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Delve into the wonders of astronomy, the scientific method, and scientific notation. Learn how science and technology shape our understanding of the cosmos.
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Science has to do with the discovering of relationships in nature. Scientists are not concerned with people's opinions of what they are doing. A scientist searches for physical facts and truths regardless of whether they are "useful" to the public or not. Technology deals with the tools, techniques, and procedures for making practical use of the facts that science discovers. Technology emphasizes "people" and is only concerned with what is practical and useful to people. Technology is very concerned with the reactions of the public. If people will not like it ‑ technology stays away from it. Science and Technology
Simply put, it is the study of the material universe that is above the Earth's atmosphere. Physics, astronomy, mathematics and even religion were intertwined early in the development of modern science. The “father of modem science”, Galileo, was both an astronomer and physicist. What is Astronomy?
Astronomy vs. Astrology • Be careful not to confuse astronomy – the natural science studying the universe above the Earth’s sky – with astrology - a pseudoscience claiming divination by the positions of the planets and sun and moon. • While the zodiac is an astronomical term, horoscopes are not scientific and have no significance in astronomy.
Science and Math About 400 years ago, it was discovered that much of nature could be described and analyzed mathematically. When scientific ideas are expressed mathematically, then the ideas become unambiguous (i.e. very clear). Science became a great success when mathematics and experimentation were united with it. • The Scientific Method • 1. Recognize a problem. • 2. Make an educated guess ‑ a hypothesis. • 3. Predict the consequences of the hypothesis. • 4. Perform experiments to test the predictions. • Make the simplest general rule that organizes • the hypothesis, prediction, and experimental outcome. • Science is "self‑correcting". If the results of the experiments contradict the • hypothesis, then there is a problem and the scientist returns to step 1. In step • 2, the previous hypothesis must either be revised or discarded altogether.
Not all great scientific discoveries are made by following the "scientific method". Sometimes great progress is made in science by trial and error, experimentation with guessing, or "by accident" (i.e. good luck). Roentgen discovered X‑rays by accident! Fact: a close agreement by competent observers of a series of observations of the same phenomena. Hypothesis: an educated guess; not accepted as factual until successfully checked out over and over again by experiment by many different scientists. Law or Principle: a statement about the relationship between natural quantities that has been tested over and over again and has not been contradicted. Theory: a large body of information that encompasses well‑tested and verified hypotheses about certain aspects of the natural world.
Scientific Notation When scientists work with very large or very small numbers, they use a system called scientific notation. This shortens numbers by substituting powers of 10 in place of long strings of zeros. For example: Number DecimalScientific Notation 45,000,000 4.5 x 107 0.0000000813 8.13 x 10‑8 36,000 3.6 x 104 0.000005421 5.421 x 10‑6 Can you figure out how to write these numbers below in scientific notation? Give it a try.
Wavelength of red light is 0.00000065 m. Wavelength of green light is 0.00000050 m. The nearest star, Alpha Centauri (Proxima), is 43,000,000,000,000 kilometers (km) away. The nearest large galaxy, Andromeda, is 2.2 million light‑years away, ...or 22,000,000,000,000,000,000 km away. Venus is 40,000,000 km from the Earth. The radius of the Earth is 6378 km. The diameter of the sun is 1,392,000 km. Length of a white blood cell is 0.00001 cm.
6.5 1.392 1 Wavelength of red light is 0.00000065 m. Wavelength of green light is 0.00000050 m. The nearest star, Alpha Centauri (Proxima), is 43,000,000,000,000 kilometers (km) away. The nearest large galaxy, Andromeda, is 2.2 million light‑years away, ...or 22,000,000,000,000,000,000 km away. Venus is 40,000,000 km from the Earth. The radius of the Earth is 6378 km. The diameter of the sun is 1,392,000 km. Length of a white blood cell is 0.00001 cm. 5.0 4.3 2.2 4 6.378
Constellations • A natural human tendency is to see patterns and relationships between objects even when no true connection exists, and people long ago connected the brightest stars into configurations called constellations. • In the Northern Hemisphere, most constellations were named after • mythological heroes and animals. (e.g. Greek mythology - Orion) • The stars making up a particular constellation are generally NOT close • together in space. They merely are bright enough to observe with the • naked eye and happen to lie in the same direction in the sky as seen from • Earth. • Constellations provide a convenient means for astronomers to specify • large areas of the sky, much as geologists use continents
The Celestial Sphere Over the course of a night, the constellations appear to move across the sky from east to west, but the relative positions of stars remain unchanged. It was natural for the early astronomers to conclude that the stars were attached to a celestial sphere surrounding Earth—a canopy of stars like an astronomical painting on a heavenly ceiling. Figure P.2 The Celestial Sphere Planet Earth sits fixed at the hub of the celestial sphere, which contains all the stars. This is one of the simplest possible models of the universe, but it doesn’t agree with the facts that astronomers now know about the cosmos.
The apparent motion of the stars is the result of the spin, or rotation, of the Earth. Even though the celestial sphere is an incorrect description of the heavens, we still use the idea as a convenient fiction that helps us visualize the positions of stars in the sky. The point where Earth’s axis intersects the celestial sphere in the Northern Hemisphere is known as the north celestial pole; it is directly above Earth’s North Pole. In the Southern Hemisphere, the extension of Earth’s axis in the opposite direction defines the south celestial pole. Midway between the north and south celestial poles lies the celestial equator.
The star Polaris, often called the “North Star”, indicates the direction—due north—in which the axis of Earth’s rotation points.
Celestial Coordinate System – Method 1 • The simplest method of locating stars in the sky is to specify their • constellation and then rank the stars in it in order of brightness. The • brightest star is denoted by the Greek letter (alpha), the second brightest • by (beta), and so on. • Because there are many more stars in any given constellation than there are • letters in the Greek alphabet, this method is of limited utility. However, for • naked-eye astronomy, where only bright stars are involved, it is quite • satisfactory.
Celestial Coordinate System – Method 2 • If we think of the stars as being attached to the celestial sphere centered on Earth, then the familiar system of latitude and longitude on Earth’s surface extends quite naturally to the sky. The celestial analog of latitude is called declination, and the analog of longitude is called right ascension. • Just as latitude and longitude are tied to Earth, right ascension and declination are fixed on the celestial sphere. So the stars may appear to move across the sky because of Earth’s rotation, but their celestial coordinates remain constant. over the course of a night. North Celestial Pole Right Ascension Lines Earth Declination Lines Celestial Equator South Celestial Pole Declination is measured in degrees. Right ascension is measured in hours, minutes and seconds.
A Solar Day vs. A Sidereal Day Sun Earth Earth’s orbit One sidereal day later (aligned with stars) One solar day later (aligned with Sun)
Short-Term (Daily) Changes • I. The sun rises in the east and sets in the west each day due to the Earth's • rotation. Length of day varies with season. • II. The moon rises in the east and sets in the west each day due to the • Earth's rotation. Moonrise is about 50 minutes later each day. • III. The planets rise in the east and set in the west each day due to the • Earth's rotation. The times will depend on the rate of the planet's motion • with respect to the stars. • IV. The stars rise in the east and set in the west each day due to the • Earth's rotation. At our 40o latitude, some stars never set. They are • called circumpolar stars. A timed‑exposure picture of the night sky • shows that the stars appear to rotate about the "north star" (Polaris). • Star rise is about 4 minutes earlier each day.
Seasonal Changes • In six months Earth moves to the opposite side of its orbit, and • we face an entirely different group of stars and constellations • at night. Because of this motion, the Sun appears, to an observer • on Earth, to move relative to the background stars over the course • of a year. This apparent motion of the Sun on the sky traces out • a path on the celestial sphere known as the ecliptic. North Celestial Pole • The 12 constellations • through which the Sun • passes as it moves along • the ecliptic — that is, the • constellations we would • see looking in the direction • of the Sun if they weren’t • overwhelmed by the Sun’s • light — are collectively • known as the zodiac. The ecliptic lays in the plane of Earth’s orbit around the Sun. Earth 23 ½ o Celestial Equator South Celestial Pole
Autumnal Equinox Winter Solstice Sun Summer Solstice Vernal Equinox Plane of the Ecliptic autumnal equinox The Earth’s orbital plane as seen from above the north pole. The orbit’s ellipticity has been greatly exaggerated for clarity. winter solstice Sun aphelion perihelion summer solstice vernal equinox
The Solstices • The point on the ecliptic where the Sun is at its northernmost point above • the celestial equator is known as the summer solstice. This occurs on or • near June 21—the exact date varies slightly from year to year because the • actual length of a year is not a whole number of days. On that date, • points north of the equator spend the greatest fraction of their time in • sunlight, so the summer solstice corresponds to the longest day of the • year in Earth’s Northern Hemisphere and the shortest day in Earth’s • Southern Hemisphere. • Six months later the Sun is at its southernmost point below the celestial • equator. We have reached the winter solstice (December 21), the • shortest day in Earth’s Northern Hemisphere and the longest in the • Southern Hemisphere.
The Equinoxes • The two points where the ecliptic intersects the celestial equator are • known as equinoxes. On those dates, day and night are of equal • duration. (The word equinox derives from the Latin for “equal night.”) • In the fall (in Earth’s northern hemisphere), we have the autumnal • equinox (on September 21). The vernal equinox occurs in spring, on or • near March 21, as the Sun crosses the celestial equator moving north. • The vernal equinox plays an important role in human timekeeping. The • interval of time from one vernal equinox to the next—365.242 solar • days—is known as one tropical year.
Long-Term Changes • The time required for Earth to complete exactly one orbit around the Sun, • relative to the stars, is called a sidereal year. One sidereal year is 365.256 • solar days long, about 20 minutes longer than a tropical year. The reason for • this slight difference is a phenomenon known as precession. Like a spinning • top that rotates rapidly on its own axis while that axis slowly revolves about • the vertical, Earth’s axis changes its direction over the course of time.
Earth’s precession is caused by the combined gravitational pulls of the • Moon and the Sun and a complete cycle of precession takes about 26,000 • years. • Because of this slow shift in the orientation of Earth’s rotation axis, the • vernal equinox drifts slowly around the ecliptic over the course of the • precession cycle. So the seasons slowly shift - eventually January will be • a summer month and Orion will be a summer constellation! • This precession also causes the pole star to change over time. For • example, in the year 14,000 AD, Vega will be our pole star.
Measuring the Night Sky One distance-measurement method is called triangulation. It is based on the principles of Euclidean geometry and finds widespread application today in both terrestrial and astronomical settings. Knowing two angles in a triangle and the length of the side shared by the angles (called the baseline in the diagram), then the lengths of the other two sides of the triangle can be determined.
The apparent displacement of a foreground object relative to the background as the observer’s location changes is known as parallax. The closer an object is to the observer, the larger the parallax. The amount of parallax is inversely proportional to an object’s distance. Small parallax implies large distance. Conversely, large parallax implies small distance. So parallax is a powerful method for measuring astronomical distances.
When an object is nearby, it spans a greater arclength than when it is far away. The ball has an angular diameter of when it is close by, and an angular diameter of , which is smaller, when it is far away. The angular diameter of an object will depend on its distance.
Simple Measuring Instruments • The unit used to measure angles in astronomy is the degree. There are 3600 • in a circle. Each degree is divided into sixty equal parts called minutes (or • arcminutes). Each minute is divided into sixty equal parts called seconds • (or arcseconds). So we have: 1 arcminute = 1/60th degree 1 arcsecond = 1/60th minute = 1/3600th degree
mirror 1 C A mirror 2 eyepiece B moveable arm vernier O • Sextant • A sextant provides two coordinates for position of object in sky: often • elevation (or altitude) which is the angle above the horizon, and azimuth • which is the angular position along the horizon, measured clockwise from • north.
The Human Hand • While not terribly accurate, can be used to estimate angles in the sky.
Horizon and Zenith The horizon is the imaginary line where the sky and earth meet if there were no terrain in the way ‑ ocean level at the shore is the horizon. The zenith is the point directly overhead (altitude angle = 900).
Measuring the Size of the Earth, Moon and Sun • Eratosthenes, a Greek mathematician and geographer, measured the • circumference of the Earth (235 B.C.) to within 5% of our modern day • estimate.
Aristarchus measures the moon's diameter and distance from the Earth by watching eclipses of the moon (240 B.C.) He was also within 5% of the modern day accepted values.
Aristarchus measured the sun's diameter and distance from the Earth by taking angular measurements when the moon was half full. (His results were not as successful here because of his crude measurements and perhaps his bias. He determined the sun to be 20 times more distant than the moon, when in fact it isreally 400 times more distant.)
Gerver's Method for Measuring the Earth's Diameter at the Ocean Shore Apparatus: a pointed rock on a hill, a line of string, a meterstick
Procedure: 1. Find a hill that gives you a clear view of the ocean horizon in opposite directions (a peninsula) with a pointed rock at the top. Ideally the hill should be between 100 and 1000 feet above sea level. 2. Mount the meterstick upright about 15 ft. from the pointed rock. Measure this distance exactly. This is b. 3. Stand on the other side of the meterstick from the rock and adjust your eyelevel until the pointed rock lines up with the ocean horizon. Note where your line of sight intersects the ruler. (The string may be helpful for this.) 4. Now move to the other side of the rock and repeat step 3. The distance between the two points of intersection on the meterstick is a. 5. Your height above sea level is h. If you don't know your height above sea level, then you will have to come up with some clever means of determining it. Perhaps you can devise a geometry trick similar to this method in order to calculate it.
6. Calculate the radius of the Earth as approximately 8hb2 /a2 . Because of light refraction in the atmosphere, your sighting of the horizon will be in slight error. This refractive effect makes Gerver's computed radius too large by about 20%. So the radius of the Earth will be closer to But if a<<b, then the radius of the Earth can be approximated as:
Rawlins' Method for Measuring the Earth's Diameter at the Ocean Shore CAUTION: This procedure requires you to "watch" a sunset. Even at sunset looking directly into the sun for any length of time can harm your eyes. The greatest danger is from the ultraviolet radiation which is invisible to your eye and can cause damage to your eye before you feel any pain. Keep track of the sun's motion by looking off to the side of it, or by giving it an occasional quick glance. It is best to not gaze until the sun is mostly below the horizon. You may wish to consider purchasing "eclipse glasses" from a scientific company or getting an appropriate welding shield from a welding supply store. Apparatus: stopwatch, meterstick
Procedure: (NOTE: Use standard S.I. Units…meters for distances and seconds for time.) 1. Find a place where you have a clear view of the sunset* on a beach or one of the Great Lakes. The water should be calm the day you perform your measurements. Approximate the height of the waves on the ocean in meters. This amount is ho, It will probably be about 0.6 meters or so. 2. Observe the first sunset while sitting on the beach. (Laying down to observe is possible, but only if the body of water is particularly calm.) Measure the height of your eyes above sea level. This amount is h1. 3. As soon as the last visible part of the sun ducks below the horizon, start your stopwatch and run quickly up the steps on the boardwalk to a higher elevation. (Simply jumping to your feet raises you eyelevel some ‑ perhaps enough if you are very accurate with the stopwatch.) * This procedure is for sunset. Appropriately revising the procedure should work for sunrise.
4. Being at a higher elevation, you will see the sun set AGAIN! Stop the stopwatch as soon as you see the last visible part of the sun duck below the horizon. The time on your stopwatch is t. The height of your eyes above sea level at this new observing position is h2 5. A couple of corrective factors must be made since the speed at which the sun sets will depend on your latitude and what time of year it is. To account for these, find the values for A and B in the charts below that correspond to your latitude and date (or as close to it as you can approximate). There is also an error due to the refraction of light caused by the Earth's atmosphere. This will be approximately accounted for in the equation below, so you don't have to worry about it. 6. Calculate the radius of the Earth as:
