About This Course

This course is for a reader who is at home with calculus, differential equations, linear algebra, and constrained optimization, and who has done little physics. Newtonian mechanics is assumed only as a memory and is rebuilt where it is used. No thermodynamics, fluid mechanics, or orbital mechanics is assumed at all. The text builds the physics of launch vehicles from conservation laws, one stated system at a time, and it leans on your mathematics instead of reteaching it. When a step needs a result from the mathematics library, the text says which result, under which hypotheses, and gives its library identifier once.

The aim is that you can size a multistage launch vehicle for a stated payload and orbit from first principles and defend each number: where it came from, what was assumed, what its units are, and how it was checked. By the end you can derive the velocity budget from orbital speed, ascent losses, the Earth’s rotation, and orbital maneuvers; divide it between stages with a Lagrange multiplier; estimate an engine’s exhaust velocity from its chamber gas and its nozzle; integrate an ascent numerically and read off its losses; choose a steering law and say what it saves; check that the vehicle can be held on its path; follow a spent stage back into the atmosphere; and state how much payload is at risk from each assumption. Twelve chapters do this in four arcs: mechanics and mass (Chapters 1 and 2), propulsion (Chapters 3 to 6), flight and orbits (Chapters 7 to 9), and optimization, control, and synthesis (Chapters 10 to 12). What you get is a sizing method and one worked design. The course confers no qualification, and nothing in it is engineering data for a real vehicle.

Three habits run through every chapter. First, before any equation the text names the system: what is inside, what crosses its boundary, and what is neglected. Second, every quantity carries SI units through every line of a calculation, and each result is checked by its dimensions, by a limiting case, or against a real vehicle. Third, real data are cited and invented data are labeled. A short parenthetical such as “(Falcon User’s Guide; see sources)” points to the sources named at the end of this section; a value marked illustrative was chosen for the example and describes no real hardware.

Two conventions are worth learning now. The symbol \(\dot m\) always means the propellant mass flow rate, a positive number in \(\mathrm{kg/s}\) ; the vehicle’s mass \(m\) therefore obeys \(\mathrm dm/\mathrm dt=-\dot m\) . And \(g_0=9.80665\ \mathrm{m/s^2}\) is standard gravity, a defined constant used to convert units; the local gravitational acceleration is written \(g\) .

A single design problem threads through the course: a two-stage launcher burning kerosene and liquid oxygen that must place \(5000\ \mathrm{kg}\) in a circular orbit at \(400\ \mathrm{km}\) altitude, launched due east from latitude \(28.5^\circ\) . The text calls it the reference launcher, and it is issued three times. Chapter 1 shows why it cannot be built as one stage. Chapter 2 sizes Revision A for a provisional requirement of \(9.4\ \mathrm{km/s}\) and arrives at \(177\,812\ \mathrm{kg}\) at liftoff. Chapters 3 to 6 give Revision A its engines, nozzles, tanks, and pumps, and test the specific impulses and structural coefficients that Chapter 2 assumed. Chapter 7 flies Revision A, Chapter 8 states its target orbit, and Chapter 9 replaces the provisional requirement by a derived budget of \(9306.3\ \mathrm{m/s}\) and resizes the vehicle as Revision B, \(162\,985\ \mathrm{kg}\) at liftoff. Chapter 10 improves the steering of both revisions, and Chapter 11 holds Revision A on course through its worst moment in the atmosphere. Chapter 12 follows the spent upper stage down and then runs the whole design loop to convergence as Revision C: a budget of \(9259.8\ \mathrm{m/s}\) taken from the vehicle’s own flight, and \(162\,889\ \mathrm{kg}\) at liftoff including a payload fairing of \(570\ \mathrm{kg}\) that the earlier revisions left out. Each table of launcher numbers says which revision it belongs to. All three revisions are course design values and describe no real vehicle.

Work each example with paper before reading its solution, and attempt the exercises before opening the worked solutions, which follow the last chapter. Each chapter has twenty exercises, ranging from recall and computation through proofs and diagnoses of wrong arguments to problems that reach back to earlier chapters; every chapter includes at least one marked as a computation, to be done in a language of your choice. About three in five exercises have full solutions, and nearly all of the rest have a hint or a final answer. Exercises are numbered within a chapter, so Exercise 7.3 is the third exercise of Chapter 7, and inside a chapter the text may say only “Exercise 3”. The Cumulative Review after Chapter 12 has twenty problems that do not say which chapter they belong to; most need two or three chapters at once, and several ask for a design decision on the reference launcher and a defence of it with numbers. Its solutions are keyed R.1, R.2, and so on.

Real data are cited where they are used, by a short name. Launch-vehicle thrusts, dimensions, and timelines come from the SpaceX Falcon User’s Guide of May 2025 (spacex.com) and the Rocket Lab Electron Payload User’s Guide, version 7.0. Planetary constants come from the NASA Earth Fact Sheet (nssdc.gsfc.nasa.gov) and the NASA Moon Fact Sheet, and defined constants from the NIST tables. The three-zone atmosphere model, the heat-capacity ratio of air, and the stability rule for model rockets come from pages of the NASA Glenn Research Center. The ascent losses of six real launch vehicles, on which the velocity budget’s allowance rests, come from slides of the Georgia Tech course AE 4451 that reproduce a table from Humble, Henry, and Larson. Three sets of MIT OpenCourseWare lecture notes are cited where the text compares its numbers or conventions with theirs or borrows a correlation: 16.07 Dynamics (ocw.mit.edu), 16.50 Introduction to Propulsion Systems, cited by lecture number, and 16.346 Astrodynamics. Chapters 10 to 12 also cite a tutorial of the control-toolbox project on the Goddard problem, Barrowman’s report on the aerodynamics of slender vehicles, the NASA monograph SP-8009 on propellant slosh, the Sutton and Graves report on stagnation-point heating, and a table of the standard atmosphere published by Public Domain Aeronautical Software (PDAS). Manufacturers do not publish stage masses or specific impulses for Falcon 9, and most of the engine, propellant, and material figures used here are not published by their makers either, so those come from encyclopedia articles. The text cites Wikipedia by article title, or simply as a secondary compilation: in Chapters 1 and 2 that means the articles “Falcon 9 Full Thrust”, “SpaceX Merlin”, “Saturn V”, “S-II”, and “Rocketdyne J-2”, and in later chapters the articles on the engines, vehicles, and space station under discussion. Such figures are good enough for the order-of-magnitude comparisons made here and should not be treated as engineering data.