Download Ellipses

Name: _______________________________________
LAB: Ellipses
Adapted from Exploration in Earth Science, The Physical Setting, United Publishing Company, Inc.
INTRODUCTION: Earth revolves around the Sun in an orbit which is a special
geometric figure called an ellipse. An ellipse has two “center points”. Each one is called
a focus. The Sun is not at the exact middle of Earth’s orbit. Rather, it is found at one of
the foci.
OBJECTIVE: You will be able to compare the shape of Earth’s orbit and the orbits of
other planets with the shape of a circle.
VOCABULARY:
Ellipse:
Eccentricity:
Focus (plural is foci):
Major Axis:
Circle:
PROCEDURE:
1. Cut a piece of string about 27cm in length and tie the ends together to form a
loop.
2. On plain white paper, draw a line lengthwise down the middle of the paper
(hotdog style).
3. Near the center of this line, draw 2 dots 3cm apart.
4. Placing the paper on a piece of cardboard or corkboard, put a thumbtack at each
dot (focus).
5. Loop the string around the thumbtacks and draw the ellipse by placing your pencil
inside the loop as shown below
6. Label this ellipse #1.
7. Measure the distance between 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 your Report Sheet.
9. Move each take out 1cm and draw another ellipse. Label it #2 and measure and
record d and L.
10. Move each take out another 1cm and draw a new ellipse. Label it #3 and measure
and record d and L.
11. Move each take out another 1cm and draw another ellipse. Label it #4 and
measure and record d and L.
12. Place a dot at the exact middle of the first 2 foci. Place a single thumbtack in the
dot. Using a red pencil, construct a circle (using the same technique as used in
drawing the ellipses).
13. Using the given equation, calculate the eccentricity (e) of each of the five figures
(to the thousandths place: three decimal places). Show all work on you report
sheet.
REPORT SHEET
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)
d = ___________________
L = ___________________
e = ___________________
Calculations
Discussion Questions: Answer using data from the lab and in complete thoughts.
1. What change takes place in the eccentricity of the ellipses when you increase the
distance between the foci?
2. Which of the ellipses you drew was most eccentric?
3. Which of the ellipses you drew (not counting the circle) was least eccentric?
4. What is the minimum eccentricity an ellipse can have?
5. What is the name of the geometric which has a minimum eccentricity?
6. How does the numerical value of “e” change as the shape of an ellipse approaches
a straight line?
7. Where is the Sun located on a diagram of Earth’s orbit?
8. What is the eccentricity you calculated for Ellipse #1?
9. Which is less eccentric (rounder), the orbit of the Earth or your Ellipse #1?
10. List the planets in the table Eccentricity of the Planets in order from most circular
to most out of round based on their eccentricities.
CONCLUSION: Describe the true shape of the Earth’s orbit.
Reading Comprehension Read the portion of the article on elliptical orbits below and
answer the following questions based on the reading. Use complete sentences
Elliptical Orbit
by Tega Jessa on July 20, 2009
http://www.universetoday.com/34493/elliptical-orbit/
For the longest time astronomers thought the Universe existed as a perfect sphere; each planet and star
following a perfect spherical path. During the early times of the church, the accepted belief was the Earth
was the center of the Universe. This would later be disproved by astronomers.
Johan Kepler discovered the elliptical orbit. Kepler was the first person to theorize that the planets actually
move in ovaloid orbits. The equation he used to prove this would later become known as the Planetary
Laws of Motion and was further supported by Sir Issac Newton’s Theory of Gravity. According to Newton,
gravity is the reason planets and stars and other celestial objects orbit around each other. The bigger the
celestial body, the more mass it can exert on smaller objects around it. One massive body, acting alone
would create a circular orbit. If there’s more than one massive celestial body, the orbiting object will have
have an eccentric or elliptical orbit.
This has many consequences, not on how we observe space but also how navigate it. Other than the threat
of running into random objects, gravity is one of the greatest concerns for spaceflight. Normally a planet or
some other celestial object has enough mass and speed to avoid being completely pulled into a star’s center.
But in the case of man made space the difference of size is so great that this danger can’t be discounted. To
cope with this threat from gravitational fields Aeronautics has come up with two solutions. One is speed.
Thanks to advances in rocketry we now have craft that can match the orbit speeds of larger more massive
objects in space this helps to reduce the pull of gravity on the craft. We can actually harvest gravity’s
power. This is known as a gravity assist or gravity slingshot. Due to the elliptical nature of most orbits,
There is are two extreme points in the orbit called the apsis. One point is closest to one of foci and the other
is farthest away from that same focus. This causes a change in the speed of an object’s orbit. The closer it
gets the faster it moves the farther it gets the slower it moves. A spacecraft can take advantage of this to
boost its speed and escape orbit which also has the added benefit of saving fuel.
Sources: NASA Earth Observatory
1. What are two concerns for spaceflight?
2. How can a small object like a rocket overcome the mass (and gravitational pull)
of a massive object (a planet)?
3. According to the article and your lab, where would a planet travel fastest in its
orbit around the Sun?
4. According to information in the article, state the relationship that exists between
the mass of a planet and its gravitational pull.