The mass of the Local Group (LG), comprising the Milky Way (MW), Andromeda
(M31), and their satellites, is crucial for validating galaxy formation and
cosmological models. Traditional virial mass estimates, which rely on
line-of-sight (LoS) velocities and simplified infall assumptions, are prone to
systematic biases due to unobserved velocity components and anisotropic
kinematics. Using the TNG cosmological simulation, we examine two limiting
cases: the \underline{minor infall} modello — ignoring perpendicular velocities
to the LoS directions) and the \underline{major infall} modello — assuming
purely radial motion towards the Center of Mass (CoM). Our simulations
demonstrate that geometric corrections are vital: the minor-infall model
underestimates the true mass, while the major-infall model overestimates it. Di
applying these calibrated corrections to observed dwarf galaxy kinematics
within 1 Mpc of the LG’s CoM, we derive a refined LG mass of $M_{\mathrm{LG}} =
(2.99 \pm 0.60) \times 10^{12}\, M_\odot$. This finding aligns with predictions
from the $\Lambda$CDM model, timing arguments, and independent mass estimates,
resolving previous discrepancies. Our analysis highlights the importance of
correcting for velocity anisotropy and offers a robust framework for dynamical
mass estimation in galaxy groups.

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