Classroom reconstruction of the Schwarzschild metric
A promising way to introduce general relativity (GR) 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 GR. 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 GR.