i - time interval -t - length of interval a - engine acceleration t[i] - time to reach the target at its position at time interval i Ve[i] - shuttle velocity at time interval i -Ve[i+1] - shuttle velocity at the next interval V[h] - heading vector -A[h] - angle of V[h] V[tc] - vector of the target (at time of calculation) (in relation to shuttle) -D[tc] - magnitude of V[tc] -A[tc] - angle of V[tc] V[tf] - vector of the target (after travel time) (in relation to shuttle) -A[tf] - angle of V[tf] V[sp] - vector of the shuttle's position (at time of calculation) -D[sp] - magnitude of V[sp] -A[sp] - angle of V[sp] V[sm] - vector of the shuttle's movement -D[sm] - magnitude of V[sm] -A[sm] - angle of V[sm] ~~~~~~~~~~ Base Equations time * velocity = distance time * acceleration = velocity Ve[i+1] = Ve[i] + (a * t) t[i] = sum(t) while i++ sum(t * Ve[i]) <= D[tc] Use t[i] to find target planet's location at that time (represented by V[tf]) V[h] = V[tf] - V[s] ~~~~~~~~~~ At each step, the time that would be needed to make a straight path to the target planet's current location is calculated. Then, the target's location after that is calculated. The resulting position is used as the heading for the shuttle's acceleration. ~~~~~~~~~~