Download Titus Bode Law

Titus Bode Law
The Titus-Bode Law is rough rule that predicts the spacing of the planets in the Solar System.
The relationship was first pointed out by Johann Titus in 1766 and was formulated as a
mathematical expression by J.E. Bode in 1778. It lead Bode to predict the existence of another
planet between Mars and Jupiter in what we now recognize as the asteroid belt.
The law relates the mean distance
of the planets from the sun to a simple mathematic progression of numbers.
Body
Actual distance (A.U.)
Bode's Law
distance in A.U.
Mercury
0.39
0.4
Venus
0.72
0.7
Earth
1.00
1.0
Mars
1.52
1.6
?
2.8
Jupiter
5.20
5.2
Saturn
9.54
10.0
Uranus
19.19
19.6
Neptune
Pluto
Do you notice a pattern in the distances? What should belong in the location with the? Make a
prediction on the Bode’s Law distances for Neptune and Pluto and write it in the last column of
the table.
Planetary Science
Page 1
Titus Bode Law
METHOD USED BY TITUS: To find the mean distances of the planets, beginning with the
following simple sequence of numbers:
1. 0
3
6
12
24
48
96
192
384
With the exception of the first two, the others are simply twice the value of the preceding
number.
2. Add 4 to each number
3. Then divide by 10
These numbers are a geometric sequence and are closely related to the actual distance of many
of the planets in the solar system.
Use the table below to follow Titus’ mathematical process.
Number Sequence
0
3
6
12
24
48
96
192
384
Add 4
Divide by 10
Identify the Planet
This method correctly predicted the existence of Ceres and Uranus.
1. Write the actual average distance (in AU) to Neptune and Pluto in the table provided on the
front.
2. DOES IT CORRECTLY PREDICT THE LOCATION OF NEPTUNE AND PLUTO?
3. Make a prediction on why you think these two planets do not follow the geometric sequence.
Planetary Science
Page 2