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Asteroids, Part II

The Titius-Bode Law

When investigating a natural phenomenon, such as planetary motion or weather, finding a repeating pattern is an important discovery. A predictable pattern suggests that there is an underlying order that can be understood and modeled. It also enables you to test whether the pattern can explain other events. In the late 18th century, astronomer Johann Bode and mathematician Johann Titius found that the planets’ orbits around the sun were spaced according to a mathematical relationship:

                                        (n + 4)
Distance from one planet to the next = --------- where n= 0, 3, 6, 12, 24, 48 ...
Consider the information in the following table:
Titius-Bode Law
(relates the average distances of the planets from the sun
to a simple progression of numbers)
Planet Distance from Sun
Titius-Bode’s Sequence of Numbers
(except for the first two, twice the value of the preceding number)
Add 4
(representing the orbit of Mercury in AU)
Predicted Distances
(Divide by 10)
Mercury 0.4 0 4 + 0 = 4 0.4
Venus 0.7 3    
Earth 1.00 6    
Mars 1.5 12    
No planet   24    
Jupiter 5.2 48    
Saturn 9.6      
Uranus 19.2      
Neptune† 30.1      
Pluto‡ 39.2      

* One Astronomical Unit (AU) is the distance from the Earth to the Sun: 93 million miles.

† Neptune was not discovered until 1846, about 60 years after Titius and Bode presented their model.

‡ Pluto is now reclassified as a "dwarf planet." However, it is still useful to include it in a discussion of the Titius-Bode Law. Pluto was discovered in 1930.

What to Do

First, calculate the values required to fill in the table above.

Next, obtain a piece of graph paper. Put the distance of each planet from the Sun on the x-axis. These distances are given in Astronomical Units (AUs). Set the maximum for the graph based on the values in the chart and then space them so the highest value will fit. Use groups of 2, 5 or 10 boxes in your scale. Put the Titius-Bode Predicted Distance values on the y-axis. The maximum for this scale is near 80. Put 80 as near the top of the graph paper as you can after you decide the widest spacing between values on the graph. Again, use groups of 2, 5 or 10 boxes. Use the whole sheet of graph paper for this graph by carefully selecting your scales.

Finally, answer the questions on the back of this handout.

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Answer the following questions based on the calculations and graph you have made.

  1. The first asteroid was discovered in the early 19th century, decades after Titius and Bode developed their law. Yet, the Titius-Bode Law anticipates the existence of the Asteroid Belt, the collection of widely scattered rocks orbiting between Mars and Jupiter. Explain.
  2. Which planets match up well with the orbits predicted by the Titius-Bode law?
  3. Which planets do not match up well?
  4. If the Titius-Bode law made good predictions about the locations of the planets’ orbits, what would the graph you made look like? Sketch it.
  5. How is the graph you made different from the graph that you described in the answer to the previous question? What does that tell you about the Titius-Bode law?
  6. What evidence suggests that the Titius-Bode law is imperfect?
  7. The Titius-Bode Law describes how the planets are spaced in the solar system. It does an imperfect job of it but it is a decent starting point. What is does not do is explain why the planets are spaced out the way they are. Models in science attempt to describe the way things are. Theories in science attempt to explain why things are the way they are. Try to come up with a physically reasonable theory about why the planets are spaced well away from each other. Write down what you come up with here:
Asteroids, Part I
Asteroids, Part III
Asteroid Facts Worksheet
Asteroids: What should be done about Apophis?
Last updated: Nov 30, 2009 Home
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