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.
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: