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Orbital Eccentricity (page 2)

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Author: Christopher Crockett

Going Further

Draw scale models of the orbits of all the planets! The first thing you’ll need to do is decide what sort of scale to use. For the inner planets (Mercury, Venus, Earth, and Mars), using 1 AU = 10 cm should work pretty well. For the outer planets, you will need to use either a much larger sheet of poster board or switch to a different scale. Try and figure out what scale would be useful for drawing Jupiter, Saturn, Uranus, and Neptune on a single poster board. What challenges do you run in to if you try to draw all the orbits using one scale?

You also need to calculate how far apart the foci need to be based on the orbital data in Table 2. The distance between the foci is simply the difference between the aphelion and perihelion distances: f = a – p.

Follow these steps to make your scale drawing:

  1. Convert the aphelion and perihelion distances of the planets to centimeters and record your results in Table 3. Example: Earth aphelion = 1.02 AU x 10 cm/AU = 10.2 cm.
  2. Calculate the distance between the foci for each orbit. Record these distances in Table 3.
  3. Follow the steps from the original drawings to place the pushpins the right distance apart and set up the string and pencil. To get the string to be the right length, you will need to cut it to be equal to twice the sum of the aphelion and perihelion (plus a few centimeters extra to make room for the knot). Record the length of the string you’ll need in Table 3.
  4. Draw the orbits for each of the inner planets on a single poster board. Which is the most eccentric? Which is the least?


Aphelion (cm)

Perihelion (cm)

Foci distance (cm)

String length (cm)









































Table 3.

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