  We use numerical simulations to study the relation between the velocity of
the Local Group and its gravitational acceleration. This relation serves as a
test for the kinematic origin of the CMB dipole and as a method for estimating
beta. We calculate the misalignment angle between the two vectors and compare
it to the observed value for the PSCz survey. The latter value is near the
upper limit of the 95% confidence interval for the angle; therefore, the
nonlinear effects are unlikely to be responsible for the whole observed
misalignment. We also study the relation between the amplitudes of the LG
velocity and gravity vectors. In an Omega=1 Universe, the smoothed gravity of
the LG turns out to be a biased low estimator of the LG (unsmoothed) velocity.
In an Omega=0.3 Universe, the estimator is biased high. The discussed biases
are, however, only a few per cent, thus the linear theory works to good
accuracy. The gravity-based estimator of the LG velocity has also a scatter
that limits the precision of the estimate of beta in the LG velocity-gravity
comparisons. The random error of beta due to nonlinear effects amounts to
several per cent.
