Constructing. Ellipses BEGIN
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1 Constructing Ellipses BEGIN
2 In 1609, astronomer Johannes Kepler theorized that planets orbit the Sun along elliptical paths, rather than circular paths.
3 But what exactly is an ellipse?
4 But what exactly is an ellipse? A round shape that can be very circular, very oval, or anywhere in between.
5 But what exactly is an ellipse? These are all examples of ellipses.
6 But what exactly is an ellipse? Let s try drawing an ellipse...
7 Materials 1 pencil 1 piece of pressboard 2 push pins 1 loop of string 1 orange colored pencil 3 sheets of printer paper 1 calculator
8
9 Step #1 Fold a sheet of printer paper in half.
10 Step #2 And then fold it in half again (you are trying to create four equal-sized quadrants)
11 Step #3 Open up your folded paper and lay it flat in a landscape orientation
12 Step #4 Draw a small dot in the center of the page (where the two creases meet)
13 Step #5 Measure 1 cm to the left of the center point and make a dot
14 Step #6 Measure 1 cm to the right of the center point and make a dot
15 Step #7 Label the dot on the left F1 and the dot on the right F2. These are your two foci.
16 Step #8 Measure the distance between the two foci (it should be 2.0 cm)
17 Step #9 Label this sheet Ellipse A and record the foci distance on the top right side of the sheet
18 Step #10 Push a pushpin through each of the foci until they are secure in the pressboard but do not push it all the way in.
19 Step #11 Loop the string around the two pushpins. Be sure the string is on the metal part of the pins, not the plastic part.
20 Step #12 Using the string as a guide for your pencil, draw an ellipse.
21
22
23 Step #13 Once your ellipse is completed, measure the length of the major axis (the distance across the ellipse, through the two foci) major axis
24 Step #14 Record your major axis beneath your foci distance
25 Step #15 Find the formula for eccentricity on the cover of your ESRT
26 Step #16 Record the eccentricity formula on the top left side of your sheet
27 Step #17 Substitute in your measurements
28 Step #18 Use a calculator to solve the equation
29 Step #19 Record your answer to the nearest thousandth (three places). Eccentricity DOES NOT get any units.
30 Step #20 Choose one of your foci (either one) and draw an orange circle around it. This focus will represent the Sun.
31 Step #21 On the side of the ellipse closest to the Sun, mark an X and label it as seen here.
32 Step #22 On the side of the ellipse farthest from the Sun, mark an X and label it as seen here.
33 please Repeat all of these steps Two more times according to the following measurements: Ellipse B foci distance = 5 cm Ellipse C foci distance = 8 cm
34 Answer all of the following questions on the back of your Ellipse A sheet.
35 Diagram #1 Moon Planet F 1 F 2 (Drawn to scale) 1. What is the eccentricity of this ellipse? (Round to the nearest thousandth)
36 Diagram #1 Moon Planet F 1 F 2 (Drawn to scale) 2. On which side of this orbit is the Moon traveling at the highest velocity (top, bottom, left, right)?
37 Diagram #2 Mars Earth Venus Mercury Star Planet D Line of major axis of orbits Second focus of planet D s orbit 3. What is the eccentricity of the orbit of Planet D? (Round to the nearest thousandth)
38 Diagram #2 Mars Earth Venus Mercury Star Planet D Line of major axis of orbits Second focus of planet D s orbit 4. Describe how the shape of Planet D s orbit differs from the shape of Earth s orbit?
39 Diagram #3 D 5. What is the eccentricity of A Star C this orbit? Foci (Round to the nearest thousandth) Direction of movement B
40 Diagram #3 D 6. At which point A Star C will the object be traveling at Foci the lowest velocity? Direction of movement B
41 Diagram #4 147,600,000 km 152,600,000 km Sun 7. What is the eccentricity of this ellipse? (Round to the nearest thousandth) You re Done! Go Back Home
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