An analytical analysis of the first moment (intensity weighted velocity average) of a spectral line in an infalling spherical core is presented, following the seminal works of Anglada et al. (1987, 1991). A finite spectral resolution and finite angular resolution are taken into account in the analysis, as well as a finite radius of the infalling core. The predicted first moment as a function of the impact parameter is obtained, and the maximum negative value of the first moment at the origin as a function of the central mass and the angular resolution.
These results are applied to the analysis of the ammonia (J,K)= (1,1) and (2,2) inversion transitions observed with the VLA toward L1287. The ammonia emission is separated in three different structures: two elongated filaments, and a core with a guitar shape. The "Guitar" core shows characteristics of a pre-stellar core (low temperature and turbulence), but the velocity first moment map shows a blue spot at the center, a clear signature of infalling motion. The fit with the model described above gives a central mass ~4 solar masses.