Aerocapture offers a near propellantless and quick method of orbit insertion at atmosphere bearing planetary destinations. Compared to conventional propulsive insertion, the primary advantage of using aerocapture is the savings in propellant mass which could be used to accommodate more useful payload. To protect the spacecraft from the aerodynamic heating during the maneuver, the spacecraft must be enclosed in a protective aeroshell or deployable drag device which also provides aerodynamic control authority to target the desired conditions at atmospheric exit. For inner planets such as Mars and Venus, aerocapture offers a very attractive option for inserting small satellites or constellations into very low circular orbits such as those used for imaging or radar observations. The large amount of propellant required for orbit insertion at outer planets such as Uranus and Neptune severely limits the useful payload mass that can delivered to orbit as well as the achievable flight time. For outer planet missions, aerocapture opens up an entirely new class of short time of flight trajectories which are infeasible with propulsive insertion. A systems framework for rapid conceptual design of aerocapture missions considering the interdependencies between various elements such as interplanetary trajectory and vehicle control performance for aerocapture is presented. The framework provides a step-by-step procedure to formulate an aerocapture mission starting from a set of mission objectives. At the core of the framework is the ``aerocapture feasibility chart", a graphical method to visualize the various constraints arising from control authority requirement, peak deceleration, stagnation-point peak heat rate, and total heat load as a function of vehicle aerodynamic performance and interplanetary arrival conditions. Aerocapture feasibility charts have been compiled for all atmosphere-bearing Solar System destinations for both lift and drag modulation control techniques. The framework is illustrated by its application to conceptual design of a Venus small satellite mission and a Flagship-class Neptune mission using heritage blunt-body aeroshells. The framework is implemented in the Aerocapture Mission Analysis Tool (AMAT), a free and open-source Python package, to enable scientists and mission designers perform rapid conceptual design of aerocapture missions. AMAT can also be used for rapid Entry, Descent, and Landing (EDL) studies for atmospheric probes and landers at any atmosphere-bearing destination.