3 April 2007

Back when I was attending AAA meetings John Pazmino would often speak of observing the image of the Sun projected through the lattice work around the windows of Grand Central Terminal onto the floor of the terminal. I have often looked for it but have never seen it until today. When passing through the terminal around 1230 EDT I saw splotches of light lined up on the floor from around the center of the terminal to the west and up onto the banister along the stairs there. I was hoping that they might be images of the sun but as I approached them they blurred out and merged together. I walked across the floor past each set of light spots and up onto the steps. Turning around from there the effect was very pronounced. There were chains of circles. But as I moved close to each one it became indistinct and merged with its neighbor. I suspect that the holes in the lattice are too big to project a sharp image and that only huge sunspots would be visible in this way.

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I found a web site today that has instructions for calculating the focal length of an eyepiece but they assume you are making the eyepiece and know the focal length of the component lenses.

Effective Focal Length=(f₁*f₂)/(f₁+f₂-d) Where f1 is the focal length of the eye lens, f2 is focal length of the field lens, and d is the distance between them in mm.

In a post by Don Taylor to the sci.astro forum I found these instructions for inferring the focal length of a lens based on a projected image.

If you want to try measuring the focal lengths of your eyepieces here is a simple way that seems to give me good accuracy of about +-0.1 mm in the focal length even for the short focal length eyepieces. It also works if the eyepiece is used with a Barlow and gives the effective focal length of the eyepiece+Barlow combination so you can thus get the amplification factor.

Its based on measuring the magnification seen when you use the eyepiece to project a Ronchi grating on to a distant screen (im my case a white wall). To use it you put a Ronchi grating behind the eye end of the eyepiece, with a flashlight behind the Ronchi to illuminate it. You then carefully adjust the separation of the eyepiece from the Ronchi so that a sharp (greatly enlarged) image of the grating is shown on the wall. You the measure the separation of the projected lines on the wall (I measure the span of about 5 cycles and then divide by 5). Knowing the # of lines/inch on the grating you divide the separation on the grating itself into the measured separation as projected to get the magnification. The only thing left is to measure the separation of the eyepiece from the wall. To a first approximation the eyepiece focal length is that distance divided by the magnification. If the distance to the wall is much larger than the focal length the error will be small. To get a better approximation you have to allow for the separation of the eyepiece principle planes. You can correct for that by changing the distance to the wall and repeating the measurement. The math for that is not hard but perhaps a bit long for a post here. By the way I posted on this in sci.astro.amateur back on about Feb 10,2000.

If you don't have access to a Ronchi grating, a transparent ruler with a mm scale can also be used but the projected mm separation is large for short focal length eyepieces and distortion may then throw off the result.

Now I have to find where my transparent ruler has gone to and rig something to hold it and the eyepiece without damaging either while keeping them parallel with the wall.

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Since I missed the smallest full Moon of the year last night due to clouds, I decided to look at apogee and perigee distances tonight. I looked up the distance for each event during 2007 is the Observers Handbook 2007 and graphed them.

I was surprised to see that there is more variability in the perigee distance than in the apogee distance. I am not sure why that is.

	Perigee	Apogee
Maximum Distance	368,891	406,671
Minimum Distance	356,753	404,150
Difference	12,138	2,521

Looking at the graph I noticed that each of the distances followed a sine wave curve. I wondered if there was any relationship between the two curves but it wasn’t easy to see on this graph so I tried redrawing it as a line graph. To get the curves to appear in the proper spatial relationship I had to leave blank lines between subsequent apogees and perigees and then Excel wouldn’t draw a line graph. It appeared that the two covers were converging and diverging in synchronicity but without the lines it is a little rough to see. So next I interpolated the missing data to get a complete line.

Apogee	3Apr07	406,329		Apogee	22Jul07	404,150
Perigee	17Apr07	357,136		Perigee	3Aug07	368,891
Difference		49,193		Difference		35,259

It does look to me like the Moon is farthest away at perigee when it is also farthest away at apogee. But this graph is only for one year so it is possible that this is just chance and that if the graph covered a longer timeframe the curves would not exhibit the same periodicity.