Roemer Redux

Last updated Sun Feb 3 2002

Introduction

The first ever determination that the speed of light was finite took place in the majestic theater of the solar system over 3 centuries ago, took 8 months, and featured the king of planets himself, Jupiter, and his close companion, Io.

Not really knowing what I'm getting into, I'd like to recreate this experiment from the comfort of my suburban home, using commonly available tools and maybe a little tinkering. For astronomical reasons it is likely to also take 8 months of data collection, and may well extend beyond 2002. At this point I seriously doubt I will be able to generate data as good as that generated by Olaus Roemer in 1876.

My initial thought was to record here everything I tried, good or bad. More interesting, I now realize, is to focus on what I am now doing and how I am going about it.

Model

One needs a model of what one is trying to measure. One ounce of theory is worth ten pounds of tinkering. Here is mine -- a work in progress of course.

First I determine that of all tme Jovian satellite events (eclipses, occultations, body transits and shadow transits), eclipses are simplest to study. So I'll focus my investigation on eclipses.

Next with the help of a parametrized model, I anticipate what can be observed, how best to display it and how I can extract the number I'm looking for: c.

Telescope

My telescope is the very compact Meade ETX-90 (90 mm = 3.5 inch aperture, 125 cm effective focal length). I bought this unit a few years ago, and it is still a best seller. The newer models are computerized and have other niceties, but for this experiment none of the extra gew-gaws are going to matter. If the old model can't succeed at this experiment, then the new computerized features are not going to help. I have seen the old ETX-90 on ebay for $250, a fraction of what I paid for mine new!

Observations

Using my 3.5 inch telescope I have started recording the Jovian satellite events that I witness. I will try to draw conclusions only when enough data has accumulated.

I track Jupiter with a small magnification eyepiece (26mm yielding 48X magnification) until the time for the event predicted by the 'Jovian Events Calendar' draws close. Then I switch to higher magnification (9.7mm eyepiece yielding 129X). To collect 1 data point takes only 15 to 20 minutes so I typically don't bother doing a polar alignmnet of the scope and track by hand.

Occultation events occur when a satellite is in the line of sight of a limb of the planet. At an illuminated limb it is hard to track or spot the satellite's speck of light in the glare of the planet. At the shadowy limb, tracking or spotting is much easier and a much better time resolution is possible. However, because of line of sight effects, an occultation is a relative effect and understanding its correct timing is more tricky than for an eclipse.

Eclipse events occur when a satellite enters or leaves the shadow cone of the planet. The challenge in this case is that the speck of light doesn't switch off or on in an instant. For an EC-I it dims for several minutes before flickering off and for an EC-E it slowly brightens over several minutes. An eclipse is an intrinsic effect: it happens from all vantage points at the same time so it is easier to understand their timing than that of an occultation.

I call an EC-I event when I conclude I have lost track of the speck, and an EC-E when I think I have caught my first glimpse of it. As the language reflects, there are some error bars somewhere in there! Actually, when I saw my first clear EC-E of Io (I), I was impressed by how unambiguous the reemergence is. Timing to within a few seconds should be possible with a chronometer close at hand.

I am not too worried that my observations don't match the predicted values to the minute. It is reasonable to argue that by using the same instrument with the same eyepice and the same eyeball, my data will be consistent. Mixing data from different instruments and different observers would be more open to question. One would have to devise less subjective criteria to time the events.

                                          Visibility
Predicted                       Observed  1=worst,    Estimated Timing Error
Date and Time         Event     Time      5=best        +/- seconds
--------------------------------------------------------------------------------
2002-02-04 03:13:00   I  OC-I   03:09:00  4            60/30
2002-02-04 06:16:41   I  EC-E   06:14:30  5            30/60
2002-02-08 02:32:30  II  EC-E   02:30:00  3            30/60
2002-02-13 02:40:36   I  EC-E   02:38:30  4            30/60
2002-02-17 00:18:53 III  EC-I   00:11:00  1           300/30
2002-02-24 04:18:23 III  EC-I   04:19:20  5            10/10

2002-10-19 08:28:00  II  EC-I   08:28:23  4            20/20