There’s thermal control … Juno and other spacecraft are out in space where sometimes it’s too cold and sometimes it’s too hot, depending on the trajectory. Juno approached close to the Sun before our Earth Flyby, and for our main science mission we’re going to be way out at Jupiter, over six times as far away. We have to deal with both of those extremes. A lot of missions have similar challenges. One way is to put on thermal blankets, which are layers of insulation made partly of metal. You also have to be able to deal with maneuvers when the spacecraft’s orientation changes and your thermal conditions change as a result. Some of it is handled with heaters. When you’re not operating an instrument it will get cold, so if you turn an instrument off, you typically turn a heater on to compensate. Same for some of the other subsystems. There’s some combination you have to work out for the whole spacecraft, with the power that’s available. And you have to deal with the fact that the solar cells can generate 450 watts at Jupiter but they’re capable of putting out many thousands of watts at Venus range, and you have to be able to handle that somehow … Stuart Stephens Mission Planner, Juno Chapter 1: Why go to space? Space is a harsh environment for both the living and inanimate. Apart from the lack of air or moisture, the extreme hot and cold temperatures and the high ambient radiation levels, there are more subtle hazards for humans. You can lose about one percent of your bone mass for every month you spend in space, making returning to a weight-bearing environment, like Earth, difficult. You may experience up to a 45% loss in your body’s ability to synthesize proteins. You are at increased risk of kidney stones just after launch and just after you return to Earth. Your eyeballs may flatten, causing vision problems. And this is nothing compared to what our robotic spacecraft have to endure: electrical connections, such as solder joints, may become brittle and fail; the radiation environment causes metals and plastics to deteriorate, lose strength and flexibility; a fast-moving micrometeoroid can not only put a hole in the spacecraft but can shatter and destroy the spacecraft’s contents. Finally, there’s the trauma of going into space: at launch, you and the spacecraft are subject to many times the normal force of gravity. Joints and connections may fail, hollow spaces may collapse and loose objects may become missiles during launch. But since you are intent on going and we are not going to be able to talk you out of it, let’s make sure you and your spacecraft are as well-prepared as possible. Like many human endeavors, most of the preparation is not physical but mental. For space exploration, this requires an understanding of the disciplines of mathematics, physics, chemistry, astronomy and engineering. Rest assured, we are not going to cover those topics in gross detail; that’s what upper division and graduate-level courses are for. Rather, our intent is to coach you with enough background material, including stories of

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failed attempts, from those disciplines so that the basic ideas of putting an object into space make sense. We’ll start with a little math… Units give meaning to numbers On July 23, 1983, Air Canada flight 143 was on its way from Montreal to Edmonton. It ran out of fuel over Manitoba; fortunately for everyone on the plane, the pilots were skilled enough to glide the Boeing 767 aircraft to a safe landing at a former Royal Canadian Air Force base runway being used as a race track. Modern aircraft running out of fuel on a normal flight path is unheard of; what went wrong with this flight. The culprit turned out to be a failed fuel quantity indicator system and an assumption on the part of the ground crew. The failed fuel quantity indicator forced the ground crew in Montreal to manually calculate the amount of fuel needed to fill the airplane’s tank. The airplane’s fuel capacity was given in kilograms, a unit of mass. The airport’s fuel truck dispensed fuel in liters, a unit of volume. To convert the fuel needs of the airplane into an amount the truck can dispense, there is a conversion factor called the density, which is used to convert kilograms into liters and vice versa. The fuel company’s documentation stated their fuel had a density of 1.77. The ground crew assumed the density had units of kilograms per liter because Canada uses, as does most of the world, the metric system, so why would it be in any other units? However, the fuel company, which worked with a lot of airplanes whose fuel requirements were measured in pounds (in fact, the Boeing 767 was one of the first planes to specify a fuel requirement in kilograms), assumed that anyone who read their documentation would know the units of the density given were in pounds per liter. Let’s see how this slight change in units would make a difference. The ground crew thought the density was 1.77 kilograms/liter, and was able to measure the volume of fuel left in the airplane as 7682 liters. They needed to know how much this fuel weighed because the airplane’s manufacturer gave its fuel capacity in kilograms. So use the density as a conversion factor to figure out how many kilograms 7682 liters weighs:

7682  𝑙𝑖𝑡𝑒𝑟𝑠  1.77  𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠

1  𝑙𝑖𝑡𝑒𝑟 = 13597  𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠 Before we discuss the result, let’s go over the calculation above. The conversion factor of liters to kilograms appears in the parenthetical unit conversion factor in the equation. It could have been equally well written   !  !"#$%

!.!!  !"#$%&'() because the quantity in the

numerator represents the same amount as the quantity in the denominator. The particular way it was written in the equation (with “liter” as the unit in the numerator) is not a stylistic choice; rather, it was to allow the unit of “liter” to cancel out algebraically – note that “liter” appears as the unit in the numerator in the quantity on the left, and “liter”

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appears as the unit in the denominator of the unit conversion factor. This cancellation of the kilogram unit leaves only “kilograms” in the numerator of the resulting value on the right side of the equation. Now to discuss the result: The ground crew in Montreal thought there was 13597 kilograms of fuel left in the airplane’s tank. They knew from Boeing that the capacity of the airplane’s tank was 22300 kilograms, so they figured that they should add 22300 – 13597 = 8703 kilograms. Since the fuel dispenser measured fuel in liters, they had to convert the kilograms needed back into liters:

8703  𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠  1  𝑙𝑖𝑡𝑒𝑟

1.77  𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠 = 4917  𝑙𝑖𝑡𝑒𝑟𝑠

Note that in this conversion, the unit conversion factor was “flipped” in order to cancel out the “kilogram” unit to leave only “liters”. So the ground crew dispensed 4917 liters into the airplane’s fuel tank – normally a very small amount for a long flight. But the ground crew did not know where the airplane’s destination was. So how much fuel was actually on the plane? There was 7682 liters already in the tank and the ground crew added 4917 liters, for a total of 12599 liters at take-off for the airplane. How does this value compare to the actual capacity of the fuel tank? We’ll need one last conversion, and two final conversion factors – the density of the fuel in the units that the fuel company used, 1.77 pounds/liter, and the conversion from pounds to kilograms (1 kilogram is the same amount as 2.2 pounds):

12599  𝑙𝑖𝑡𝑒𝑟𝑠  1.77  𝑝𝑜𝑢𝑛𝑑𝑠1  𝑙𝑖𝑡𝑒𝑟

1  𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚2.2  𝑝𝑜𝑢𝑛𝑑𝑠 = 10136  𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚𝑠

Note that in this conversion, two unit conversion factors (the correct density and the pound/kilogram conversion) were serially used, with the result that “liter” cancelled and “pound” cancelled, leaving only “kilogram”. Thus, Canada Air flight 143 took off from Montreal with less than a half tank of fuel – no wonder it did not have enough fuel! Units made a significant difference in the flight’s outcome. Quantifying space requires a clever unit system and/or a better notation As noted, space is a large place. The scale of planets, interplanetary travel, stars, galaxies and, well, the whole universe is quite beyond our everyday experience. Yet to have any chance of determining the principles under which the universe works, we have to be able to describe space by measuring it.

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La Système International d’Unités, abbreviated SI, was adopted in 1960 by the 11th meeting of the General Conference on Weights and Measures, the international body that determines standards for measurements. Member states (including the US) agree to abide by the conference’s decisions. At the core of the SI unit are metric units, such as the meter and gram and second, and the prefixes modifying those units, such as nano- and milli- and kilo-, and their abbreviations. Thus, for most sciences, the base unit of meters (abbreviated “m”) for length, grams (g) for mass and seconds (s) for time describe most measurements accurately and precisely. Additional units for other quantities have been introduced over time, such as Newtons (N) for force and Joules (J) for energy. Appendix A contains the relevant SI units for this book. In astronomy and space sciences, the meter is quite a short distance. The diameter of a planet may be several million meters: for instance, the Earth’s diameter is about 12,756,000 m which is quite a large number. Writing it, let alone calculating with it, is a chore. There are two ways to address the issue of large numbers: (1) Use the appropriate SI prefix. 12,756,000 m is the same thing as 12,756 km (kilometers) or even 12.756 Mm (megameters). These metric conversions are based on the amount represented by each prefix: the “k” in km stands for “kilo-“ which means “thousand”. Thus 12,756 km equals 12,756 thousand meters or 12,756,000 m. Even larger distances require different prefixes: The distance from the Sun to the Earth, on average, is around 149,600,000,000 m, which is 149,600,000 km, which is 149,600 Mm, which is 149.6 Gm (gigameters). (2) However, a lot of the prefixes are not commonly used with distances, so we can fall back on non-SI unit systems. With interplanetary distances, the standard distance is an astronomical unit (AU), adopted by the International Astronomical Union in 1976. This distance has been defined as the average distance of the Earth to the Sun (there are, recently, more precise definitions), so the Earth is about 1 AU from the Sun, whereas Mars is about 1.4 AU from the Sun. Note how much easier it is to make the comparison between Earth’s distance from the Sun and Mars’s distance from the Sun using AU rather than comparing 149,600,000 km with 229,000,000 km. There are even more informal measurement systems. You’ll hear about an asteroid coming within seven “moon-Earth” distances of colliding with the Earth. Or that a newly-discovered exoplanet is 1.5 “Earth-diameters” in size. Regardless of which solution is chosen, there is still the issue of how to do calculations with these sometimes-large numbers. Often, a formula to calculate some exciting quantity will require that the input values be in certain units. When this is the case, rarely will the number be enterable on a calculator keypad (or tedious to do so on a keyboard).

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Scientific notation was developed to address this issue. Suddenly, numbers like 149,600,000,000 could be reduced to a more manageable (and calculator-friendly) 1.496 × 1012. In fact, using scientific notation allowed quick comparisons (and estimations) of order of magnitude, so “Which number is bigger?” and “About how much is it bigger?” became manageable questions. The special section on scientific notation will explain the details of how to write a number in this notation, and how to enter such a number in a calculator (see “Scientific Notation and the SI System” box). To return to the idea of comparisons, consider the atom, which is the building block of all materials. The size of an atom is roughly 100 picometers (100 pm) or 0.1 nanometers (0.1 nm). Expressing this number in scientific notation and in units of meters, the size of an atom is 1 × 10–10 m (the negative exponent indicates the number is a fraction of 1). On the other hand, the Milky Way galaxy, the one in which we reside and of which the Sun is but one of a couple hundred billion stars, is roughly 100,000 light years (100,000 ly). Using unit conversions (specifically, the conversion factor 1 ly = 9.46 × 1015 m), you can express the size of the Milky Way galaxy as

100,000  𝑙𝑦  9.46  ×  10!"  𝑚

1  𝑙𝑦 = 9.46  ×  10!"  𝑚

Note that 9.46 × 1020 m is roughly 1 × 1021 m. Now compare the Milky Way Galaxy to an atom. How much bigger is the galaxy than the atom? The Milky Way Galaxy is !  ×  !"!"

!  ×  !"–!"= 1  ×  10!" times bigger than the atom.

In standard notation, that would be 10,000,000,000,000,000,000,000,000,000,000 times bigger. In this book, both atoms and galaxies are discussed so having scientific notation will allow a more succinct discussion. We’ll leave numbers for the moment, and begin tackling some large concepts. Though I am presenting the following ideas of physics in a purely qualitative sense, there is a robust mathematical treatment for all of these laws. A trilogy of three laws is the basis of the physics needed in this book Physics is the science that studies motion and energy in all its forms, and how it may change between those forms. Even as you read this (assuming you are reading this electronically), the electrical energy is being converted into light energy by the screen. Physicists study the quantitative relationship between different forms of motion and energy. A relationship in a set of motions that leads to predictable results is a theory. Like all scientific theories, it can be falsified – this means that it is possible to see or measure a

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different outcome than a result predicted by the theory – and it can be tested and the outcomes repeated. Like all physics theories, it can be quantified, meaning that the theory’s predictions are not vague claims, but precise numerical statements. Natural philosophers, the precursors to physicists who dabbled in many different sciences, deemed particularly useful theory “laws”. The significance of a law, as opposed to a theory, seems to be its widespread applicability. But at the heart, a law is simply a theory – falsifiable, testable, repeatable and quantifiable. There are three sets of three laws that will help you understand the notion of space travel – Kepler’s Three Laws of Planetary Motion, Newton’s Three Laws of Motion and the Three Laws of Thermodynamics. The first two will be covered in detail in other parts of the book; we shall reveal the last one here. Thermodynamics is the subdiscipline of physics that studies the nature and movement of heat energy. For instance, a flame will transfer its heat energy to the pot of water above it. Measuring the increasing temperature of the water is evidence that heat is flowing out of the flame and into the water. A lot of research in the nineteenth century went into working out the details of the three laws of thermodynamics. It is not coincident that the Industrial Revolution in Europe was occurring during the same decades – thermodynamics is at the core of the conversion of the stored energy in fuels (such as burning wood or coal) into the motion energy of an engine, a principle that drove engineers of the time into designing more and more efficient engines. Because of the widespread interest in the topic, there is not one person’s name associated

with the three laws (as is the case with Kepler’s Laws or Newton’s Laws). For instance, the statement of the first law of thermodynamics is attributed to the English physicist James Joule, who published it in 1845. This was based on a famous experiment he had done the previous year in which he was able to melt ice in a sealed flask (like a Thermos) only using a paddle in the flask turned by a crank – he showed that heat could be “made” from mechanical energy. His apparatus is shown to the left.

The notion of the “heat equivalent” amount of mechanical energy had been raised two decades prior by French engineer Sadi Carnot.

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The first law of thermodynamics is called a conservation principle. “Conservation” means that a measureable quantity, in this case energy, does not change during a process. A ball at a height has a certain amount of potential energy. When dropped, the ball loses potential energy but gains kinetic energy such that the sum of its potential and kinetic energies is equal to the original amount of potential energy it had. When the ball hits the ground, its potential energy is gone, and it stops so it loses all its kinetic energy. However, the sound the ball gives off and the heat it imparts to the floor due to the collision are energies that add up to the original amount of potential energy. In short, energy is neither created nor destroyed; it only changes form. The second law of thermodynamics is often called the definition of entropy, which is a measure of disorder in a system. Using this idea, the second law states that the total amount of entropy in the universe is continually increasing. The second law can also be stated as heat flow, the property that allows a hot object to warm a cooler object. Whichever statement is used, the second law helps to explain the presence of volcanoes, earthquakes and mountain ranges on the Earth’s surface – it’s how the heat at the core of the Earth eventually reaches the cool of space. Both statements of the second law are attributed to German physicist Rudolf Clausius, who published the heat flow statement in 1850 and the entropy statement in 1865. The third law of thermodynamics is the simplest: it states that no system can achieve absolute zero, the temperature at which there is no motion, not even small atomic vibrations. This definition gave rise to the Kelvin temperature scale: zero Kelvins (not “degrees Kelvin”) is equivalent to – 273° Celsius. Abbreviated, that’s 0 K = –273°C. In fact, it’s simple to convert between Kelvin and Celsius temperature scales: to go from °C to K, simply add 273 to the °C temperature. To go from K to °C, subtract 273 from the K temperature. The statement of the third law is attributed to German physicist Walther Nernst, who published it in 1906. The combination of the second and third laws of thermodynamics effectively destroys the notion of a perpetual motion machine – a machine that continues to run (forever, in fact), even when it has no input of energy. We end this chapter on this note: the Three Laws of Thermodynamics are the basis of every technology developed since the steam engine. The deeper meaning here is the difference between science and engineering. Science is a methodology to study natural phenomena, like how heat moves from the atmosphere to the ground and back again. If there are a sufficient number of observations of heat movement behavior, then the scientists can develop a general theory about how heat transfer is supposed to work. As every fifth-grader knows, then the theory must be tested by other scientists and its predictions must match experimental observations, otherwise the theory must either be revised or, rarely, discarded entirely.

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The work of the engineer begins when the scientists have developed a good theory (that is, one that has been tested, replicated and thought by most scientists to be an accurate description of the natural phenomenon). Engineering is the discipline that develops technology based on a scientific theory – for instance, utilizing the understanding of heat transfer to make a steam engine. Though it seems from the description above that engineers wait around for scientists to come up with the next great theory, in practice the relationship between scientists and engineers is more symbiotic – engineers, using current theories, develop more advanced technology for making better observations that, in turn, help scientists develop more complete theories. In this textbook, I have talked to many scientists and engineers; interestingly, a number of them started off as a science major or an engineering major, then later in their careers, ended up doing the other thing. The common point in both career paths was a strong foundation in calculus, physics and chemistry. Even if your interests lie more towards biology or medicine, finance or business, design or archiving, the knowledge of the mathematical nature of the physical sciences is a crucial lynchpin. So let’s get started using some of the math tools in this chapter to explain a bit about how we even make observations of distant worlds.