Robert F. Stengel
Princeton University

The dream that Jules Verne portrayed in 1865 became reality a century later when Project Apollo landed men on the Moon and returned them safely to Earth. Men first circled the Moon 55 years ago and last landed there in 1972. Nine manned missions were flown to the Moon, and then they stopped, giving the impression that this feat was an end in itself rather than the first chapter of a new human saga. The development of technology, as remarkable as it was, proved not to be the limiting factor; more "down to Earth" priorities took precedence ... until now.

There has been a resurgence of interest in lunar exploration, not only in the U.S. but around the world. The Sept 2013 launching of the Lunar Atmosphere and Dust Environment Explorer (LADEE) spacecraft from NASA's Wallops Flight Facility and Odysseus (IM-1, 2024) are recent American examples. China's Chang'e 3 lander delivered the Jade Rabbit rover to the Moon's surface in 2013. Chang'e 4 landed on the far side of the Moon (Chang'e 4), and Chang'e 5 returned samples of the Moon's surface to Earth (Chang'e 5). The Queqiao communications relay satellite was launched to halo orbit about the L2 point in preparation for Chang'e 4's landing. India's Pragyan (Chandrayaan-3) and Japan's SLIM landed in 2023. Many unmanned missions have progressed to the development phase, and many more are planned (See Future Lunar Missions). The Artemis Program intends to return American astronauts to the lunar surface in 2027.

The goal of From the Earth to the Moon is to reveal the freedoms and limitations of technological development, with a focus on space flight. We investigate the scientific, political, and economic factors that made Project Apollo possible. The seminar provides an introduction to orbital mechanics, launch, and re-entry, as well as to the basic principles of space-vehicle design and rocket propulsion, using flight from the Earth to the Moon and back as a focal point. We study space travel as portrayed in history and fiction, and we develop an understanding of the critical roles played by organizations, management principles, and budget.

Syllabus and Course Readings

Seminar Slides

Co-Planar, Point-Mass Lunar Trajectories, a MATLAB program

Insight regarding lunar trajectories can be gained from co-planar, point-mass trajectories. A MATLAB script (CoPlanarTraj.m) and two functions (RoundEarth.m and LunarTrajDynamics.m) describe simplified two- and three-body problems. Trajectories of a spacecraft with negligible mass compared to the Earth and Moon are generated using analytical and numeric equations. For this introductory model, the position of Earth is fixed, and the Moon is in a circular orbit about the Earth.

For the example, the spacecraft departs from a circular orbit about Earth with a semi-major axis of 3748 km and an impulsive horizontal velocity increment of 3.087 km/s. The Moon's true anomaly increment is -40 deg from the intercept point that would occur in the absence of the Moon's gravitational field. In addition to numerical values and plots of state variables, animations of the spacecraft and Moon trajectories reveal the significance of lunar gravity's "sphere of influence." Effects of varying the true anomaly increment (i.e., the phasing of Moon position and spacecraft launch time) and launch velocity increment are of particular interest.

The script has the following chapters and sections:

1. Elements of Circular Parking Orbit about Earth
2. Elements of Transfer Orbit from Parking Orbit to Moon Radius
3. Elements of Moon Circular Orbit About Fixed Earth
4. Elements of Circular Parking Orbit about Earth
5. Lunar Transfer Trajectory, without Lunar Gravity
---5.1 Numerical Solution (Command Window)
---5.2 Animation, Inertial Frame
6. Lunar Transfer Trajectory, with Lunar Gravity
---6.1 Numerical Solution (Command Window)
---6.2 Animation, Inertial Frame
---6.3 Animation, Rotating Frame

Download and run CoPlanarTraj in a MATLAB, SciLab, or GNU Octave environment:



key words: Earth, Moon, lunar exploration, space flight, Apollo Program, orbital mechanics, attitude dynamics, space launch vehicles, interplanetary travel, solar system, science fact, science fiction, space race, aerospace industry, NASA programs, rocketry.
Last updated March 10, 2024.
Copyright (c) 2024 by Robert F. Stengel. All rights reserved.