# Part 1: Science and Engineering Fundamentals

**1.0 - Introduction**[edit | edit source]

The design and development of space systems is a part of **Aerospace Engineering**, which in turn is a specialized field within the wider subject of **Engineering**. Engineering in general is the creative application of knowledge from mathematics and the sciences towards useful ends. So this first part of Volume II reviews the fundamentals of those subjects. We pay the most attention to the parts that apply to space systems, but by no means cover the whole of these areas of knowledge.

The technologies, projects, and programs presented later in this book are mainly aimed at people who want a deeper understanding of, or to actually work with future space projects. We assume basic knowledge of mathematics and the sciences at a secondary education (high school) or first year university science or engineering level. If you do not have such a background, you can get it from online sources. These include open source textbooks from the **CK-12 Foundation** and the **Open Textbook Library**, as well as video lectures from the **Khan Academy**. Traditional printed books and classes are also available.

We try to keep the discussion in this book is at an introductory engineering level. It is not a complete survey on any topic. In many cases there is simply too much detail to fit it all. In others the technical level is too advanced, and, in the case of some future technologies and projects, the ideas have not been fully developed yet. So other books, articles, and materials are referenced throughout, including in the **References** section.

The Seed Factory Project, of which these volumes are a part, has compiled an extensive reference library for members, but we cannot share copyrighted works from it without permission. We can supply a **List of Library Contents** (pdf file) and share items we have permission for. For the remainder, and other works outside our library, you can use general library and information sources. These include the **Internet Archive**, **Library of Congress** and interlibrary loan, sister projects to Wikibooks (← see left sidebar of this page), tutorial videos such as found on YouTube, and new and used booksellers. Readers are encouraged to gp deeper into any topics that interest them.

Sections 2-5 below introduce the fields of mathematics, the sciences, engineering, some design principles, and how they relate to space projects. The remaining chapters in Part 1 cover these subjects in more detail.

**2.0 - Mathematics**[edit | edit source]

The importance of mathematics to science and engineering can be summarized in one sentence:

**Our Universe appears to follow mathematical laws.**

By that we mean mathematical formulas and calculations produce results which match what we see when we look at the real world. This is a very powerful circumstance, because we can do the calculations **before** we look, even before something exists, and so predict the future.

Why mathematics works so well in describing reality is a philosophical question to which we don't have a good answer. This was pointed out by Eugene Wigner in 1960 in an article entitled **The Unreasonable Effectiveness of Mathematics in the Natural Sciences** (pdf file), which is also discussed in a **Wikipedia article**. Regardless of why, it does work in practice. That allows us, among other things, to design systems that will work as intended.

One of the earliest examples of prediction is the motion of the Sun, Moon, and planets in the sky. Even in ancient times people were able to predict where they would be in the future. Those predictions allowed useful results, like knowing when to plant crops. Seasons are caused by the Earth's axial tilt and motion around the Sun. The ancients didn't know that, but their calendars and counting of days still worked. **w:Empirical_evidence Empirical Knowledge** gained from experience and experiment can still be useful, even if the underlying science isn't known.

The match of mathematical predictions to the real world is not just a general one. In many cases it can be astoundingly exact. Today we can predict the motion of **Solar System** bodies with amazing accuracy. For example the 2012 landing of the Curiosity rover on Mars was within 2 km of the intended location, after a trip of 566 million km. This could not have been done without predicting both the spacecraft trajectory and the future location of the landing point on a moving and rotating planet to 4 parts per billion.

Further examples of using mathematics in engineering are all around us. Every tall building and bridge relies on the simple mathematical relationship that the strength be greater than the sum of all the loads. When you design such structures you calculate the strength, and calculate the loads, and then make sure the first is more than the second. Proof that this method works is that tall buildings and bridges rarely fall down.

Like other engineering fields, space system engineering uses mathematical formulas and calculations. They are derived either from the sciences or practical experience and measurements within engineering. We present many of these formulas and calculations in this book. To get the best use of them, knowing the following subjects at a basic level is desirable (links are provided to introductory textbooks):

**Algebra**- How to manipulate algebraic formulas and how to obtain a numeric answer given input values, the relationship of formulas and functions to graphs, and exponents and polynomials.**Geometry**- The types of geometric shapes and angles, and how the dimensions of two and three dimensional shapes (perimeter, area, and volume) are calculated.**Trigonometry**- Basic trigonometric functions and graphing them, vectors, and polar coordinates.**Probability and Statistics**- The ideas of averages, random error, distributions, and regressions.

More advanced topics in mathematics, such as **Mathematical Analysis**, **Calculus** and beyond are helpful in understanding how the formulas are derived, or in solving more complex problems in engineering. They are mostly not needed for an introductory book like this one.

**3.0 - Science**[edit | edit source]

**Science** is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The predictions are often in the form of results from mathematical formulas and calculations. Science is pursued partly because knowledge about the Universe satisfies human interest and curiosity. But it often turns out that understanding how and why things work is useful in some practical way.

It isn't known in advance what knowledge will turn out to be useful, so scientists as a whole study everything. Knowledge is a seamless whole, but from its history, and for the purposes of teaching and study, it is divided into branches according to the object of study. The ones most relevant to space systems include:

**Physics**- This is the study of the forces and interactions of matter and energy, the results of those interactions, and the fundamental laws and components of which things are made.**Astronomy**- This is the study of objects and phenomena outside the Earth's atmosphere. This where all space systems operate, so it is highly relevant. Planetary Science in particular studies condensed objects orbiting stars.**Chemistry**- This is the study of matter at the atomic, molecular, and larger scales as far as how they react and their physical properties.**Biology**- This is the study of life in general, which matters for space projects that include living things, especially people.

At least a basic understanding of the above areas of science is useful for working with space systems, since their engineering and design is derived from that knowledge. Other fields may also prove useful depending on the type of project. Beyond particular branches of science, understanding the **Scientific Method** is important. This is where ideas are generated, experiments and observations are made to test those ideas, and then they are validated or rejected.

Peer review, statistics, and repeatability are among the ways to make sure observations and conclusions are reliable. Absolute truth is never reached in science, only increasing confidence in a given explanation. Sufficiently well tested ideas join the body of knowledge considered settled, but they are always subject to revision or replacement by better data and ideas. Collecting such data and generating ideas is how science advances.

**4.0 - Engineering**[edit | edit source]

Mathematics and science are developed for their own sake, and for their ability to predict the future. **Engineering** applies the accumulated knowledge from the sciences and experience towards useful ends. This is by designing, building, and operating systems to perform intended functions.

If you have no prior background in engineering, or in space systems in particular, you may want to start with a book like **Engineering - an Introduction** by the CK-12 Foundation. You can get additional background from articles referenced in Wikipedia's **Outline of Engineering** and some of the book-length sources in the **References** section of this book.

Simple projects and systems can be directly designed by one or more people using their knowledge and experience. When projects are very complex, as is often the case for space systems, methods like **Systems Engineering** and other **Project Management** tools and techniques are used across an entire project to organize and optimize the work. Systems engineering and project management are described in more detail in Chapter 1.5.

The total accumulated engineering knowledge is much too large for any single person to know more than a small part. So engineering in general is divided into major fields of specialization, each of which has it's own training path. It starts with a common basis in science and mathematics, then concentrates on particular areas of application, such as Mining, Chemical, Mechanical, and Electrical Engineering.

Working engineers often further specialize their study and experience. They, or the organizations they work for, are called on as needed for each project. This is more efficient than keeping full time staff for every possible subject area. The specialists who are called on also have more experience in their area from having worked on similar projects. Since the teams working on a project are not permanent, how you manage their interaction then becomes important. Project organization is covered in Chapter 1.8.

**Aerospace Engineering** is the specialty most relevant to space systems. Space systems are projects which operate in the space environment in the same way that ships and airplanes operate in the water or through the air. The particular environment imposes differences in how things are designed. But they all rely on the same knowledge base of subjects like mechanics, materials science, and thermodynamics.

A complex space project will use engineers from multiple specialty areas like mechanical, chemical, and electrical engineering. This is in addition to aerospace engineers who specialize in the methods and environments that apply to space. We identify these and other specialties Chapter 1.7, but will concentrate on subjects that apply to space. There are many information sources about the other specialties for those who are interested.

**5.0 - Design Principles**[edit | edit source]

Through training and experience, engineers develop a sense of what will work or not, and how to optimize a design. Partly this is through broad principles that apply in their specialty. We note a few of the more important ones that apply to space systems here. These and others will appear throughout the book and we will try to highlight them:

**Earth vs Space**- On Earth, transport involves friction of various kinds, and most things are moving slowly in relation to each other. Therefore energy and cost are proportional to distance, but not time. Space is a nearly frictionless medium, and things are moving at relatively high velocity with respect to each other. So difficulty and cost are more related to kinetic and potential energy, which governs the paths you follow. It also depends more on the time you start than absolute distance, since everything in space is in relative motion to each other. Distances are generally much larger in space than on Earth.

**Non-Linearity**- Many of the formulas and variables related to space systems have values raised to a power or an exponential. So the difficulty of a task does not have a one-to-one relation to the magnitude of the desired goal. This is called a**Nonlinear System**. Understanding the direction and amount of the non-linearity is important, as this can greatly help or hinder a given task. One of many examples is atmospheric pressure, which decreases exponentially with altitude, decreasing aerodynamic drag proportionally.

**Uncertainty and Margins**- Although some values, like the orbit of a planet, are known quite accurately, no physical parameter is known with absolute accuracy. Anything built by people will deviate by some amount from the ideal defined by the design. The natural environment can also vary over time unevenly from measured averages. For example, one third of the Martian atmosphere can freeze at the poles seasonally, lowering its pressure globally.

- Engineering designs have to account for these uncertainties in the environment and how the equipment is built and used. One way to do this is to use
**Design Margins**beyond the expected conditions, which are larger than the uncertainties. How much margin to use is based on cost, experience, and the use to which the design is put. For example, a passenger airplane would generally have higher margins than a drone with no crew, even though both are aircraft.