Download 7E Astronomy Module by Dexter Clamohoy
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Kepler’s Laws of Planetary Motion Learning Outcomes After completing this module, you should be able to: • List and explain Kepler's Laws of Planetary Motion; and • Describe how Kepler formulated each law based on his observations of Mars. ELICIT: Draw-What-You-Know According to your present knowledge of planetary motion. Draw a diagram showing the planets' orbits around the Sun. ENGAGE: Find and Match! Find the hidden words in description of the terms. S E C H I H U G O C Y I F O D G I D M U P M R E S A S S O D S D R A A M F J O S O M S F Q M O A S F E C C E N T M A C J P F P J S F O S A N F A X J J P O J Q S A O F S the crossword puzzle. Match it with the correct D F T U D A O R O X A J H T O M S M A I P K M R J C T P S F T C Q X K O I L O T S U E I K J E T L F X I L F U T Q I A C V I M O S P O Y K M A A S L V N R S R O F P E R F E D F S P Q S J R S T R L Z S O J M R G X N O Y D V U S O K R J H R R U O N I S S M K O M N P ___________ 1. It is not derived from any existing law and is evidence-based descriptions. ___________ 2. The instrument Tycho Brahe use for gathering comprehensive astronomical data. ___________ 3. The planet Kepler analyze to formulate his Laws of Planetary Motion. ___________ 4. The deviation of a shape from a perfect circle. ___________ 5. The movement of the planets around the Sun. EXPLORE: DIY Gravity Well! Materials: • Large bowl • Stretchy fabric, like a cotton blend t-shirt • Rubber band, big enough to go around the bowl, or binder clips • Heavy ball, like a golf ball or something similar • Marble, round bead, or something similar Instructions: 1. Place the stretchy fabric over the top of the bowl. Stretch the fabric tightly and use the rubber band or binder clips to hold it in place. 2. Place the heavy ball in the center of the fabric. 3. First place the marble on the side and let it go . • What path does it follow? Why? 4. Next, roll the marble along the side of the bowl. • What path does it follow now? Why? EXPLAIN Based on empirical laws, assumptions can be directly observed and gather physical evidence that a law is true. For this part, we are going to explain how Brahe’s innovations and an extensive collection of data in observational astronomy paved the way for Kepler’s discovery of Laws of Planetary Motion. How did Kepler use Brahe’s accurate data of Mars? • After years of calculating and analyzing the data on Mars, he discovered that Mars and the other planets move in an ellipse around the sun. His discovery showed a discrepancy of 8 minutes of arc between what was expected from a circular orbit. • Before, it was believed that planetary orbits are a perfect circle, but Kepler proved that they were ellipses. A circle has an eccentricity of zero while an ellipse has an eccentricity between 0 and 1. Eccentricity describes the deviation of a shape from a perfect circle. Kepler’s Laws of Planetary Motion 1. First Law: Law of Ellipses The calculation of Mars’ orbit led Kepler to arrive at the idea that the planets moved around the sun in an elliptical orbit. “The orbits of the planets are ellipses with the sun at one focus.” Figure 1. The Law of Ellipses 2. Second Law: Law of Areas Kepler also observed that if a planet transverse two separate arcs, it would still define the same area in 30 days. He came up with this observation after studying individual portions of the orbit of Mars. “The line joining a planet to the sun sweeps out equal areas in equal times.” Figure 2. The Law of Areas 3. Third Law: Law of Harmonies Using Brahe’s data, Kepler tried to discover the relationship between the periods of the planet or the time it takes a planet to complete one revolution and the planet’s distance from the sun. “The square of an orbit’s period is proportional to the cube of the average distance between the planet and the sun.” ELABORATE: Assess the Situation Assess the situation and answer the query that follows. Laws can be considered as axioms or empirical laws. An axiom is a wellestablished statement. If you have made assumptions first before giving an example, then that is the first sign that this is an axiom. An axiom holds true only within the context that it is applied. On the other hand, empirical laws are descriptions supported by factual observations and are not derived from existing laws. As long as a scientific law can be tested using experiments or observations, it is considered an empirical law. Based on your understanding, is Kepler’s Laws of Planetary motion considered as axioms or empirical laws? Why? EVALUATE 1. How did Kepler formulate the 2nd Law of Planetary Motion? A. He observed the phases of Mars. B. He studied individual portions or slices of Mars’ orbit. C. He calculated that there is a discrepancy in the eccentricity of Mars’ orbit. D. All of the above. 2. What instruments does Tycho Brahe make use for gathering comprehensive astronomical data? A. Astrolabe B. Protractor C. Sundials D. Telescope 3. What relationship was determined in the 3rd Law of Planetary motion? A. The relationship between the periods of the planet and the planet’s distance from the sun. B. The relationship between the periods of the planet and the rotation of a planet on its own axis. C. The relationship between the size of the planet and the planet’s distance from the sun. D. The relationship between the size of the planet and the rotation of a planet on its own axis. 4. ___________ is not derived from any existing law and is evidence-based descriptions. A. assumption B. axiom C. empirical law D. theory 5. What planet did Kepler analyze for him to formulate his Laws of Planetary Motion? A. Earth B. Mars C. Jupiter D. Venus EXTEND Showcase the knowledge and skills you have learned in this lesson by answering this additional activity. 1. What is eccentricity and how is it determined? 2. Why is a planet‘s orbit slower the farther it is from the sun? 3. Where is Earth when it is traveling the fastest? ANSWER KEYS ELICIT Close or similar to the following illustration ENGAGE S E C H I H G O C Y I F D G I D M U M R E S A S O D S D R A M F J O S O S F Q M O A F E C C E N M A C J P F J S F O S A F A X J J P J Q S A O F ___________ 1. ASSUMPTION ___________ 2. PROTRACTOR ___________ 3. MARS ___________ 4. ECCENTRICITY ___________ 5. REVOLUTION U O P S A M S T P N O S D F T U D A O R O X A J H T O M S M A I P K M R J C T P S F T C Q X K O I L O T S U E I K J E T L F X I L F U T Q I A C V I M O S P O Y K M A A S L V N R S R O F P E R F E D F S P Q S J R S T R L Z S O J M R G X N O Y D V U S O K R J H R R U O N I S S M K O M N P EXPLORE 3. What path does it follow? Why? Linear because we just let the marble go without pushing (simulates centripetal force) and thus the downward curvature of the fabric attracts the ball towards center (simulates gravity). 4. What path does it follow now? Why? Now, it follows and eccentric orbit around the heavy ball because we pushed the ball sideways-outwards and it balances with the attraction force of the curvature. Gradually, it falls into the center because of friction. But in real life, outer space has no friction that’s why the forces stay balance unless acted upon. ELABORATE Based on your understanding, is Kepler’s Laws of Planetary motion considered as axioms or empirical laws? Why? - Kepler's laws of planetary motion are empirical laws because they are based on observation and evidence. EVALUATE 1. d 2. b 3. a 4. a 5. b EXTEND 1. What is eccentricity and how is it determined? - The eccentricity of an elliptical orbit is defined by the ratio e = c/a, where c is the distance from the center of the ellipse to either focus. The range for eccentricity is 0 ≤ e < 1 for an ellipse; the circle is a special case with e = 0. 2. Why is a planet‘s orbit slower the farther it is from the sun? - A planet moves slower when it is farther from the Sun because its angular momentum does not change. For a circular orbit, the angular momentum is equal to the mass of the planet (m) times the distance of the planet from the Sun (d) times the velocity of the planet (v). 3. Where is Earth when it is traveling the fastest? - It follows from Kepler's second law that Earth moves the fastest when it is closest to the Sun. This happens in early January, when Earth is about 147 million km (91 million miles) from the Sun.