solved simultaneously when baryonic physics is properly taken into account, extending a model that has been shown to solve also the CCP and AMC. Appendix \[Dynamics of the satellites\] gives the detail of the modified model, compared with Del Popolo [*et al.*]{} (2014). Sect. 3 describes the results, including a discussion. Sect. 4 is devoted to conclusions.

Solving the remaining small scale problems of $\Lambda$CDM
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As we use a model that solves the other problems, we will concentrate here on the problems regarding the number and mass of satellites. Several solutions have been proposed to the MSP and TBTF problems (Strigari et al. 2007; Simon & Geha 2007; Madau et al. 2008; Zolotov et al. 2012; Brooks & Zolotov 2012; Purcell & Zentner 2012; Vera-Ciro et al. 2012; Di Cintio et al. (2012); Wang et al. 2012). B13 proposed an interesting baryonic solution to those two problems: instead of running SPH simulations of different galaxies, they tried to introduce baryonic effects in large N-body dissipationless simulations, like the VL2, showing that the result obtained is in agreement with observations of MW and M31 satellites.

In the following, we will partly follow their steps to obtain the corrected circular velocities 