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LAB: Orbits & Ellipses | Earth2Class, Study notes of Plasma Physics

In this investigation you will draw several ellipses, calculate their eccentricity, and explore the relationships between the shape of each orbit and the motion ...

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Name: _______________________________ Date: ___________
LAB: Orbits & Ellipses
As you know, each planet in the Solar System revolves around the sun. The shape of each planet’s
orbit is an ellipse (or elliptical). Unlike a circle, which is a curved shape drawn around a central
point, an ellipse is a curved shape that is drawn around two points. Each of these points is called a
focus, and together, they are called the foci of the ellipse. When comparing the shapes of
planetary orbits, it is most helpful to describe the eccentricity (degree of flattening) of each
ellipse. A perfect circle has an eccentricity of 0 because there is a no flattening. An ellipse that is
completely flat has an eccentricity of 1.
In this investigation you will draw several ellipses, calculate their eccentricity, and explore the
relationships between the shape of each orbit and the motion of its planet.
MATERIALS
pencil
1 sheet of unlined paper
2 thumbtacks or pushpins
piece of strong approximately 15 cm long
piece of cardboard at least as large as the
sheet of paper
metric ruler
calculator
PROCEDURE
1. Fold the piece of paper the long way (hot dog style). Without opening it, fold it in half the short
way (hamburger style). Open the paper and locate the center of the paper.
2. Make one point 4 cm from each side of the center point. Place a pushpin at each of these
points. The pins should be 8 cm apart.
3. Place your string around the pins, not too tightly.
4. Use a pencil to gently pull the string away from the pins, and in a smooth motion, draw an
ellipse. Remove the string and write “8 cm” along the top of the ellipse.
5. You will now draw a second ellipse. Make one point 2 cm from each side of the center point, so
that the pins are 4 cm apart. Label the top of this ellipse as “4 cm.”
6. Draw a third ellipse with the pins a total of 2 cm apart (each one should be 1 cm from the
center point). Label this “2 cm.”
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Name: _______________________________ Date: ___________

LAB: Orbits & Ellipses

As you know, each planet in the Solar System revolves around the sun. The shape of each planet’s orbit is an ellipse (or elliptical ). Unlike a circle, which is a curved shape drawn around a central point, an ellipse is a curved shape that is drawn around two points. Each of these points is called a focus , and together, they are called the foci of the ellipse. When comparing the shapes of planetary orbits, it is most helpful to describe the eccentricity (degree of flattening) of each ellipse. A perfect circle has an eccentricity of 0 because there is a no flattening. An ellipse that is completely flat has an eccentricity of 1.

In this investigation you will draw several ellipses, calculate their eccentricity, and explore the relationships between the shape of each orbit and the motion of its planet.

MATERIALS

pencil 1 sheet of unlined paper 2 thumbtacks or pushpins piece of strong approximately 15 cm long piece of cardboard at least as large as the sheet of paper metric ruler calculator

PROCEDURE

  1. Fold the piece of paper the long way (hot dog style). Without opening it, fold it in half the short way (hamburger style). Open the paper and locate the center of the paper.
  2. Make one point 4 cm from each side of the center point. Place a pushpin at each of these points. The pins should be 8 cm apart.
  3. Place your string around the pins, not too tightly.
  4. Use a pencil to gently pull the string away from the pins, and in a smooth motion, draw an ellipse. Remove the string and write “8 cm” along the top of the ellipse.
  5. You will now draw a second ellipse. Make one point 2 cm from each side of the center point, so that the pins are 4 cm apart. Label the top of this ellipse as “4 cm.”
  6. Draw a third ellipse with the pins a total of 2 cm apart (each one should be 1 cm from the center point). Label this “2 cm.”
  1. Because an ellipse is not a circle, it is said to be eccentric. The eccentricity can be calculated and expressed as a number using the following equation:

Eccentricity = distance between foci ___ length of the major axis

Use the formula above to calculate the eccentricities ( rounded to the nearest 0.001 ) of each ellipse that you have drawn. Enter your data in the table below. Be sure to use either mm or cm – do not alternate between the two!

QUESTIONS

  1. If you were drawing an ellipse, what would happen to its shape (NOT its size!!) if you used the same size string but moved the foci farther apart?
  2. Does the eccentricity of an ellipse increase, decrease, or remain the same if its shape becomes more circular? Why?
  3. What is the relationship between the eccentricity of an ellipse and how round it appears to be?

Ellipse you drew Distance between the foci (cm or mm)

Length of the major axis (cm or mm)

Eccentricity

First

Second

Third

  1. The shape of Earth’s orbit is a(n) _________________ with the sun located at one __________.
  2. Earth is a satellite of the sun. What is Earth’s major satellite? ______________________
  3. Earth is closest to the sun (perihelion) in the month of _______________________.
  4. Earth travels in its orbit most slowly in the month of ________________________.
  5. Which planets travel faster in their obits, the inner planets or outer planets? ______________
  6. Label each of the following as a cyclical or noncyclical change:

a) the changing distance between Earth and the sun _________________________

b) the changing speed of Earth in its orbit _________________________

c) the changing apparent diameter of the sun _________________________

  1. What length of time is required for one complete cycle of the changes listed above?
  2. Which planets are the terrestrial planets? __________________________________________
  3. Which planets are the gas giants? ________________________________________________
  4. a. Which of the gas giants has the greatest density? __________________________

b. What is its density? _____________________

c. Which of the terrestrial planets has the lowest density? ________________________

d. What is its density? _____________________

  1. Which two planets have almost circular orbits? ________________ and ________________