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We extended the modified Lemaitre-Tolman model taking into account the effectof angular momentum and dynamical friction. The inclusion of these quantitiesin the equation of motion modifies the evolution of a perturbation, initiallymoving with the Hubble flow. Solving the equation of motions we got therelationships between mass, $M$, and the turn-around radius, $R_0$. Knowing$R_0$, the quoted relation allows the determination of the mass of the objectstudied. The relationships for the case in which also the angular momentum istaken into account gives a mass $\simeq 90$ \% larger than the standardLemaitre-Tolman model, and two times the value of the standard Lemaitre-Tolmanmodel, in the case also dynamical friction is taken into account. As a secondstep, we found relationships between the velocity, $v$, and radius, $R$, andfitted them to data of the Local Group, M81, NGC 253, IC342, CenA/M83, and tothe Virgo clusters obtained by Ref.[New Astronomy 11(4):325, A&A 488(3):845].This allowed us to find optimized values of the mass and Hubble constant of theobjects studied. The fit gives values of the masses smaller with respect to the$M-R_0$ relationship method, but in any case 30-40\% larger than the $v-R$relationship obtained from the standard Lemaitre-Tolman model. Differently frommass, the Hubble parameter becomes smaller with respect to the standardLemaitre-Tolman model, when angular momentum, and dynamical friction areintroduced. This is in agreement with Ref.[New Astronomy 11(4):325, A&A488(3):845], who improved the standard Lemaitre-Tolman model taking intoaccount the cosmological constant.  Finally, we used the mass, $M$, and $R_0$ of the studied objects to putconstraints to the dark energy equation of state parameter, $w$. Comparisonwith previous studies show different constraints on $w$.

Improved Lemaitre-Tolman model and the mass and turn-around radius in group of galaxies