1 A more in depth explanation from last week: If Earth had no tilt, what else would happen? The equator would be much hotter due to the direct sunlight which would lead to a lower survival rate and little life. The poles would receive less direct light and thus be colder making the survival rate there lower as well. The species would have evolved differently (micro-evolution), thus different life would be on Earth. But we would have a habitable zone between the poles and the equator, but unfortunately it would be a smaller habitable region than we have now.
2 Solar & Sidereal Motion and Models of the Solar System (Week 7)
3 Why does Sidereal Motion (Time) matter? It is a system of timekeeping used by astronomers, useful because a star rises and sets at the same sidereal time every day, but not at the same solar (synodic) time which is our typical time system. Because local sidereal time is the right ascension (RA) of a star on the observers meridian, it is a direct indication of whether a celestial object of known right ascension is observable at that instant. Our clocks are based upon Solar time and we measure stars rising about 4 minutes earlier each day. Why does this happen? The short version because of Earth s motion around the Sun. What types of motion can be measured with the Sidereal system? Sidereal Day, Sidereal Periods of Celestial Bodies to include the Sidereal Month of the Moon
4 Sidereal Time vs. Solar (Synodic) Time A time-keeping system astronomers use to keep track of the direction to point their telescopes to view a given star in the night sky. One sidereal day corresponds to the time taken for the Earth to rotate once with respect to a distant star. A time keeping system based upon when the Sun is highest in the sky (~12 pm). One solar day corresponds to the time taken for the Earth to rotate once with respect to the Sun.
5 Prior to Tutorial completion, the Instructor will: a) define parallel lines b) define period c) define high noon (in the diagram below) d) in the diagram below illustrate a 360 degree rotation of person/earth with a ruler (students use toothpick) while Earth is still orbiting the Sun & sketch the Earth/person in a later snapshot e) help students visualize distant stars (see top of page) and have them draw similar stars on their Tutorial f) provide every student with a toothpick
6 Solar vs. Sidereal Day - Lecture Tutorial (pg 11-12; minutes) STOP the Tutorial just after the Note: on page 12, put name on it and turn it in to Instructor next Tuesday. Be ready to struggle a little bit, this is a discovery! Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don t understand what the Lecture Tutorial is asking, ask one of us for help.
7 Follow up to Tutorial Using the angle that the Earth sweeps out as it goes once around the Sun and the number of days in a year, the number of degrees per day that Earth moves in orbit about the Sun is: A) 365 days/180 degrees = 2 days/degree B) 365 days/180 degrees = 0.5 degrees/day C) 360 degrees/365 days = 1 degree/day D) 360 degrees/24 hours = 15 degrees/hour E) none of the above ANSWER: C or 1 degree/day for Earth revolving about the Sun [Realize that choice D or 15 degrees/hour is the rotation rate of the Earth about its axis, which is also the rate the celestial sphere appears to rotate.]
8 Follow up to Tutorial During what type of a day does the Earth rotate through slightly more than 360 degrees? A) Synodic day which is 24 hrs B) Solar day which is less than 24 hrs C) Sidereal day which is less than 24 hrs D) Sidereal day which is more than 24 hrs E) Both A) & B) above ANSWER: A One solar/synodic day corresponds to the time taken for the Earth to rotate once with respect to the Sun which is more than 360 degrees and takes 24 hours.
9 Follow up to Tutorial During what type of a day does the Earth rotate through 360 degrees? A) Synodic day in 24 hrs B) Solar day in less than 24 hrs C) Sidereal day in less than 24 hrs D) Sidereal day in 24 hrs E) Both A) & B) above ANSWER: C One sidereal day corresponds to the time taken for the Earth to rotate once with respect to a distant star.
10 One sidereal day lasts approximately 23 hours and 56 minutes during which time the Earth rotates 360 degrees (~4 minutes shorter than a solar day). One solar (synodic) day lasts 24 hours during which time the Earth rotates more than 360 degrees.
11 Local Sidereal Time Clock Apparent Movement of a Star
12 Synodic (Solar) vs. Sidereal Period of the Moon ( & brief intro. to Moon phases)
13 In this video, be sure to: a) notice how the Earth s orbit around the Sun makes the Moon s sidereal period different from its synodic period b) try to identify several Moon phases at various points in the animation c) read the blue writing, see next slide for a snapshot of it
15 Sidereal vs. Synodic Period of the Moon (zooming in) Sidereal Period is days, Moon rotates to the purple line (which should be parallel to the leftmost red dotted line), 360 degrees; not back to New Moon - same phase as leftmost image Synodic Period is days, Moon rotates to the orange line, more than 360 degrees; back to the same phase (new moon) as leftmost image.
16 Models of the Solar System Retrograde Motion of the Planets Geocentric vs. Heliocentric Kepler s Laws
17 Planets were often called wandering stars because they seem to slowly move from one constellation to the next. East South Mars prograde & retrograde motion is in red between May 1 and Dec. 31 West
18 Retrograde Motion Models of the universe MUST adequately describe this retrograde motion!
19 What did the Greeks have to say about the motion of the Solar System? The astronomer must try his utmost to explain celestial motions by the simplest possible hypothesis; but if he fails to do so, he must choose whatever other hypotheses meet the case. -Ptolemy of Alexandria (140 A.D.)
20 Ptolemy He tried to create a model that would account for retrograde motion. He placed the planets in orbits (deferments) using epicycles. What is this Earth-centered theory called? Geocentric theory: (in Greek, geo means earth) which maintained that Earth was the center of the universe
21 For most of human history, we have thought the universe was geocentric. Copernicus devised the first comprehensive heliocentric cosmogony to successfully explain retrograde motion. Copernicus ( AD) Heliocentric theory: with the Sun at the center of the universe or solar system
22 Retrograde motion is an apparent motion caused when one planet moves from being behind another planet to being in front of the other planet.
23 Let s watch a movie(s) of this motion.
24 Tycho Brahe ( )
25 Tycho Brahe ( ) is known for - 1. First telescope observations of the sun 2. First sun centered scientific model of the solar system or universe 3. Being the world s best nakedeye astronomer 4. Creating first a theoretical model to explain planetary motions 5. Creating first a theoretical model for explaining gravity
26 Tycho Brahe ( ) is known for - 1. First telescope observations of the sun 2. First sun centered scientific model of the solar system or universe 3. Being the world s best naked-eye astronomer 4. Creating first a theoretical model to explain planetary motions 5. Creating first a theoretical model for explaining gravity
27 What do we mean by Greatest Naked-eye Astronomer? No telescope!
28 Scientists use parallax to measure distances.
30 Tycho Brahe measured distances using parallax that disproved ancient ideas about the heavens He observed a supernova in 1572 and with this showed that the heavens were both changing and had a dimension of distance; this troubled scholars who previously thought the heavens were unchanging. He showed that comets were objects that occurred in the region of the planets, not in Earth s atmosphere.
31 Johannes Kepler He was rumored to have hated Tycho Brahe and was in the relationship for the data. With that data he changed the understanding of motion of heavenly bodies forever.
32 Johannes Kepler is Known for - 1. First telescope observations of the sun 2. First sun centered scientific model of the solar system or universe 3. Being the world s best naked-eye astronomer 4. Creating the first theoretical model to explain planetary motions 5. Creating the first theoretical model for explaining gravity
33 Johannes Kepler is Known for - 1. First telescope observations of the sun 2. First sun centered scientific model of the solar system or universe 3. Being the world s best naked-eye astronomer 4. Creating first a theoretical model to explain planetary motions 5. Creating first a theoretical model for explaining gravity
34 Johannes Kepler Kepler s Three Laws of Planetary Motion
35 Eccentricity, e how squashed or out of round the ellipse is a number ranging from 0 for a circle to 1 for a straight line e = 0.02 e = 0.7 e = 0.9
36 Kepler s First Law: The orbit of a planet about the Sun is an Ellipse with the Sun at one focus.
37 What is the shape of Earth s orbit around the Sun? Earth, e = 0.016
38 Kepler s Second Law: A line joining a planet and the Sun sweeps out equal Areas in equal intervals of time.
39 Kepler's Second Law Movie &ns= 0
40 Kepler s SECOND LAW A line drawn from the planet to the Sun sweeps out equal Areas in equal times orbital speed is not constant for an ellipse only for a circle planets move faster when near the Sun (perihelion) planets move slower when they are far from the Sun (aphelion)
41 SECOND LAW The speed a planet travels during its orbit is related to the distance from the star When the planet is near the sun the planet goes faster than when the planet is farther from the sun Planet travels slow here Planet travels fast here
42 Kepler s THIRD LAW The size of the orbit (a is the length of its orbit s semi-major axis) determines the orbital period, T a 3 AU= T 2 years Thus planets that orbit near the Sun orbit with shorter periods (T) than planets that are far from the Sun
43 THIRD LAW The size of the orbit determines the orbital period planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun
44 Kepler s Third Law: The square of a planet s sidereal (orbital) period is proportional to the cube of the length of its orbit s semimajor axis (T 2 a 3 ). =,T T 2
45 The Second and Third Laws The Second Law tells us what a particular planet does when it orbits a Star The planet will move faster when it is close to the Sun and slower when it is farther from the Sun The Third Law how the orbital periods are related to the orbital distances for all the planets in the Solar System planets that are in an orbit located near the Sun have short orbital periods planets that are in an orbit located far from the Sun have long orbital periods
46 THIRD LAW The size of the orbit determines the orbital period planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun T = ~ 12 years T = 1 year
47 THIRD LAW The size of the orbit determines the orbital period planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun MASS DOES NOT MATTER Both have T = 1 year
48 According to Kepler s second law, a planet with an orbit like Earth s would: A. move faster when further from the Sun. B. move slower when closer to the Sun. C. experience a dramatic change in orbital speed from month to month. D. experience very little change in orbital speed over the course of the year. E. none of the above.
49 Which of the following best describes what would happen to a planet s orbital speed if it s mass were doubled but it stayed at the same orbital distance? A. It would orbit half as fast. B. It would orbit less that half as fast. C. It would orbit twice as fast. D. It would orbit more than twice as fast. E. It would orbit with the same speed.
50 Kepler s second law says a line joining a planet and the Sun sweeps out equal areas in equal amounts of time. Which of the following statements means nearly the same thing? A. Planets move fastest when they are moving toward the Sun. B. Planets move equal distances throughout their orbit of the Sun. C. Planets move slowest when they are moving away from the Sun. D. Planets travel farther in a given time when they are closer to the Sun. E. Planets move the same speed at all points during their orbit of the Sun.
51 If a small weather satellite and the large International Space Station are orbiting Earth at the same altitude above Earth s surface, which of the following is true? A. The large space station has a longer orbital period. B. The small weather satellite has a longer orbital period. C. Each has the same orbital period
52 Kepler s 2 nd & 3 rd Laws - Lecture Tutorials: (pg 21-27) Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don t understand what the Lecture Tutorial is asking, ask one of us for help.
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