lew@ihuxr.UUCP (12/14/83)
Earlier I reported that a correct analysis of the data presented in an Astronomical Journal article (Vol 78 no. 1, Feb 1973, pg. 122) gave a value of "C" about 8% low. The data consisted of observations of Io's ingress and egress in and out of Jupiter's shadow made by Ole Roemer from 1668 thru 1678. I had adjusted a set of 40 numbers labled "obs. minus calculated time" to obtain this figure. I found I needed to SUBTRACT 8% of the nominal delay time for each datum to obtain the best fit. This meant that the fitted delays were 8% longer than nominal. Well, I had another surprise. In trying to reproduce some of the calculations, I found that the data was REALLY the predicted minus observed times. I was therefore reducing the delay times with my adjustment meaning that the best value of "C" is 8% high. I got on to this trail becuse I got a high value of "C" when I did a "naive orbit" calculation. As I added refinements it didn't change much and I finally found out why. I found that I couldn't precisely reproduce much of the tabulated data, even though the intermediate results in the paper should have allowed me to do so. The discrepancies are never great enough to change the result, though. I ended up redoing enough of the calculation that I readjusted the longitude of the ascending node of Io (wrt the plane of Jupiter's orbit). I reduced the residual rms error from 1361 to 1326 microdays this way. This gave a predicted "C" about 6% high with an 8.6% expected error. Plotting the predicted versus observed delay times showed that most of the data was crowded around the average delay time. There were two points way out at one end that controlled the fitted value. The "ballast" around the average controlled the rms error, though, so that kept things honest. It occurs to me that since Io is "pinned" in Jupiter's equitorial plane it should be easy to calculate the longitude of Io's ascending node circa 1670. This would only depend on the precession of Jupiter's axis of rotation, which I would expect to be very slow (period >> 10k yrs). I can't find boo about the precession of Jupiter's axis anywhere. Even the Explanatory Supplement is no help. It just refers the reader to Sampson's definitive work. Anybody happen to know the orientation of Jupiter's axis? Finally, I'll note that I got into this whole thing because this paper was referenced in a creationist work. I'll confine my remarks on that subject to net.religion, so look there if you're interested. Lew Mammel, Jr. ihnp4!ihuxr!lew