This lab document instructs students on how to construct three ellipses with different eccentricities using string and push pins. It has the students measure and record the distance between foci and length of the major axis for each ellipse, and calculate the eccentricity. It then has the students answer questions about how the eccentricity changes with the ellipses' shapes and relates to planetary orbits.

1. Name:_______________________________ Period:_____ Date:______________
Lab: Eccentricity of an Ellipse
The ellipse is the geometric shape of most orbits. In this lab, you'll construct 3 ellipses,
examine and measure them to determine some of the fundamental properties of ellipses.
Follow the directions below, making sure you draw and measure carefully along the way.
When you have completed the construction and measurement of your ellipses, carefully
and thoughtfully answer the questions posted at the end of this lab.
2. Fold your paper in ½
lengthwise (hot¬dog fold). Label
the fold "major axis"
Major Axis
1. Gather up the materials you need to complete this lab
(See Fig. 1):
• A piece of cardboard
• 1 sheet of white paper
• 2 push pins
• A string loop (tie 26 cm of string into a loop)
• Ruler
• A pen or sharp pencil
3. Place the sheet of paper on the
cardboard, and draw 2 dots in the
center of the page 3cm apart. Place
the 2 push pins into the dots as shown
in Fig. 2.
4. Place your loop of string around the 2 push
pins, and, keeping the string tight, use the
string as a guide to carefully draw an ellipse
around the push pins. (See Fig 3.) Be patient
- you may have to try it a few times before
you get the hang of it!

2. F1 F2
1
F3 F4
2
3
Sun
F6
6. Record Data for Ellipse 1 on Answer Sheet
 Measure the distance (d) between foci 1 & 2 to the nearest tenth.
 Measure the length (L) of the major access of ellipse 1 to the nearest tenth.
 Calculate the eccentricity (e) to the nearest hundredth using the equation
e=d/L
8. Record Data for Ellipse 2 on Answer Sheet
 Measure the distance (d) between foci 3 & 4 to the nearest tenth.
 Measure the length (L) of the major access of ellipse 2 to the nearest tenth.
 Calculate the eccentricity (e) to the nearest hundredth using the equation
e=d/L
10. Record Data for Ellipse 3 on Answer Sheet
 Measure the distance (d) between the focus sun & F6 to the nearest tenth.
 Measure the length (l) of the major access ellipse 3 to the nearest tenth
 Calculate the eccentricity “e” to the nearest thousandth using the equation
e=d/L
5. After you've drawn your ellipse,
remove the push pins. The 2 pinholes are
called the foci of the ellipse (each one is
called a focus). Label the 2 foci F1 and F2
as indicated below.
Label this ellipse 1
F1 F2
1
F1 F2
1
F3 F4
27. Ellipse 2 - Move EACH pin out 1
cm and draw a new ellipse. Label
the foci F3 & F4. Label the ellipse
2.
9. Ellipse 3 - Move EACH pin out 1 cm
and draw a new ellipse. Label the foci
Sun & F6. Label the ellipse 3.

3. 11. When the planet is closest to the sun it travels the fastest in its orbit because
the force of gravity is the strongest. Draw an “x” on the ellipse 3 and label it FAST
where the planet would have the most speed!
12. Where does the sun appear to be the largest to an observer on Earth? Label this
position on ellipse 1 with a large L. Label where the sun appears to be the smallest to
an observer on Earth. Label this with an S on ellipse 1. The apparent size of an object
in the sky is known as its apparent diameter.
Data:
Ellipse 1:
d-________________ Calculations (show your work)
L-________________
e1-________________
Ellipse 2:
d-________________ Calculations
L-________________
e2-________________
Ellipse 3:
d-________________ Calculations
L-________________
e3-________________

4. Discussion Questions: Answer below
1. What changes do you see in the eccentricity (e) of your ellipses as you
INCREASE the distance between the foci (pins).
2. Out of the 3 ellipses you drew, which is the most eccentric?
3. Out of the 3 ellipses you drew, which is the least eccentric?
4. How does the numerical value of "e" change as the ellipse approaches a
straight line?
5. What is the minimum eccentricity an ellipse can have? What is the name
of the geometric figure that has the minimum eccentricity?
6. Which is less eccentric, the orbit of the Earth or Ellipse #1?
7. Which planet has the most eccentric orbit? Which planet has the least
eccentric orbit?
8. Where is the Sun located on a diagram of Earth’s orbit?
9. Describe the relationship between how circular an ellipse appears and it’s
eccentricity.
CONCLUSION: Describe the true shape of the Earth's Orbit.