lew@ihlpa.UUCP (Lew Mammel, Jr.) (02/26/85)
Following up on my remark concerning the measurement of the precession of the perihelion I found it was Hipparchus, not Aristarchus, that first detected the irregularity of the earth's orbit. Other than that mix-up my remark was correct. Most introductory texts don't elaborate much further, but I would like to make the following note. It is "original" insofar as I didn't copy it directly from a source, but I'm sure I've seen something like it at one time or another. Hipparchus assumed uniform circular motion of the earth around an eccentric, or a point displaced slightly from the sun. It's interesting to compare the results of this assumption with the Keplerian results. The earth's orbit is very nearly circular. In fact, it's circular to within the width of a pencil line on a scale of an 8" diameter orbit. Thus the major part of the discrepancy is accounted for by assuming the law of equal areas on a circular orbit. A quick diagram shows that Hipparchus would require twice the correct eccentricity to account for his observations. To see this make the following diagram: draw a circle and place a point for the sun just off center. Draw a diameter through the sun, then draw the perpendicular to it through the sun. Finally, draw the radii to the points where the perpendicular intersects the circle. The time of transit from one end of the perpendicular through perihelion to the other end is proportional in Hipparchus's model to the area enclosed by the radii last drawn in the diagram. In Kepler's model it is proportional to the area enclosed by the perpendicular itself. Comparing these areas to a half circle, which is proportional to one half the orbital period, we see that the difference is twice as great in the Kepler model as in the Hipparchus model, so Hipparchus would require twice the eccentricity to calculate the same difference, as stated. If anybody has any corrections or additions to the above, please post them. Lew Mammel, Jr. ihnp4!ihlpa!lew