A method of onboard guidance of a powered ballistic missile, the method comprising: in real time, during flight of the missile, and using an onboard computer on the missile, numerically simulating a flight path of the missile using a model with at least three degrees of freedom; and updating both of a predicted intercept point of the missile and an aim point of the missile, in real time and using the onboard computer, using results of the numerical simulation; wherein the updating includes: updating the aim point if a heading error between a trajectory of the missile and the predicted intercept point, is above a predetermined heading error threshold, wherein the heading error is the angle by which the missile will miss the predicted intercept point if no course correction is taken; updating the predicted intercept point if the heading error is below the predetermined heading error threshold and a calculated predicted time of flight exceeds an initial predicted time of flight by a predetermined time of flight threshold; and wherein the method includes sending the aim point to a guidance system of the missile if the heading error is below the predetermined heading error threshold and if the calculated predicted time of flight does not exceed an initial predicted time of flight by the predetermined time of flight threshold. in real time, during flight of the missile, and using an onboard computer on the missile, numerically simulating a flight path of the missile using a model with at least three degrees of freedom; and updating both of a predicted intercept point of the missile and an aim point of the missile, in real time and using the onboard computer, using results of the numerical simulation; wherein the updating includes: updating the aim point if a heading error between a trajectory of the missile and the predicted intercept point, is above a predetermined heading error threshold, wherein the heading error is the angle by which the missile will miss the predicted intercept point if no course correction is taken; updating the predicted intercept point if the heading error is below the predetermined heading error threshold and a calculated predicted time of flight exceeds an initial predicted time of flight by a predetermined time of flight threshold; and wherein the method includes sending the aim point to a guidance system of the missile if the heading error is below the predetermined heading error threshold and if the calculated predicted time of flight does not exceed an initial predicted time of flight by the predetermined time of flight threshold. updating the aim point if a heading error between a trajectory of the missile and the predicted intercept point, is above a predetermined heading error threshold, wherein the heading error is the angle by which the missile will miss the predicted intercept point if no course correction is taken; updating the predicted intercept point if the heading error is below the predetermined heading error threshold and a calculated predicted time of flight exceeds an initial predicted time of flight by a predetermined time of flight threshold; and wherein the method includes sending the aim point to a guidance system of the missile if the heading error is below the predetermined heading error threshold and if the calculated predicted time of flight does not exceed an initial predicted time of flight by the predetermined time of flight threshold.