This book describes a new (2015) analytical solution for a circular orbit trajectory for spacecraft propelled by engines with very low thrust, typically electrically powered spacecraft. The solution is derived, explained in detail, and expanded with several additional equations. The fundamental laws of physics and mathematics of calculus are used to derive the solution.
Example space missions such as a round-trip to Mars, travelling to the Moon, and escaping from the Solar system, are analysed in some detail.
Solutions by other researchers are noted, especially the work of Theodore Edelbaum; "Propulsion Requirements for Controllable Satellites" published in 1961. Edelbaum and other publications used different methods but achieved the same answer for the basic delta V equation. Edelbaum was the first researcher to discover the relationship between orbital speed and delta V.
Many example problems with solved answers are included to explain the equations and how to use them. The examples cover simple applications such as lifting a satellite from a lower into a higher orbit, or higher to lower, to much more complex trajectories such as a round-trip expedition to another planet. Realistic comparisons are made between the usual chemical rockets in everyday use, and the newer technology electrical rockets.
These equations make it possible to quickly find answers to problems that would otherwise require complex programs and significant processing power to find useful results. The simplicity of the new equations allows anybody with a reasonable knowledge of physics and mathematics, and a basic scientific calculator, to use it productively.
The methods described should be useful to plan space missions based on low-thrust rocket spacecraft. It will help with the design of new spaceships that can significantly reduce the cost of space exploration. As a matter of educational value, this book demonstrates the use of fundamental laws of nature, applied to solving a problem in astronautics.
Readers should note that a full understanding of this work requires a good knowledge and understanding of physics and advanced mathematics.
