Before we get into Bruce's challenges, readers should note that Bruce never makes things easy! I guess this is goodƒƒ Well, OK, it IS good! Bruce comes up with the weirdest and wildest astronomical phenomenae, and if you take the time to thing about the things he writes and actually observe them, too, then you are always rewarded! My work is cut out for me in any Bruce McCurdy Challenge! Read onƒ..

From Bruce McCurdy <bmccurdy@telusplanet.net

January 17, 2003

Hey Rick, you wrote:

> Great RASClist article!

Thanks, eh. Funny thing is, I wrote one part of it poorly enough that I feel obliged to issue a correction. Other funny thing is, *four* people -- which is to say, four more than usual -- wrote me a note saying how much they enjoyed it, including the editor of the Victoria Centre newsletter asking permission to publish it. (Although come to think of it, a similar thing happened with my last post, An Evening With the Quadrantids, which upon the request of Bob Lunsford will be published verbatim in Meteor Trails, the newsletter of the American Meteor Society. But usually my posts, Stardust articles, and JRASC articles don't even go bump in the night.)

> I will be posting a version of the attached figure on the Gt Can Challenge Page as I own Geoff Gaherty of Toronto this challenge. (I have yet to report the results, but will)!

Very cool. Your sketches are excellent; I wish I had the knack.

One detail that brings home a subtle point from my essay, is that the shadow of Io is catching up to the GRS throughout, because Io's shadow was going 40% faster, even when the GRS was on the meridian and displaying its fastest apparent speed. The *rate* at which Io caught up would have been variable, and likely could be represented by the ubiquitous sine curve that describes all things jovian. However, in the case of Ganymede and the white oval that I observed, there was a game of cat-and-mouse due to Ganymede's slower real speed. Again the relationship between the two would be some sort of sine curve, but *one which crosses the zero line*.

So here's my observing challenge, Door Number One: using eyepiece, watch, and inductive reasoning, measure the rotational speed of Jupiter and of each of its four satellites. You are welcome to use whatever tables may be at your disposal, and to conduct computer simulations if they will help you to visualize an event, although I would prefer you not user this method to conduct measurements through the old right-click-and-drag method.

Making the dangerous assumption that it will be clear, I in particular invite you to observe in the evening hours of Thursday, February 27, when the following events will occur:

Feb 28 UT

0248 III TrI

0251 GRS Centre of spot on E. limb*

0437 III Transits central meridian

0516 III ShI

0520 GRS Transits central meridian*

0625 III TrE

0655 IV OcD

0705 III Shadow transits central meridian

0749 GRS Centre of spot on W. limb*

0854 III ShE

(*Assuming 80Á System II longitude and using the tables on P.193 of the new Handbook.) So this is not an ideal situation in that the GRS will be *in between* Ganymede and its shadow. Using them as a frame of reference, observe the GRS lag behind, begin to catch up, then lag further behind. Transit timings are not enough, as the central meridian would be the point of zero acceleration as seen from Earth; to see variations in speed you need to measure it against some other benchmark, and dark moons and their darker shadows and their constant speeds are ideal. If Jupiter is 45" in diameter, how far apart are Ganymede and its shadow? Think of these as your "comparison stars", and the GRS should oscillate slightly in between them, in a manner not dissimilar to retrograde motion. Do a series of sketches, and compare them to your Io/GRS sketches.

This might prove to be too subtle to see unless the features are right next to each other, such as I observed the other night. At a differential speed of only ~1.5 km/s, in the hour right around its central transit the GRS would only make up some 4-5% of a jovian diameter on Ganymede, or about 2 arc seconds. In a perfect world one would observe an event in which Ganymede or Callisto and/or their shadows happened to be "captured" *in* the GRS during a transit; if this happened anywhere near the central meridian the moon/shadow would appear to rock back and forth in the GRS. Particularly Callisto, I would imagine, due to its considerably slower relative speed, although its shadow might be fairly difficult to observe in the GRS. Unfortunately, the entire satellite system is now migrating to the northern hemisphere, and there will be no satellite events involving the GRS for more than six years. I likely missed an opportunity to make an observation of this nature some time in the past year or so.

So, why stop there? Measure as exactly as possible the times of first and second, and/or third and fourth contacts between Ganymede (not its shadow)and the limbs of Jupiter. If you've already figured its speed by other means, what does this tell you about its diameter (either actual, or in arc seconds)?

If you wish to tackle a greater challenge (Door Number Two), conduct a series of observations of a similar type of event, for an entire apparition of Jupiter (from heliacal rising to setting). Plot the results, and from the changing intervals from one event to the next, calculate the speed of light. (I know, it's been done, but it'd be a *real* cool obs.) You cannot use transits or occultations as they are affected by Earth's, only "light" events, eclipses and shadow transits, would be appropriate. I recommend using shadow transits of Io which are a) frequent b) can be measured from meridian transits as well as an average of ingress and egress; c) are not hidden from sight for half of the apparition, as are eclipse reappearances before opposition and disappearances after. Alternately, using the known speed of light, calculate the distance of an astronomical unit.

You won't be able to observe a complete curve due to the impossibility of observing events near conjunction, so you might have to fill in the gaps. Get enough good obs, though, and it would be like a light curve and you could fill in the blanks. Indeed, you could conduct a similar measurement by taking frequent measurements of any regular timepiece, e.g. minima of Algol. I'm sure one could examine the tables of such events and if one knew its angle to the ecliptic and also knew how to do spherical trigonometry (which I don't, believe it or not), one could derive such info about the size of Earth's orbit. So given your predilection for variable stars, why not do it that way (Door Number Three): choose a VS of absolute regularity, preferably one with a fairly short period and a readily identified minimum (or maximum as the case may be); it should be somewhere near the ecliptic to maximize Earth's changing distance (a point *on* the ecliptic, like say Jupiter, would max out at +/ 500 seconds, the NEP would be zero (which paradoxically is the opposite of what you'd want if you wanted to observed parallax, so presumably you use a sine instead of a cosine somewhere along the way); but maybe a little north of the ecliptic so that you can observe it for most of the year, and *through observation* measure time lags which yield information about Earth's orbit. This could be done in a fairly straightforward manner using tables, I believe; the challenge is to create your own tables as a log of actual observations, then use that information to derive some information about the movements of your observing station on Earth.

OK, so that gives you a choice of three challenges. Take your pick. Just let me know which one, because the others might become articles some day. I'll let *you* write the article on the one you choose.

regards, Bruce