Catalyzes the specific attachment of an amino acid to its cognate tRNA in a 2 step reaction: the amino acid (AA) is first activated by ATP to form AA-AMP and then transferred to the acceptor end of the tRNA. ATP + L-aspartate + tRNA(Asp) = AMP + diphosphate + L-aspartyl-tRNA(Asp) Homodimer (PubMed:2642907). Part of a multisubunit complex that groups tRNA ligases for Arg (RARS1), Asp (DARS1), Gln (QARS1), Ile (IARS1), Leu (LARS1), Lys (KARS1), Met (MARS1) the bifunctional ligase for Glu and Pro (EPRS1) and the auxiliary subunits AIMP1/p43, AIMP2/p38 and EEF1E1/p18 (By similarity). Belongs to the class-II aminoacyl-tRNA synthetase family. Type 2 subfamily.