1) That the visible planets were not self-luminous objects? Didnt they think that these fast-moving objects were actually smaller stars that were much closer to the earth?

I am sure when Galileo saw the phases of venus, he could conclude that they arent self luminous (like the moon). Wondering whether people knew prior to that..

2) how to measure the right-ascension (or equivalent) of a planet as it moved across the sky?

I was reading about how Tycho Brahe measured planetary positions in the sky, and how Kepler used that to figure out that the orbits were ellipses, and then the "Law of Equal Areas". Very fascinating. I myself am keeping an eye on how Jupiter's moving through Capricorn right now, and faster-moving Mars is moving through Gemini and Cancer. And I wonder how Tycho Brahe made those quantified measurements.

I look forward to more definitive answers on this, but my understanding is that the ancient Greeks tended to favor self-luminous because of their apriori view of the luminous essence of the celestial sphere. Nevertheless, other Greeks likely countered this view because of the more apparent illumination explanation for the Moon.

By this time, I think illumination was favored anyway. He also observed Mercury's phases, too.

Think how you would measure dots moving very, very slowly on a sheet of paper. I'd use a compass and protractor if I had nothing fancier for tools. The Arabs had some very large instruments for this and produced at least one major star chart in the 13th century. Apparently they used arcminute graduation as did Tycho. Tycho's work, no doubt, was superior.

It was Tycho's data for Mars that confounded Kepler for a very long time before he realized that the ellipse solved the puzzle, along with non-uniform motion. Had he not fully trusted Tycho's data, it is questionable that he would have continued since there was not a lot of variation comparing the orbit of Mars as an ellipse with a circle. The circlular orbit for all celestial orbits was a given in those days.


You can Google to see his instruments and astronomical island. One particular thing he did that is very interesting to me: he obtained 1/2 arcminute resolution for some objects. This is incredible given that the human eye is limited to 1 arcminute resolution. Care to guess how he did it?

__________________
Lighten up! This is a stellar board!

He squinted?

My first guess was that he went beyond the naked eye.. possibly magnifying glasses in some crude form.. well, he lived just a wee bit before the telescope's invention.

My next guess would be that a division-by-2 operation was performed somewhere on the actual observations to get down to the 0.5 arcminute accuracy. I googled further, and got this:
"Though accurate to one arcminute for a single observation, Tycho greatly refined his values by repeating the same observations over months or years so that when his observations were reduced in the nineteenth century, they were found to be accurate to 24 arcseconds"

And he probably squatted, but neither would help.

Nope, no optics.

That I didn't know, but it is close [to the answer]. For some objects he used multiple observers that allowed him to do an averaging of their results to derive a more accurate value.

BTW, Tycho recruited Kepler as he was not up to the task of completing the work. Kepler was a better mathematician.

__________________
Lighten up! This is a stellar board!

When Galileo studied Venus' phases, I wonder whether he was consciously looking for evidence that Venus orbits the Sun (and thus evidence for Copernicus' theory)

Or did he just 'stumble' across that evidence, while observing the most prominent features of the skies?

I would guess he used a diffraction grating to provide a pin-hole like resolving effect. I would think a loosly-woven black silk cloth would have done the trick.

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

They took multiple measurements and averaged... however, I'd like to point out that though the eye is limited to 1 or 2 minutes of resolution, by having the instrument eclipse the object, the eye can be used to detect much smaller spatial positions. No optics required, and by Brahe's team, none used.

__________________
Forming opinions as we speak

I'm interested in this device. Do you have a description of it somewhere? How do they control for the position of the eye itself?

Brahe used several devices. Here's a link to his descriptions of the earlier ones in his collection. You'll need to scan to page 10 to start seeing the actual instruments. In some cases it is obvious how he handled the eye placement problem.

Please note that before Brahe, Ulugh Beg had an observatory in Samarqand that was much larger and afforded slightly more precise measurements than Brahe's equipment.

__________________
Forming opinions as we speak

In Latin!

I see the illustrations though. Which one specifically?

Sorry about the Latin...

I made a replica of the one seen on page 26, and used it. It's good to about 3 or 4 minutes, because it depends on eye-slits, and is only about eight feet long along the site.

The one on page 36 is the one that Brahe got his best measurements from.

__________________
Forming opinions as we speak

And better than the 1 arcminute?

Wait, page 37 doesn't have an illustration, it just has SEX- at the bottom. O, nevermind...

The first diffraction grating was by Rittenhouse, circa 1785, so it's unlikely Kepler used one, or Brahe. SEE:http://gratings.newport.com/library/...k/chapter1.asp


pete

__________________
A third rate theory forbids.
A second rate theory explains after the fact.
A first rate theory predicts.
A. Lomonosov

The instrument itself as markings in units of 15 seconds.

__________________
Forming opinions as we speak

[Nice link!] Why do the eye-slits hurt the resolution?

__________________
Lighten up! This is a stellar board!

There are some practical limitations based on how much light can come through a slit of a given size. To see a star of 1st magnitude with your eye, the slits have to be a couple millimeters wide. This, and the diameter of your pupil lead to some uncertainty as to the exact angle. The longer the sighting bar the more accurate an angle you can get.

If someone were to build a geometrically stable parallaticum (or triquetum, or dreistab as it is variously known), with a 100 foot sighting arm, you could easily and reliably get angles much better than the 1 minute limitation of the human eye. Manufacturing such a device was difficult or impossible in Brahe's time.

__________________
Forming opinions as we speak

I can see that

The image on the eye from a point at infinity is going to be approx. the same as the image at the 1mm slit, so for a 6mm pupil (area 28 mm²) it's going to be receiving only 1 mm x 6 mm light, or 6/28, of what it would without the slit. Isn't that a decrease of 1 2/3 magnitudes?

How does the eclipsing affect this?

Concerning the dimming, my slits were about half a millimeter, and I could find and observe 1st magnitude at best. I calculated the numbers just like you did, and figured I should be able to see 2nd with little trouble... but no. The tool was great for seeing the clock stars.

Eclipsing lets you see the object at full brightness on either side of the eclipsing object, and so the angular range of when you are doubting what you are seeing is much smaller.

__________________
Forming opinions as we speak

I assume the slit is at the far end of the sighting rod. I also assume, for narrow slits, that the diffraction, of which you've mentioned, from the slit spreads the light so that the dim objects become too dim to resolve effectively.

Yes, I see now. A wider slit can be used at a further distance to gain accuracy without much dimming. But they were limited in their ability to make very straight guides.

Was their likely desire for greater length called "guide length fever", prestaging today's "aperture fever"?

__________________
Lighten up! This is a stellar board!

I dunno, pete - I've been putting my fingers together to make pinholes which improves distance vision since the third grade.

It's highly likely given various weaves of fabric that an accidental diffraction grating was stumbled on hundreds, if not thousands of times since the dawn of fabric.

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Thanks for all the inputs guys, appreciate it. Got to appreciate how dedicated the pioneers were. Brahe.. 25 years of research!! I also envy that they lived in times when there was no light pollution, and thus could carry on research more conveniently. I wonder how modern astronomers carry out their research, esp in the NorthEast US.

More questions..
3) I read that "In 1846, the planet Neptune was discovered after its existence was predicted because of discrepancies between calculations and data for the planet Uranus".

I understand that there are significant gravitational influences by the neighbouring giant (or otherwise) planets, but what exactly are the observable outcomes? Does the planet stray from its elliptical orbit a wee bit? like.. tugged out or pushed in? And these are really observable from earth as arcminute deviations?

I think that technique works because it reduces the circle of confusion, and mostly in near-sightedness. For stars, which are point sources in good seeing, wouldn't that just reduce the amount of light, making them harder to see? Kinda like the slits we were discussing earlier.

Yes, it strays a wee bit. To the best of my memory, Uranus wandered as much as 20 arcseconds from its predicted position between 1781 and 1846, an amount readily observable by skilled observers with the telescopes of the time. This was after allowing for perturbations by Jupiter and Saturn. Master mathematicians such as Laplace made the calculations possible before the advent of electronic computers. Unfortunately I cannot put my hands on any references immediately, so don't take that as gospel without some corroborating research. I saw accounts of the observations in various books and in Sky and Telescope over the past few decades.

This resource says that the error was 70 arcseconds by 1841.

Thanks for the reference. That is upward of an arcminute. If we could magically make the planet about 1st magnitude, Tycho might have been able to detect the discrepancy.

The planets were originally considered "wandering stars." The fact that they scintilllated ("twinkled") less than others, were shining with a steadier light and, most importantly of all, moved through the sky all staying within the zodiac made them different.

I'm not exactly sure when their true nature became clear but I would guess that once we saw the ice caps of mars, the bands of Jupiter and the ring of Saturn whilst stars remained mere points of light, it was pretty clear they were very different kettles of fish.

I think this understanding may have just crept up and evolved rather imperceptibly rather than all coming in one "Eureka!" moment. But I'm not really sure and may well be wrong.

__________________

According to Wiki, he sextant had a radius of 36m, giving an optical separability of 180" of arc. http://en.wikipedia.org/wiki/Ulugh_Beg

I went on a tour of Ulugh Beg's observatory on New Year's Eve 1988. We stayed until after dusk and were shown how it was used. Always been interested in him since then (and I bought all the lapel badges of him I could find).
He was ruler of the Timurid Empire and built a (beautiful) school in Samarkand to which he invited leading astromers and mathematicians. He was murdered by his son in league with the local religious community. It's always been dangerous being an astronomer, it seems. We got a minor earthquake as we left.