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SpeedyMajesty969

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Grand Valley State University

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astronomy celestial mechanics exam review astrophysics

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This document is a review for the Phy 105 Exam 1, covering topics such as coordinate grids, the daily and annual motion of the Earth, and constellations. It also includes sample questions to test understanding of astronomical concepts.

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Phy 105 Exam 1 Review Name: 1 Coordinate Grids In astronomy we use two main systems of locating objects in the sky. (a) Horizon Coordinates (b) Equator Coordinates Horizon based: Altitude/Azimuth 1. Az...

Phy 105 Exam 1 Review Name: 1 Coordinate Grids In astronomy we use two main systems of locating objects in the sky. (a) Horizon Coordinates (b) Equator Coordinates Horizon based: Altitude/Azimuth 1. Azimuth is measured around the local horizon starting at north and going to east, south and west. North = 0°or 360° East = 90° South = 180° West = 270° 2. Altitude is measured from the horizon, straight up to the object. 0°is on the horizon. 90°is straight overhead. Equator based : Right Ascension/Declination 1. Right ascension is measured around the equator starting at the point where the equator crosses the ecliptic, 2. Declination is measured from the equator up (or down) to the object 0°is on the equator, +90°is at the north pole, -90°is at the south pole. Phy 105 Exam 1 Review Name: 2 Sample questions easy Your phone app tells you your campsite is Azm: 180°from your current location. Which direction should you hike? North, south, east, or West. medium A star guide tells you to look for a constellation at approximately Alt:75°Azm:270°. Where should you look for the constellation? hard Your friend tells you that they saw the moon a few days ago at Alt:5°and Azm:180°. Is that reasonable or unlikely, why? easy What is the declination of the north star (Polaris)? medium If you stand at the equator on the equinox, what is the declination of a star directly overhead? hard What is the minimum declination for north circumpolar stars when you are at lati- tude 20°? Daily motion of earth Summary The earth rotates on it’s axis in a counter clockwise direction (viewed from above the north pole), I refer to this as earth’s spin. As a result of the spin every thing in the sky appears to rotate around the earth. Most objects rise and set for locations here in the northern hemisphere, there are objects that remain above the horizon full time. (north circumpolar objects) Solar noon is when the sun crosses the meridian (middle of the sky, Azm 180°). The average time from one solar noon to the next solar noon is 24hrs. It varies by a few minutes over the year. The time for a star to travel from the meridian around to the meridian again is 23h 56m 4.01s. It is called the Sidereal Day. The difference between mean solar day and sidereal day is caused by Earth’s orbit around the sun. Each day our planet moves about 1°around its orbit. So after rotating 360°earth will be pointed 1 degree away from the sun. The earth has to rotate one more degree to return to solar noon. Consequently, if you view the same star at the same clock time each day it will appear about 1 degree further west. Over the course of the full year the star will go 360 degrees around the sky. Phy 105 Exam 1 Review Name: 3 Sample Questions Easy The bright star Vega is easy to find in the summer sky. on July 1 Vega crosses directly overhead at midnight sky time. Where will you look to find Vega 4 hours later? Medium The bright star Vega is easy to find in the summer sky. on July 1 Vega crosses the meridian at midnight (sky time). Where would you look to find Vega 2 months earlier (May 1) at midnight (sky time)? Hard The bright Star Vega has a declination of +38°47’18.9” At what latitude, to the nearest degree, would Vega Just be a circumpolar star? Notes Annual motion of earth Summary The earth revolves around the sun (the orbit) once per year. The axis of the spin of earth and the axis of the orbit of earth are out of alignment by 23.5 degrees. As a result of the tilt earth experiences annual swings up and down in the energy we receive from the sun. In the northern latitudes we receive the maximum energy from the sun on summer solstice (June 21) In the northern latitudes we receive the minimum energy on winter solstice (December 21) Southern latitudes have reverse seasons. Phy 105 Exam 1 Review Name: 4 On Vernal and Autumnal Equinox we (March 21 and September 21) the night and day are roughly equal. The sun is directly overhead at the Equator on the equinoxes The sun is directly overhead at the Tropic of Cancer on summer solstice The sun is directly overhead at the Tropic of Capricorn on the winter solstice. The arctic circle is the furthest south location that experiences at least one day without a sunrise and one day without a sunset. (antarctic circle is the other end.) The Axis of the tilt (and the location in the sky of the equinox) precesses once every 25700 yrs. as a result of the precession of the equinox, the north star will not always be at the pole. It will move by 2°- 3°in your lifetime. Sample Questions Easy What day, during this semester, would you expect to find the sun rising exactly in your rear view mirror as you drive from GR to Allendale on M45? Medium This graph shows the rise and set times of the sun in grand rapids for one year. Phy 105 Exam 1 Review Name: 5 0:00 23:00 Sun set (top) Solar noon (middle) and Sunrise (bottom) for one full year 22:00 in Grand Rapids MI. 21:00 20:00 19:00 18:00 17:00 16:00 15:00 14:00 13:00 12:00 11:00 10:00 9:00 8:00 7:00 6:00 5:00 4:00 3:00 2:00 1:00 0 30 60 90 120 150 180 210 240 270 300 330 360 what time was the earliest sunrise? what time was the earliest sunset? What day had the latest sunset? Phy 105 Exam 1 Review Name: 6 Notes Motion of Moon Summary The Moon orbits around the earth As a result we see a different amount of the moon illuminated each day. Half of the moon is always illuminated. Sometimes we see the illuminated side, sometimes the illuminated side faces away. Usually we see some of each. it takes 27.25 days for the moon to orbit 360 degrees around the earth. Sidereal month. it takes 29.5 days for the moon to complete the cycle of phases. Synodic month. The difference in sidereal and Synodic month comes because the earth orbits the sun 13°during each lunar cycle. The moon is tidally locked with earth, the same side faces earth at all times. To do this the moon must spin exactly once for each orbit. The plane of the moons orbit is not exactly aligned with the plane of earths orbit. It is off by 5.14°. Sometimes the moon is above the plane of earths orbit, sometimes below. When the moon crosses the plane of earths orbit during a full or new moon phase, the result is an eclipse. When the moon passes directly between the earth and the sun, the result is a solar eclipse. When the moon passes directly behind the earth, into the shadow of earth the result is a Lunar eclipse. Phy 105 Exam 1 Review Name: 7 Sample Questions Easy A blue moon is a term for the second full moon in a calendar month. If we find a blue moon in June, what day was the first full moon in June? Medium A supermoon is a term for when the full moon (or new moon occurs when the moon is near it’s closest point in the orbit. If a new supermoon eclipses the sun, would you expect a total eclipse or a anular eclipse? Notes Keeping Time Summary The motion of the earth, sun and moon form the basis for our time keeping system. the Mean solar day is divided into 24 hours. Each hour is divided into 60 minutes. Each minute is divided into 60 seconds. If seconds are divided, they are divided into decimals. In modern science we have defined the second more precisely and then work up from there. mean solar day is 24 hours Sidereal day is 23h56m4.09s The tropical year (The time from one equinox to the same equinox again) is 365.2422 days. This is our usual year. Phy 105 Exam 1 Review Name: 8 The sidereal year (The time for one exact 360°orbit) is 20 minutes longer due to the precession of the equinox 365.256 days) A lunar year (12 lunar months) is 354 days. A lunar month is one lunar cycle. Because there are an un-even number of days in a lunar month and because there an un-even number of months in the tropical year, our calendar months do not correspond exactly to a lunar month. All but February are longer. Sample Questions Easy On our current Gregorian calendar, What day is new year’s day? medium On a traditional calendar which places the new year on the vernal equinox, what day (in our Gregorian calendar) is “new Years day” Hard Suppose there is a holiday celebrated on a traditional Lunar Calendar. This year (2025) the holiday is celebrated on June 12, when will it be celebrated next year (2026)? Notes Planets and a bunch of other stuff Summary Our solar system consists of the objects that are primarily under the influence of the sun’s gravity. There are planets, dwarf planets, moons (satellites), and small solar system objects. There are five planets visible in the sky without a telescope. in order Mercury, Venus, (Earth), Mars, Jupiter, Saturn. Phy 105 Exam 1 Review Name: 9 Uranus and Neptune are only visible with a telescope. There are many dwarf planets including Ceres and Pluto. Dwarf planets are smaller and have not cleared their orbit. Mercury, Venus, Earth and Mars are primarily rocky materials. They can be referred to as the inner solar system. Jupiter, Saturn, Uranus, and Neptune are much larger and have more gas and ice. They can be referred to as the outer solar system. Small solar system bodies may be rocky or icy, they may have very elliptical orbits or more circular orbits. Small Solar System bodies may be given other designations depending on orbital properties. Small solar system bodies with more circular orbits are called asteroids. An icy small solar system body with a very elliptical orbit is often called a comet. Small solar system bodies trapped by the gravity of a planet, but not in orbit around the planet are called Trojans. Small solar system bodies between Jupiter and Neptune that are not trapped in the gravity of a planet are called Centaurs. When they interact with the gravity of one of the planets they can: – be pushed toward the sun and possibly become a comet. – move to a new centaur orbit, – be pushed further out from the sun, possibly ejected from the solar system all together. Sample Questions Easy Name one rocky from the inner solar system. Medium Name one reason why Pluto is classified as a Dwarf Planet. Hard If a Small Solar system body orbiting near Neptune gets a bump from Neptune’s gravity and zooms in near the sun in a very elliptical orbit, what would we call the body? Phy 105 Exam 1 Review Name: 10 Notes Constellations Constellations are groups of stars near each other in a region of the sky. Ancient as- tronomers and astrologers used constellations in building the calendar, navigating, story telling and fortune telling. Modern astronomers use constellations to divide up the sky, to do that they filled in the gaps in the Classical Greek/Roman constellations. Other cul- tural groups have different constellation groupings. Some are based on the same asterisms, others are different groupings. Phy 105 Exam 1 Review Name: 11 Summary Pleiades is a common asterism recognized by nearly all cultures. Stories center around 7 children (sisters, or kids). Constellations along the path of the sun through the sky (the ecliptic) are useful in building a calendar and in navigation. We call them the Zodiac. The classic names are (in order from vernal equinox) – Aries, – Taurus, – Gemini, – Cancer, – Leo, – Virgo, – Libra, – Scorpio, – Sagittarius, – Capricorn, – Aquarius, – Pisces In northern latitudes a group of constellations near the celestial north pole will not set below the horizon, instead they will always be above the horizon, circling the celestial north pole. These are north circumpolar constellations. At our latitude, they include Ursa Major (big dipper), Ursa Minor (little dipper), Draco, Cassiopeia, Cepheus and Camelopardalis. Orion is another easy to spot constellation. You can find Canis major, Taurus and Gemini in the neighborhood. In the summer sky The summer triangle can help you find Cygnus, Aquila, and Lyra. Circumpolar constellations can help find directions, and latitude. they can also be used to tell time. Latitude can be easily calculated by measuring the altitude of the celestial pole. “Altitude of polaris”=“latitude on the globe”. Longitude is harder to tell from the sky without a precise clock. With a precise clock you can compare rise, set and transit times from a home base to your current location. Phy 105 Exam 1 Review Name: 12 Sample Questions easy What constellation is Polaris (the north star) in? easy If you go outside at midnight and you find the big dipper straight up from the north star, where will you find the big dipper in 3 hours? medium if you are sailing the ocean and you find that polaris is 30°above the horizon in the north, what is your latitude? hard If you see a full moon right in the middle of Virgo, what month is it? Notes

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