Class Information for PHYS/ASTR 1050 can be found at: www.physics.utah.edu/ Click on students Click on courses Then follow link to your class Everything about the class HW, Exams, Syllabus, etc can be found on the class Homepage.

The Solar System Knowing the Heavens

The Night Sky 1/27/17 1-hr after sunset, Colorado Springs

Ursa Major — The Big Dipper Figure 2-6 The Big Dipper as a Guide The North Star can be seen from anywhere in the northern hemisphere on any night of the year. This star chart shows how the Big Dipper can be used to point out the North Star as well as the brightest stars in two other constellations. The chart shows the sky at around 11 P.M. (daylight savings time) on August 1. Due to the Earth’s orbital motion around the Sun, you will see this same view at 1 A.M. on July 1 and at 9 P.M. on September 1. The angular distance from Polaris to Spica is 102°.

The Winter Triangle Figure 2-7 The “Winter Triangle” This star chart shows the view toward the southwest on a winter evening in the northern hemisphere (around midnight on January 1, 10 P.M. on February 1, or 8 P.M. on March 1). Three of the brightest stars in the sky make up the “winter triangle,” which is about 26° on a side. In addition to the constellations involved in the triangle, the chart shows the prominent constellations Gemini (the Twins), Auriga (the Charioteer), and Taurus (the Bull).

Why are stars tracing out circles in the sky? Is the Earth rotating CCW about an axis? or is the sky rotating CW around Polaris? The Earth’s rotation makes stars appear to trace out circles in the sky. (Gemini Observatory)

Question Which of the following heavenly objects remains fixed in the sky relative to an observer's horizon? Polaris, the north star. the Moon. the Sun. Mars. the Primum Mobile.

The Celestial Sphere — A crystalline sphere in which all the stars are embedded surrounds the Earth and rotates CW once every ~24 hr!

Latitude & Longitude Salt Lake City: 410 N. 1120 W. Earth’s surface is 2-d Require only 2 numbers to specify a location. Those 2 numbers are angles.

Celestial Coordinates Box 2-1 Celestial Coordinates Your latitude and longitude describe where on the Earth’s surface you are located. The latitude of your location denotes how far north or south of the equator you are, and the longitude of your location denotes how far west or east you are of an imaginary circle that runs from the north pole to the south pole through the Royal Observatory in Greenwich, England. In an analogous way, astronomers use coordinates called declination and right ascension to describe the position of a planet, star, or galaxy on the celestial sphere. Declination is analogous to latitude. As the illustration shows, the declination of an object is its angular distance north or south of the celestial equator, measured along a circle passing through both celestial poles. Like latitude, it is measured in degrees, arcminutes, and arcseconds (see Section 1-5). Right ascension is analogous to longitude. It is measured from a line that runs between the north and south celestial poles and passes through a point on the celestial equator called the vernal equinox (shown as a blue dot in the illustration). This point is one of two locations where the Sun crosses the celestial equator during its apparent annual motion, as we discuss in Section 2-5. In the Earth’s northern hemisphere, spring officially begins when the Sun reaches the vernal equinox in late March. The right ascension of an object is the angular distance from the vernal equinox eastward along the celestial equator to the circle used in measuring its declination (see illustration). Astronomers measure right ascension in time units (hours, minutes, and seconds), corresponding to the time required for the celestial sphere to rotate through this angle.

Stars You Can See Depend on Latitude Figure 2-10 The View from 35° North Latitude To an observer at 35° north latitude (roughly the latitude of Los Angeles, Atlanta, Tel Aviv, and Tokyo), the north celestial pole is always 35° above the horizon. Stars within 35° of the north celestial pole are circumpolar; they trace out circles around the north celestial pole during the course of the night, and are always above the horizon on any night of the year. Stars within 35° of the south celestial pole are always below the horizon and can never be seen from this latitude. Stars that lie between these two extremes rise in the east and set in the west.

At North Pole, All Stars Above Horizon Never Set Figure 2-11 The Apparent Motion of Stars at Different Latitudes (b) At the north pole (latitude 90° north) the stars appear to move parallel to the horizon.

Stars Rise & Set at Middle Latitudes Figure 2-11 The Apparent Motion of Stars at Different Latitudes As the Earth rotates, stars appear to rotate around us along paths that are parallel to the celestial equator. (a) As shown in this long time exposure, at most locations on Earth the rising and setting motions are at an angle to the horizon that depends on the latitude. (David Miller/DMI)

On Equator, Stars Rise & Set ┴ to Horizon Figure 2-11 The Apparent Motion of Stars at Different Latitudes (c) At the equator (latitude 0°) the stars rise and set along vertical paths.

Day & Night Why? Is the Earth rotating CCW? or is the Sun rotating CW? Figure 2-3 Day and Night on the Earth At any moment, half of the Earth is illuminated by the Sun. As the Earth rotates from west to east, your location moves from the dark (night) hemisphere into the illuminated (day) hemisphere and back again. This image was recorded in 1992 by the Galileo spacecraft as it was en route to Jupiter. (JPL/NASA)

The Night Sky changes slowly throughout the year. Because the Earth moves around the Sun once/year … or the Sun moves slowly ‘backwards’ on the Celestial sphere around the Earth Figure 2-5 Why the Night Sky Changes During the Year As the Earth orbits around the Sun, the nighttime side of the Earth gradually turns toward different parts of the sky. Hence, the particular stars that you see in the night sky are different at different times of the year. This figure shows which constellation is overhead at midnight local time—when the Sun is on the opposite side of the Earth from your location—during different months for observers at midnorthern latitudes (including the United States). If you want to view the constellation Andromeda, the best time of the year to do it is in late September, when Andromeda is nearly overhead at midnight.

Constellations of the Zodiac Note: ‘apparent’ position of Sun in the zodiac … could get same effect with Earth at center and Sun moving around it!

Winter & Summer The Sun is ‘in’ Capricorn on Dec 21 The Sun is ‘in’ Cancer on Jun 21 Figure 2-17 Tropics and Circles Four important latitudes on Earth are the Arctic Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude), Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2° south latitude). These drawings show the significance of these latitudes when the Sun is (a) at the winter solstice and (b) at the summer solstice. An observer on Tropic of Capricorn would see Sun directly overhead at noon. An observer on Tropic of Cancer would see Sun directly overhead at noon.

The Sun at 690 N. July 19 Figure 2-18 The Midnight Sun This time-lapse photograph was taken on July 19, 1985, at 69° north latitude in northeast Alaska. At this latitude, the Sun is above the horizon continuously (that is, it is circumpolar) from mid-May to the end of July. (Doug Plummer/Science Photo Library)

Solar Energy in Summer & Winter Figure 2-13 Solar Energy in Summer and Winter At different times of the year, sunlight strikes the ground at different angles. (a) In summer, sunlight is concentrated and the days are also longer, which further increases the heating. (b) In winter the sunlight is less concentrated, the days are short, and little heating of the ground takes place. This accounts for the low temperatures in winter.

Where is the Sun on the Celestial Sphere? Tropic of Cancer Summer Solstice Autumnal Equinox Equator Vernal Equinox Winter Solstice Tropic of Capricorn

Figure 2-16 The Sun’s Daily Path Across the Sky This drawing shows the apparent path of the Sun during the course of a day on four different dates. Like Figure 2-10, this drawing is for an observer at 35° north latitude. In the winter, Sun rises in SE and sets in SW. It never rises higher than 250 above horizon (SLC). In Spring and Fall, Sun rises in E and sets in W. It rises about 48 ½ 0 above horizon (SLC). In the Summer, Sun rises in NE and sets in NW. It rises about 720 above horizon (SLC).

A ‘Geocentric’ Model 23 ½ 0 Figure 2-15 The Ecliptic, Equinoxes, and Solstices This illustration of the celestial sphere is similar to Figure 2-14b, but is drawn with the north celestial pole at the top and the celestial equator running through the middle. The ecliptic is inclined to the celestial equator by 231⁄2° because of the tilt of the Earth’s axis of rotation. It intersects the celestial equator at two points, called equinoxes. The northernmost point on the ecliptic is the summer solstice, and the southernmost point is the winter solstice. The Sun is shown in its approximate position for August 1.

A ‘Heliocentric’ Model Figure 2-12 The Seasons The Earth’s axis of rotation is inclined 231⁄2° away from the perpendicular to the plane of the Earth’s orbit. The north pole is aimed at the north celestial pole, near the star Polaris. The Earth maintains this orientation as it orbits the Sun. Consequently, the amount of solar illumination and the number of daylight hours at any location on Earth vary in a regular pattern throughout the year. This is the origin of the seasons.

Question Which hypothesis below ‘explains’ why Earth experiences 4 seasons? There are 2: (1) The fast rotating Earth slowly orbits the Sun in a plane that is tipped by 23.5o to its equatorial plane (2) The Sun moves slowly CCW along a plane that is tipped by 23.5o to the equator of the fast rotating celestial sphere. The Sun and the Earth lie in the same plane. The Earth is further away from the Sun in the winter and closer in the summer. The Sun is brighter in the summer than it is in the winter. The Earth’s orbit is perfectly circular.

Precession of a Top Figure 2-19 Precession As the Earth precesses, its axis of rotation slowly traces out a circle in the sky, like the shifting axis of a spinning top.

Precession of Earth’s Axis Figure 2-19 Precession Because the Earth’s rotation axis is tilted, the gravitational pull of the Moon and the Sun on the Earth’s equatorial bulge together cause the Earth to precess.

Projection of Earth’s Axis Onto Celestial Sphere Figure 2-20 Precession and the Path of the North Celestial Pole As the Earth precesses, the north celestial pole slowly traces out a circle among the northern constellations. At present, the north celestial pole is near the moderately bright star Polaris, which serves as the North Star. Twelve thousand years from now the bright star Vega will be the North Star.

Precession of the Equinoxes The Vernal Equinox moves slowly through the zodiac in step with the precession of Earth’s axis

Measuring Time Solar day: Time between 2 ‘transits’ of the local meridian by the Sun. Figure 2-21 The Meridian The meridian is a circle on the celestial sphere that passes through the observer’s zenith (the point directly overhead) and the north and south points on the observer’s horizon. The passing of celestial objects across the meridian can be used to measure time. The upper meridian is the part above the horizon, and the lower meridian (not shown) is the part below the horizon. Sidereal day: Time between 2 ‘transits’ of the local meridian by the Vernal Equinox.

Time Zones ~ 150 Intervals in Longitude Figure 2-23 Time Zones in North America For convenience, the Earth is divided into 24 time zones, generally centered on 15° intervals of longitude around the globe. There are four time zones across the continental United States, making for a 3-hour time difference between New York and California.

Sidereal Time 10 more (3610) for a solar day ~ 24 hr. Time to rotate 10 more is ~ 4 min. Box 2-2 Sidereal Time (a) A month’s motion of the Earth along its orbit If you want to observe a particular object in the heavens, the ideal time to do so is when the object is high in the sky, on or close to the upper meridian. This minimizes the distorting effects of the Earth’s atmosphere, which increase as you view closer to the horizon. For astronomers who study the Sun, this means making observations at local noon, which is not too different from noon as determined using mean solar time. For astronomers who observe planets, stars, or galaxies, however, the optimum time to observe depends on the particular object to be studied. The problem is this: Given the location of a given object on the celestial sphere, when will that object be on the upper meridian? To answer this question, astronomers use sidereal time rather than solar time. It is different from the time on your wristwatch. In fact, a sidereal clock and an ordinary clock even tick at different rates, because they are based on different astronomical objects. Ordinary clocks are related to the position of the Sun, while sidereal clocks are based on the position of the vernal equinox, the location from which right ascension is measured. (See Box 2-1 for a discussion of right ascension.) Regardless of where the Sun is, midnight sidereal time at your location is defined to be when the vernal equinox crosses your upper meridian. (Like solar time, sidereal time depends on where you are on Earth.) A sidereal day is the time between two successive upper meridian passages of the vernal equinox. By contrast, an apparent solar day is the time between two successive upper meridian crossings of the Sun. The illustration shows why these two kinds of day are not equal. Because the Earth orbits the Sun, the Earth must make one complete rotation plus about 1° to get from one local solar noon to the next. This extra 1° of rotation corresponds to 4 minutes of time, which is the amount by which a solar day exceeds a sidereal day. To be precise: 1 sidereal day 23h 56m 4.091s where the hours, minutes, and seconds are in mean solar time. Sidereal Day is time to rotate 3610 or 23 hr 56 min.