# Kepler s Laws Simulations

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1 Kepler s Laws Simulations Goto: 1. Observe the speed of the planet as it orbits around the Sun. Change the speed to.50 and answer the questions. a. When is the planet moving the fastest? b. When is the planet moving the slowest? 2. Adjust the e (eccentricity) slider to its highest number. Record e a. How does the speed of the planet change? b. How does the orbit change? c. How did the spacing between foci change? d. Why can t the simulation run at e = 1? 3. Adjust the e (eccentricity) slider to its lowest number. Record e a. How does the speed of the planet change? b. How does the orbit change? c. How did the spacing between foci change? 4. Set the e to.01, which is close to the Earth s eccentricity, and write down the shape of the orbit. 5. Set e to.65 again and click show lines. The lines connect each focus to the same point on the ellipse. a. Does the value of r1 + r2 change? b. Change the eccentricity. Does the value change now? 6. The Mass of the Sun, M, is set to our Sun, 1 solar, record Period a. Increase the mass of the Sun to 10, which is 10x ours, record period b. Increase the mass of the Sun to 20, record period c. Increase the mass of the Sun to 30, record period d. Increase the mass of the Sun to 40, record period e. Increase the mass of the Sun to 50, record period f. What is the relationship between the mass of the Sun and the period of revolution?

2 Name Unit 2: The Copernican Revolution Vocabulary: Define each term below in a complete sentence on a separate sheet of paper. (Terms that are *, please illustrate) Cosmology Retrograde Motion* Geocentric* Epicycle* Deferent* Ptolemaic Model* Heliocentric* Copernican Revolution Ellipse* Focus* Semi-major axis* Eccentricity Perihelion* Aphelion* Sidereal orbital period Escape Velocity* Inertia Mass Newtonian Mechanics Gravitational Field Stonehenge* Acceleration Gravity* A. Ancient Astronomy 1.Where is Stonehenge? -Salisbury Plain, When and who built it? -Began 2800-finished B.C. -took 1700 years 2.What was Stonehenge s purpose? -3-dimensional, for religious and agriculture purposes -brought in large boulders (up to 50 tons) from miles away 1 3. What ancient cultures were accomplished in ancient astronomy? -Mayans- Temple in Mexico- used for human sacrifices when the planet Venus appeared -Plains Indians- Big Horn Medicine Wheel, -Chinese- 12 th century, kept accurate records of comets, and a guest star later known as a supernova, visible during the -Muslims- a vital link between ancient Greece and the Renaissance (dark ages), saved astronomical data, developed trigonometry, names stars such as Rigel, and Vega B. The Geocentric Universe 1.What Greek word is the word planet derived from, why did they get this name? - meandering wanderer, stay close to ecliptic, why? 2. Explain the difference between retrograde and prograde motion: -Prograde motion- -Retrograde motion- 3. What did Aristotle mean by a geocentric universe? -Geo= Earth - 4. How was the geocentric Earth explained by epicycle and deferent? - - small orbits - - larger orbits C. Model of the Solar System 1.Who was Nicholas Copernicus? - - rediscovered heliocentric model from ancient Greece-Aristarchus 2. Describe the seven points of the Copernican Revolution in your own words: 1)Earth isn t the center of 2)Earth is only center to 3)All planets revolve around the Sun 4)Stars are much further away than the Sun 5)Any motions from the stars 6)Sun s motion due to 7)Retrograde motion can only be explained accurately through a 3.What was Copernicus s motivation for his geocentric model? -Wanted a simpler model to explain the motion of planets

3 D. The Birth of Modern Astronomy 1.Who was Galileo Galilei? -Italian mathematician/philosopher -, saw conflict with Aristotle s geocentric model 2. What did Galileo see with one of the first telescopes? -Moon- -Sun- had blemishes (sunspots) inferred the Sun rotates -Jupiter- Strong support for Copernican model of solar system 3. What confrontation did Galileo face based on his observations? -Galileo published -Roman Catholic Church- burned (astronomer) a few years before based on his strong belief in Copernican model -Same for Galileo unless he takes back what was said in his book -He denied his book and was placed under house arrest for life after the -Was obviously correct, Catholic Church only recently admitted it was wrong in the 1980 s, over 300 years later E. Kepler s Laws of Planetary Motion 1.Who was Johannes Kepler? - 2.What did Kepler inherit? - position as Imperial Mathematician of Holy Roman Empire and all of his observations of planets 3. How did Kepler determine the shape of a planet s orbit? -Thru of different part of Earth s orbit 4. What is Kepler s first law? -All orbits of planets are 5. How is an ellipse different than a circle? -An elongated circle -focus- -major axis- 6. What is a semi-major axis and eccentricity? -Semi-major axis- -Eccentricity- ratio of the distance between the foci to the length of the major axis -Circle- 7. What distances can we calculate from the semi-major axis and the eccentricity? - - closest approach to the Sun - - greatest distance to the Sun 8.Define Kepler s second law (in your own words): -As objects approaches perihelion they 9.Define Kepler s third law (in your own words): - 10.What are major points of the front cover: Orbital Properties of Planets: -Almost all of the planets orbits except Pluto and Mercury are almost circles= eccentricity is close to 0 F. Dimensions of the Solar System? 1.What do Kepler s laws not tell us about the planets? - 2. What are the two methods for determining the distance to the Sun? a. b. 2

4 3. What is an exact A.U., how do we know? -149,597,870 km, we ll just use 150,000,000 km, G. Newton s Laws 1.Why are Kepler s discoveries described as empirical? -Came from analysis of observational data, not derived from -in other words: Why did the planets orbit the Sun? 2. Who was Isaac Newton? - (same year Galileo died) -Discovered laws of gravity 3.What are Newton s Three Laws (in your own words): 1). 2) 3) 4.How is gravity different on Earth than the Moon? -The more massive an object = -Moon- its mass is less than Earth= less gravity 5.What is the inverse-square law? - 6. What is the formula for Newton s law gravity? - = (Mass of object #1) x (Mass of object #2)/distance 2 7.What two forces are the reason for Earth s motion? - 8.How fast is the Earth traveling around the Sun? -30 km/second or 9.How do you know the Earth is traveling this fast? -Earth s circle of radius= 1 A.U.= circumference= 2(PIE)A.U.= 940 km 10.What is the mass of the Sun and Earth? -Sun: -Earth: 11. How are the masses of the Sun and Earth calculated? -Need to know gravitational influence -Earth- need to know distance to moon and length of sidereal month -Sun- 12. How did Newton modify Kepler s third law, why? -Both planet and Sun orbit their common center of mass= 2 foci -Kepler= period(year) 2 = semi-major axis (A.U.) 3, / -Newton= 13. Define escape velocity What is the formula for escape velocity? -Escape Velocity = 15. What is the escape velocity of Earth? -To stay in orbit = constant free fall but have inertia = 7.9 km/second or -To escape Earth= 11.2 km/second or 3

5 TOPIC IV: Earth s Motions LAB 4 3: ELLIPSES Name Partner Astronomy Block Date INTRODUCTION: The earth revolves around the sun in a geometrically shaped orbit called an ellipse. An ellipse has two center points. Each one is called a focus. The sun is not in the exact middle of the earth s orbit, rather, it is found at one of the focal points. OBJECTIVE: You will be able to compare the shape of the earth s orbit and orbits of other planets with the shape of a circle. Focus 1 Focus 2 d (Distance) L (major axis) VOCABULARY: 1. Ellipse: 2. Eccentricity: 3. Focus (plural is foci): 4. Major axis: 5. Circle: PROCEDURE: 1. Cut a piece of string about cm in length and tie the ends together to form a loop. 2. On a plain white paper draw a straight line lengthwise down the middle of the paper. 3. Near the center of this line, draw two dots 3cm apart. 4. Placing the paper on a piece of cardboard put a thumbtack in each dot (focus). Page 1

6 5. Loop the string around the thumbtacks and draw the ellipse by placing your pencil inside and drawing around in a circular motion. 6. Label this ellipse #1. 7. Measure the distance between the thumbtack holes (foci). This is d. Record this on your Report Sheet. 8. Measure the length of the major axis (L) and record this on the Report Sheet. 9. Move one tack out another cm and center the tacks and draw a new ellipse. Label it #2 and measure and record d and L. 10. Move one tack out another cm and center the tacks and draw another ellipse. Label it #3 and measure and record d and L. 11. Move one tack out another cm and center the tacks and draw another ellipse. Label it #4 and measure and record d and L. 12. Place a dot in the middle of the first two foci. Using one thumb tack, construct a circle. The one thumb tack will be the radius of the circle you are to draw. 13. Using the Given equation, calculate the eccentricity (e) of each of the five figures. Show all work on you Report Sheet. ECCENTRICITIES OF THE PLANETS PLANET ECCENTRICITY Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Page 2

7 REPORT SHEET Note: Eccentricities may vary from student to student depending on where they tied the knot for the loop. However the eccentricities should be close to these values. Ellipse #1 Calculations d= L= e= Ellipse #2 Calculations d= L= e= Ellipse #3 Calculations d= L= e= Ellipse #4 Calculations d= L= e= Ellipse #5 (circle) Calculations d= L= e= Page 3

8 DISSCUSION QUESTIONS: (Answer in Complete Sentences) 1. What change takes place in the eccentricity of the ellipses when you increase the distance between the foci? 2. Which of the four ellipses you drew (not counting the circle) was the most eccentric? 3. Which of the four ellipses you drew (not counting the circle) was the least eccentric? 4. What is the minimum eccentricity an ellipse can have? 5. What is the name of the geometric figure which has the minimum eccentricity? 6. How does the numerical value of e change as the shape of the ellipse approaches a straight line? 7. Where is the sun located on a diagram of the earth s orbit? 8. What was the eccentricity you calculate for Ellipse #1? 9. Which is rounder (less eccentric), the orbit of Earth or your Ellipse #1? 10. In the table, Eccentricities of the Planets, the planets are listed in order by their distance from the sun. Is there a direct relationship between the eccentricity of its orbit and the distance a planet is from the sun? 11. List the planets in order of the increasing eccentricity of their orbits. CONCLUSION: Describe the true shape of earth s orbit? Page 4

9 Name Gravity Exploration Did you know that when the astronauts walked on the moon thirty years ago, they actually weighed less than they did when they left Earth? It wasn't because of any special diet or exercise, either--it could happen to you in outer space, too! Here's an activity that explains why. To complete this activity, you'll need to know your current weight. Gravity is a universal, natural force that attracts objects to each other. Originally defined by Isaac Newton, and redefined by Albert Einstein, gravity is basically the natural force of attraction between two objects. Two factors determine the magnitude of the gravitational force between two objects: 1) their masses and 2) the separation distance between them. Gravity is the pull toward the center of an object; let s say, of a planet or a moon. When you weigh yourself, you are measuring the amount of gravitational attraction exerted on you by Earth. The Moon has a weaker gravitational attraction than Earth. So, you should weigh less on the Moon. Isaac Newton showed that the planets do not fly off into space because the gravitational attraction between the sun and each planet holds them close together. This attracting force exists between objects because of their mass. The greater the mass, the greater the attraction of gravity. Since every planet has mass, then every planet exerts a gravitational force on nearby objects. Part A: How much would you weigh on other planets and the moon? The more mass a planet has, the more gravity it has. Planets which have more mass than Earth would have more gravity than Earth. A person would weigh more on these planets than they do on Earth. Part B: How far could you jump on other planets and the moon? Determine how far you can jump on the Earth. To do this, place a piece of tape on the floor as a starting line. Jump as far as you can off of both feet. Have your partner mark where you land not where you end up! Measure the distance and record in the table.

10 Conclusion: 1. Complete each statement: A person would weigh more on than on, because. A person could jump further on than on, because. The force of gravity between two objects depends on.. 2. Identify a planet that has a similar gravitational attraction as Earth. 3. List the planets gravitational attraction from least to greatest. 4. Compare the multiplication factors in the chart. Judging from these factors, which planet do you think has the greatest mass? 5. Another student claims that the moon s gravity is 1/6 of the Earth s gravity. Is this a true statement? Look at the chart and use mathematics to support your answer. 6. What if your doctor told your aunt that weighing 165 pounds at 5 4 makes her 20 pounds overweight--to what planet could she travel to be at an acceptable weight? Justify your answer.

11 Name Kelper s Laws Activity Part 1 - Second Law -A line joining a planet & the Sun sweeps out equal areas in equal time In the ellipse below there are two areas, which represent the same time interval. Count up the number of blocks in area A and area B. Estimate to the best of your ability partial blocks. Blocks in A: Blocks in B: A B 1. If the time passed is the same for each segment, should the number of blocks covered also be the same? 2. In which region does the planet cover more of its orbit? In other words where is more distance covered? 3. If region is greater in length than region, and the time to travel those distances is the same, in which region is the planet moving faster? Explain. 4. Why doesn t our planet have large changes in orbital speed, even though Kepler s second law would indicate that the speed does change? Part 2: Third Law -The squares of the periods of the planets are proportional to the cubes of their semi major axes: P 2 = A 3 1. Earth s period P = 1 year and the radius A = 1 AU, rewrite the above equation with the numbers substituted 2. Complete the table verifying that P 2 = A 3. Show work for conversions below the table. Planet P (days) P (yr) A (km) A (AU) P 2 A 3 Mercury ,343,169 Venus Earth ,597, Mars Jupiter ,908,924

12 Kepler Practice Quiz Name Date Directions: Show all work! Write out all equation with units. You will lose credit if these are not included. Equations: P=orbital period a= semi-major axis e=eccentricity Perihelion: a(1-e) 1 A.U. 1.5 x 10 8 km Aphelion: a(1 + e) P 2 =a 3 1. What is the importance of Kepler s 2 nd Law? 2. How long will it take Saturn to go around the Sun (orbital period,p) if it s semi-major axis (a) is equal to 9.54 astronomical units (AU)? 3. Show that Pluto is closer to the Sun at perihelion than Neptune at Aphelion. Pluto s semi-major axis is x 10 9 km and has an eccentricity of.249. Neptune s semi-major axis is x 10 9 km and has an eccentricity of.009.

13 4. It takes Venus.62 (Earth) years to go around the Sun one time. How far on average is Venus from the Sun? 5. If Jupiter s orbital period is (Earth) years, find the distance Jupiter is from the Sun when it is moving slowest. Jupiter s eccentricity is equal to.048 (Hint: Use all Kepler s Laws)

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