Computation of the different errors in the ballistic missiles range (Q420180)

Summary: The ranges of the ballistic missile trajectories are very sensitive to any kind of errors. Most of the missile trajectory is a part of an elliptical orbit. In this work, the missile problem is stated. The variations in the orbital elements are derived using Lagrange planetary equations. Explicit expressions for the errors in the missile range due to the in-orbit plane changes are derived. Explicit expressions for the errors in the missile range due to the out-of-orbit plane changes are derived when the burnout point is assumed on the equator.