The accepted ideal rocket equation for thrust, widely used in rocketry literature, is proved to be incorrect. The correct replacement is then presented and shown to obey the full form of Newton's second law \(F={\dot p}\) , so the sum of external forces on the rocket is the time derivative of its momentum. The accepted velocity equation is correct, which may explain why this error has been overlooked.

v2: Added two new sections proving the same result by alternative methods. v3: Added the case of variable relative velocity to the Conclusions; explained how to use Newton's second law to include gravity and other forces since it is commonly misused or ignored; added minor elaborations. Original results unchanged. NEW: For a VIDEO LECTURE of this paper, see: https://youtu.be/lxVbX_caSQQ