Calculating the thrust on continuously and discretely emitting rockets

Newton’s second law written as the rate of change of linear momentum of a system can be re expressed as a differential equation of motion for a rocket that continuously ejects mass. The result includes a mathematical expression for the thrust force in terms of the rate of mass loss and the relative exhaust velocity. If the rocket is instead propelled by the discrete emission of finite chunks of mass, an analogous equation for the thrust impulse can be deduced, formulated either in terms of the initial or final velocity of the rocket. Some common issues concern how to define thrust and how to write Newton’s second law in terms of that thrust and the net external force or impulse acting on the rocket (such as due to gravity and drag). Additionally, a distinction must be made between the center-of-mass velocity and the average velocity for an object of variable mass such as a rocket. The discussion is at a level appropriate for an introductory calculus-based course in physics.