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Some Cataclysmic Variables (CVs) exhibits a very long photometric period (VLPP). We calculate the properties of a hypothetical third body, initially assumed on circular--planar orbit, by matching the modelled VLPP to the observed one of four CVs studied here: {\sl LU Camelopardalis} (LU Cam), QZ Serpentis (QZ Ser), V1007 Herculis (V1007 Her) and BK Lyncis (BK Lyn). The eccentric and low inclination orbits for a third body are considered using analytical results. The chosen parameters of the binary components are based on the orbital period of each CV. The smallest corresponding semi-major axis permitted before the third body's orbit becomes unstable is also calculated. A first-order analytical post-Newtonian correction is applied, and the rate of precession of the pericentre is found, but it can not explain any of the observed VLPP. For the first time, we also estimate the effect of secular perturbations by this hypothetical third body on the mass transfer rate of such CVs. We made sure that the observed and calculated amplitude of variability was comparable too. The mass of the third body satisfying all constrains range from 0.63 to 97 Jupiter masses. Our results show further evidence supporting the hypothesis of a third body in three of these CVs, but only marginally in V1007 Her., Comment: 11 pages, 6 figures

EBLM J0113+31 is moderately bright (V=10.1), metal-poor ([Fe/H]$\approx-0.3$) G0V star with a much fainter M dwarf companion on a wide, eccentric orbit (=14.3 d). We have used near-infrared spectroscopy obtained with the SPIRou spectrograph to measure the semi-amplitude of the M dwarf's spectroscopic orbit, and high-precision photometry of the eclipse and transit from the CHEOPS and TESS space missions to measure the geometry of this binary system. From the combined analysis of these data together with previously published observations we obtain the following model-independent masses and radii: $M_1 = 1.029 \pm 0.025 M_{\odot}$, $M_2 = 0.197 \pm 0.003 M_{\odot}$, $R_1 = 1.417 \pm 0.014 R_{\odot}$, $R_2 = 0.215 \pm 0.002 R_{\odot}$. Using $R_1$ and the parallax from Gaia EDR3 we find that this star's angular diameter is $\theta = 0.0745 \pm 0.0007$ mas. The apparent bolometric flux of the G0V star corrected for both extinction and the contribution from the M dwarf ($<0.2$ per cent) is ${\mathcal F}_{\oplus,0} = (2.62\pm 0.05)\times10^{-9}$ erg.cm$^{-2}$.s$^{-1}$. Hence, this G0V star has an effective temperature $T_{\rm eff,1} = 6124{\rm\,K} \pm 40{\rm \,K\,(rnd.)} \pm 10 {\rm \,K\,(sys.)}$. EBLM J0113+31 is an ideal benchmark star that can be used for "end-to-end" tests of the stellar parameters measured by large-scale spectroscopic surveys, or stellar parameters derived from asteroseismology with PLATO. The techniques developed here can be applied to many other eclipsing binaries in order to create a network of such benchmark stars., Comment: Accepted for publication in MNRAS. 15 pages, 9 figures