal Martian
cycle. This method was validated by analyzing power spectra of chemical species
abundances in Earth's atmosphere, obtained from the NRLMSISE 00 empirical model
provided by the National Oceanic and Atmospheric Administration (NOAA). Model
executions reproduced chemical abundance data for various atmospheric species
(N$_2$, O$_2$, N, H$_2$, Ar, and He) at two reference heights (upper mesosphere
and low ionosphere) over a 1961-2021 time span. Results suggest a connection
between variability in H$_2$O vapor concentration in Mars' atmosphere and
fluctuations in the Pectinton solar flux index. We propose the Lomb-Scargle
Periodogram method as a heuristic for studying oscillatory activity in
planetary atmospheres with non-uniformly sampled data. While our results
provide valuable insights, further analysis, cross-referencing with data from
different orbiters, is required to deepen our understanding of these findings
in the fields of planetary climatology and atmospheric physics.
