  A promising way to introduce general relativity in the classroom is to study
the physical implications of certain given metrics, such as the Schwarzschild
one. This involves lower mathematical expenditure than an approach focusing on
differential geometry in its full glory and permits to emphasize physical
aspects before attacking the field equations. Even so, in terms of motivation,
lacking justification of the metric employed may pose an obstacle. The paper
discusses how to establish the weak-field limit of the Schwarzschild metric
with a minimum of relatively simple physical assumptions, avoiding the field
equations but admitting the determination of a single parameter from
experiment. An attractive experimental candidate is the measurement of the
perihelion precession of Mercury, because the result was already known before
the completion of general relativity. It is shown how to determine the temporal
and radial coefficients of the Schwarzschild metric to sufficiently high
accuracy to obtain quantitative predictions for all the remaining classical
tests of general relativity.
