This study evaluates the feasibility and implications of a mission concept to explore a Trojan asteroid of Jupiter, (624) Hektor, with a CubeSat constellation. The 12U CubeSats are released from an Interplanetary Transfer Vehicle in the asteroid proximity. The mission is based on an orbital phase of one month to investigate the target asteroid with the on-board instruments. At the end of the scientific observation, the CubeSats soft-land on the asteroid, or rendezvous with the interplanetary platform. The research presents two main parts: the first one is dedicated to the study of the gravitational field of the target asteroid, which is highly inhomogeneous because of its bilobed shape.