History of Science 3013: Exercise 6

Peter Barker

Ptolemy: Sizes and Distances

Question 1 : The absolute distance to the moon, at closest approach, is 33 earth radii (e.r.). The absolute distance to the sun, at closest approach, is 1100 e.r.
Using a calculator (there is probably one in your cell phone):
(a) use the formula for the circumference of a circle to work out the circumferences, in earth radii, of the circles corresponding to the closest positions of the moon and sun.
(b) if the moon and sun both seem to be half a degree wide when viewed from the earth, how much larger, in earth radii, is the diameter of the sun than the diameter of the moon?

Question 2 : Using the materials provided, make a scale drawing of Ptolemy's cosmos, using the figures indicated below. Label the spherical shell -- or orb -- corresponding to each object, in the correct order. From your drawing, determine which planet has the thickest orb.
Planet Relative Distance Ptolemy
Earth greatest
least
Jupiter greatest 14.4
least 8.8
Mars greatest 8.8
least 1.2
Mercury greatest 0.2
least 0.06
Saturn greatest 20.1
least 14.4
Sun greatest 1.2
least 1.1
Venus greatest 1.1
least 0.2
Hint: In each case find the largest distance first, and use that to select a scale that will fit your paper. It may be easiest to place the center of the system on the left edge of the paper and draw half or less of each orb.-- but some people have drawn the whole thing.