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What holds regions of the Universe together? Gravity. In this lesson, we set the physical foundations of astronomy, the laws that govern how everything moves and the forces involved. Chapter 2 of the text includes a brief history on how gravity was "discovered," and how we use the effect of one body upon another to determine mass.
After completing this lesson, you should be able to
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There is probably no way of getting around it—this lesson may be the hardest one of the course. On the other hand, it may also be the most enjoyable! Astronomy today is the application of the physics we know on Earth to objects and events in the Universe. The best part of this statement is that we do not need to learn any new physics; whether we are here or 15 billion light years away, it appears that the Universe operates under one set of rules. If you stop to think about it, this is truly amazing. Many students cringe at the mere mention of the word "physics," but we hope to prove that any apprehension you may have is uncalled for. We all use physics everyday. We all know about the physics, perhaps not in formal terms, but in indirect ways.
By studying all of the basic physical information in one lesson, when you read about how these things work in astronomy, you will be better prepared to concentrate more on the unfamiliar, more on the actual astronomy. Hopefully in this manner you will reach a higher level of understanding about how our universe works. We start our study with gravity.
It may seem strange, but gravity is one of the least understood forces in the Universe. Physicists understand the basics of three fundamental forces of the Universe—the electromagnetic, strong, and weak forces—but not the fourth, gravity. What holds up our knowledge is linking gravity to quantum mechanics; that is, we don't understand the very nature of what produces gravity.
Here is what we do know:
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The text covers the information on Kepler to the extent that we need to know about his work for this course. Kepler's laws of planetary motion apply more to a course on planetary astronomy, and even then on only a preliminary basis. It is highly recommended, however, that you take some time working with the demonstrations of orbits given in the relevant links for this lesson. They are educational and fun.
When reading about Kepler, remember that the term "gravity" had no meaning to him. The scientists of his day knew little about how things really worked, they were able only to mathematically describe what they observed. It took the genius of Newton to set matters straight.
Whether or not the apple actually fell on Newton's head may never be known; however, his observing objects falling to the Earth led him to extend that knowledge to the possibility that the force that caused the apple to fall might extend to the Moon. And, if the force extended to the Moon, why not the Sun? One of the cool facts of physics is that objects all fall with the same acceleration to the Earth. If you hit a tennis ball horizontally while simultaneously dropping one straight down, both balls will hit the Earth at exactly the same time. Keep hitting the tennis ball harder and harder, and it will fall farther and farther away from you. Now, climb Mt. Everest, anchor yourself, and hit the tennis ball harder and harder. Each time it falls farther away. What if you could hit it so hard that it fell all the way around the Earth? Fig. 2.11, in your textbook, examines this question in more detail.
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Newton calculated that the force of gravity diminished as the inverse of the distance squared from the center of the Earth. In his time, scientists knew the approximate distance to the Moon and, of course, how long it took to make one orbit about the Earth. From these calculations, Newton could calculate the acceleration of the Moon in its orbit and it agreed with his law of gravity. Success! Science at its best!
Newton's Law of Gravity: The (equal and opposite) force of gravity felt by two objects is proportional to the product of the two masses divided by their distance apart (from their centers) squared.
Newton's Three Laws of Motion: As you read through the section on Newton's three laws of motion, in your textbook, stop after reading about each one and express the law in terms of what happens with the momentum of the object.
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Although matter seems like an "obvious" concept in everyday life, it is really quite subtle. Matter generally consists of atoms, which consist of a nucleus made of protons and neutrons and a "smeared out" cloud of electrons. The nucleus is very tiny compared to the cloud of electrons. Each chemical element has a different atomic number, which is the number of its protons. The atomic weight (or atomic mass) of an atom is the combined number of its protons and neutrons. Atoms with different atomic weights but the same atomic number are called isotopes of one another. An electrically neutral atom must have a number of electrons that is equal to its atomic number, since protons are positively charged and electrons are negatively charged. We visit atoms in more detail when we get to the chapter on light and how it is created.
Matter can exist in the different phases. Most matter is solid at very low temperatures. At higher temperatures it may become a liquid or a gas. The process of solid matter losing some atoms (or molecules) to the gas phase is called sublimation; the process of a liquid losing atoms (or molecules) to the gas phase is called evaporation. If the matter consists of molecules made from two or more atoms, at relatively high temperatures the molecules will dissociate into individual atoms, a process called molecular dissociation. At very high temperatures, e lectrons may be stripped from atoms in what we call ionization. A gas that consists of ions (the leftover atoms that are missing one or more of their electrons) and free electrons is called a plasma.
Another description for matter is that "stuff that has mass." Whatever form that matter might be in, it can be described by its energy and its momentum.
We have a good sense of matter and energy from our everyday experience. We measure energy in units of Calories (such as provided to us by food), kilowatt-hours (that measure the amount of electrical energy we use), or joules (the favored unit for measuring energy in science). Energy comes in many forms. Three of these are: kinetic energy, which is energy of motion; potential energy, which represents energy stored for later conversion into kinetic energy; and radiative energy, which is energy carried by light.
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Potential energy is energy being stored for later conversion into kinetic energy. Kinetic energy is energy of motion. A ball has gravitational potential energy when it sits on a ledge. The instant before the ball hits the floor, all of its energy is in the form of kinetic energy. Where does that energy go? Into thermal energy heating the ball as it compresses and heating the floor. If the ball is elastic, some of the kinetic energy is converted to elastic energy and then kinetic energy again as the ball bounces. As the ball rises, the kinetic energy is converted back to potential energy. Let's consider another (more painful) example. It doesn't take a rocket scientist to convince you that it hurts much, much more if you fall from the top of a high step ladder versus falling out of a chair. That gravitational potential energy gets converted to kinetic energy which is converted to thermal energy and breaking-bone energy (perhaps, if you aren't lucky) as you hit the floor.
The gravitational potential energy (GPE) of an object, depends on its mass (m) , the strength of the gravity (g), and the distance the object falls (h). The kinetic energy (KE) of an object equals one-half times the mass of that object (m) times the velocity of the object squared (v2).
Let's take a look at gravitational potential energy (GPE) and kinetic energy (KE) in mathematical form:
GPE = mgh KE = 1/2 mv2
The more massive the object, or the stronger the gravity, or the higher it is, the more gravitational potential energy it has. The more massive the object or the more velocity it has, the more kinetic energy it has. The kinetic energy of an object is very dependent upon its velocity:
2 times the velocity, 4 times the KE 3 times the velocity, 9 times the KE 10 times the velocity, 100 times the KE!
Thermal energy, or the energy of heat, is actually a form of kinetic energy since all the individual particles in a warm substance are moving. The temperature measures the average kinetic energy of the moving particles, while the total thermal energy (heat content) depends on both the temperature and the density of particles. Thus, a sidewalk may be too hot to walk on barefoot, although you can hold your foot just above it without any injury. Another example can be found in the corona of the Sun. The temperature of the corona is millions of degrees Kelvin, yet one could theoretically pass through it without being burned because the density is very low, about one-billionth that of the Earth's atmosphere at sea level.
As an object heats up, the thermal energy is transferred to the particles. The particles absorb this energy and convert it to kinetic energy. The more heat that is applied, the faster the particles move. One of the laws of thermal dynamics is that heat flows from hot objects to cold objects. This law explains why your bath water gets cold, and it also explains why huge clouds of gas and dust that will someday form stars cool and contract.
Simply put, radiative energy is energy carried by light. At radio wavelengths, radiation carries little energy. On the other hand, at x-ray and gamma ray wavelengths, the amount of energy is damagingly high. Radiative energy is used to generate electrical energy in solar cells, such as those used in calculators.
Radiation is often used as a synonym for light. The most valuable source of radiative energy for life on Earth is the Sun. The Sun annually produces enough energy to power about 1031, 100-watt bulbs for a year. It produces about 100,000,000,000,000 more energy a year than the United States consumes: a huge, basically untapped source for our future needs.
Electric potential energy is the energy stored when negative and positive charges are separated. The amount of electric potential energy would depend on the number of charges on each surface and the distance they are apart. Electrons in an atom contain electric potential energy. When an electron absorbs energy in the form of a photon (a discrete unit of light energy), it moves to a "higher energy level." The atom is in an "excited state." To move to a lower energy state, the electron must give up its energy in the form of a photon having a specific amount of radiative energy.
To really understand how electrons gain and lose energy in an atom, we need to know a little bit about the fascinating field of quantum mechanics. You will be introduced to quantum mechanics and the more accurate way of viewing an atom in Lesson Four, when we talk about spectra and how light is formed. For now, though, let's do a comparison between gravitational potential energy and electric potential energy. Although there are some easy-to-understand similarities, there are also some striking differences.
View a Comparison of Electric Potential Energy and Gravitational Potential Energy.
One of the most important laws of nature is the law of conservation of energy, which states that energy can neither be created nor destroyed. It can only be converted form one form to another.
This law is not too hard to understand until one thinks, "Where did the energy come from originally?" According to the Big Bang theory, all of the energy in the present universe was created during that initial burst. Some of that energy went into creating mass: protons, neutrons, and electrons. Some of that energy stayed as energy in various forms: neutrinos and radiative energy. During nuclear fusion in the cores of stars, some of the mass gets converted back to energy. Earth receives energy from the Sun. The plants soak it up during photosynthesis. We draw upon that energy when we eat a salad, or burn wood in our fireplace. The original nuclear energy turned into radiative energy which was turned into chemical energy which may have been turned into kinetic energy, and so on.
Consider the various positions of the planet as it orbits the star as shown. With
respect to the star, in which position does the planet have the maximum a) speed,
b) velocity? c) momentum? d) kinetic energy? e) gravitational potential energy?
f) total energy?
From the text:
Gravity
Kepler and Orbits
Newton
