The perturbed Friedmann universe is investigated and a gauge is searched for that defines coordinates "as close to the unperturbed background ones as possible." This characterization is formulated here in a more rigorous manner that allows in the case of vanishing background pressure a mathematical derivation of the desired gauge. It turns out that in this gauge the time-time component as well as the space-space components of the perturbation metric vanish, provided that the perturbation is stable. For unstable perturbations these components are either zero or modify the corresponding background ones by a time-independent factor. Hence, the instability is present only in the space-time components. It is shown that the influence of the latter can be described faithfully by Newton's gravitational law where the gravitational force is exerted by the density perturbations provided that the test particle moves slowly. For the nondust universe, however, there is no such gauge.