LAB: Eccentricity 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: In this lab, you will be able to draw and compare the shape of the earth's orbit and orbits of other planets with the shape of a circle. 20= S Focus 1 Focus 2 15.3 d (Distance) 0.13 F L (major axis) Figure 1 Key words: Ellipse, Eccentricity, Focus (plural is foci); Major axis; Circle Materials: cardboard, 2 push pins, a string, centimeter ruler, pencil & thumbtacks (two) Procedure: 1. Take one sheet of ellipse construction paper to select 1-pairs of foci (singular focus) (A-A, B-B, C-C, D-D, E-E, F-F). Write down your selected foci and then draw two dots below two foci. Circle two foci with dots inside (figure 1) Note: A-A=1.0cm, B-B-2.0cm, C-C-3.0cm, D-D=4.0cm, E-E=5.0cm, F-F=6.0cm 2. Measure the distance between the foci (d) cm (to the nearest tenth) 3. Place this paper on a piece of cardboard and put a thumbtack in each focus (dots). 4. Loop the string around the thumbtacks and draw the ellipse by placing your pencil inside the loop. 5. Draw the Major Axis (L). (Note: the straight line goes from one end to the other and goes through both foci.) 6. Measure the length of the major axis to the nearest tenth of centimeter. cm 7. Calculate the eccentricity using the formula below. Record your answer to the nearest thousandth. distance between foci (d) Eccentricity = length of major axis (L) 8. Choose one of your foci and placed an S above your circle foci to show the position of the Sun. (see Figure 1) 9. Based on the location of the Sun (S), find the constructed orbit at aphelion (far point, lowest) at perihelion (near point, fastest) 10. Choose where the planet will travel the fastest (greatest velocity). 11. Place an X on your constructed orbit where the planet has its greatest orbital velocity (fastest). Hint: Write an X on the same side of the Sun (S). 12. Using solar system data (table 1), name the planet that has the same or closest to the eccentricity as the ellipse on this paper. Write the eccentricity of your ellipse (nearest thousandth) Eccentricity of your constructed ellipse (nearest thousandth) Planet name Coloulia Eccentricky Object of Orbit SUN MERCURY 0.206 VENUS 0.007 (Table 1) EARTH 0.017 MARS 0.093 JUPITER 0.048 SATURN 0.054 URANUS 0.047 NEPTUNE 0.009 EARTH'S MOON 0.056 13. a) Is the eccentricity of your constructed ellipse less or more or equally elliptical than the eccentricity of Earth's (0.017). b) Why? 14. How does the numerical value of 'e' change as the shape of the ellipse approaches a straight line? Questions: traveling around a star. Points A, B, C and D are four positions of this planet in its orbit. Based your answers to question 1 on the diagram below which represents the elliptical orbit of a planet 1. a) The calculated eccentricity of this orbit is approximately (1) 0.1 (2) 0.2 (3) 0.3 (4) 0.4 b) The Gravitational attraction between the star and the planet will be greatest position (1) A (2) B (3) C (4) D C) What planet could this orbit represent? Based your answers to question 2 on the diagram below, which represents an exaggerated model of Earth's orbital shape. Earth is closest to the Sun at one time of year (perihelion) and farthest from the Sun at another time of year (aphelion). Direction of movement D Star Foci B (Drawn to scale) 2. a) State the actual gèometric shape of Earth's orbits Earth perihelion at Sun Earth at Saphelion b) Give the season when Earth is at perihelion. c) Give the season when Earth is at aphelion. 3. A student constructed the accompanying elliptical orbit of a Moon revolving around a planet. The foci of this orbit are the points labeled F1 and F2. Describe how the shape of the elliptical orbit would change if the distance between the foci points was 2.5 cm. Moon (Not drawn to scale) Planet F2 (Drawn to scale) Page 2