  Dark energy must be taken into account to estimate more reliably the amount
of dark matter and how it is distributed in the local universe. For systems
several Mpc across like the Local Group, we introduce three self-consistent
independent mass estimators. These account for the antigravity effect of dark
energy treated as Einstein's cosmological constant Lambda. The first is a
modified Kahn-Woltjer model which gives a value of the Local Group mass via the
particular motions of the two largest members, the Milky Way and M31. Inclusion
of dark energy in this model increases the minimum mass estimate by a factor of
three compared to the "classical estimate". The increase is less but still
significant for different ways of using the timing argument. The second
estimator is a modified virial theorem which also demonstrates how dark energy
can "hide" from detection a part of the gravitating mass of the system. The
third is a new zero-gravity method which gives an upper limit to the group mass
which we calculate with high precision HST observations. In combination, the
estimators lead to a robust and rather narrow range for a group's mass, M. For
the Local Group, 3.2 < M < 3.7 x 10^{12} M_sun. Our result agrees well with the
Millennium Simulation based on the LambdaCDM cosmology.
