AST 3043: Web Links

MISCELLANEOUS WEB SITES

AST 3043

The pictures shown here are time exposures of the night sky. The motion of the stars over the course of the exposure causes them to leave trails, just as a night scene showing car lights would. In the southern sky as seen in Gainesville the trails look somewhat like this (without the saguaros, of course!); in the east they look something like this; and in the northern sky they look like this instead. The reason for the difference is explained in the next set of links. A really unusual photo is this one, taken atop Mt. Kilimanjaro.
This definition of the celestial sphere is from Wikipedia.
Here are some links to pages dealing with the celestial sphere and the apparent motions of the Sun and Moon from Dr. Nick Strobel: (a) daily motion of stars and celestial sphere at different latitudes; (b) Sun's apparent motion around the celestial sphere, caused by Earth's revolution around it; (c) solar and sidereal days and tropical and sidereal years and seasons; (d) coordinates including equatorial; and (e) sidereal and synodic months and Moon's phases, eclipses. There are a few minor errors in these. First, at the North Pole all directions are S, which changes a couple of things. Second, at one point it states that the equatorial coordinate system is fixed with respect to the stars, meaning that it doesn't change. That's almost right; just remember that precession does cause a slow change, as it says farther down. Thirdly, the diagram showing the celestial sphere with the ecliptic going up from right to left is backwards -- it should be the other way. (Think about it!) Fourth, the path of the North Celestial Pole with precession is seen looking up, just as in lecture. Lastly, you can ignore the mention of the Moon's perigee in connection with eclipses, and what Strobel refers to as "precession" is what I have called "regression." I think those are all the ones that count.
Dr. Strobel has kindly provided a glossary of astronomical terms on his Web site.
The Moon's path with respect to the ecliptic is shown in this figure, with the nodes marked on the ecliptic. The regression of the nodes and the turning of the line of nodes in the plane of the ecliptic are shown in an animation partway down this page. There's some other useful information about eclipses on the page. Watch out for the numbers, though -- I've only glanced at them, but some aren't quite right.
Here is a link to Wikipedia's explanation of lunar standstills. Warning: This article goes into more depth than I did in lecture. The major standstills diagram from lecture is here and minor standstills here.
Here are some links to Stonehenge; of course there are many more. First, try out this site, which has some nice pictures (and some extraneous stuff) or this site. To find out how the different parts of Stonehenge have been assigned ages, go to this link. National Geographic has a special on Stonehenge in its June issue, and I found a gallery of photographs connected with it. Notice that in one of the captions they mention a recent idea about Stonehenge, that it was a site of healing, perhaps because of the presumed powers of the bluestones. Such an idea doesn't seem unreasonable, but it could also be yet another example of the "Stonehenge one desires," especially if one is into New Age. Somewhere I saw it reported that among the human remains found at the site there were a number that showed signs of deformity; if so that would support the idea.
Ballochroy is a megalithic site in Scotland that was studied by Alexander Thom, a Scottish engineer who surveyed many such sites in the British Isles and northern France. It's discussed briefly in Hoskin.
Here's a link to some information and color pictures about Newgrange.
The configurations of inferior planets are shown in this page. Another Web page, which also gives information on the phases and location in the sky, is here.
The phases and configurations of superior planets are shown at this page.
The motions of the planets are represented by this Electric Orrery. However, it seems to be a little flaky, so if you can't reach it at first be patient and keep trying.
I've found a couple of pages dealing with retrograde motion. For an animation showing what retrograde motion looked like on the sky a few years ago as well as diagrams showing how it worked in the Ptolemaic system and how it works in the modern (Copernican) system click here. (Try to ignore the spelling mistakes and typos!)
To the Inca, the Milky Way stood out in the sky, partly because the sky was dark (unlike today in Florida, say) and partly because the most conspicuous portion lies in the southern sky. An all-sky photograph, which is a projection of the entire celestial sphere onto a flat surface, shows the dark patches which the Inca identified with so-called "dark constellations."
This is a virtual tour along the Inca Trail including views of Machu Picchu. You can actually jump directly to pictures of Machu Picchu and not make the entire trek.
Here's a link to a page with some pictures of the pyramid of Kukulcan known to the Spanish as El Castillo, including a closeup of the serpent heads at the foot of the stairs.
One of the great Chinese astronomers was Guo Shoujing, who was also an engineer and mathematician. More details about the measurements made with the Sky Measuring Scale at Gaocheng Observatory and Guo's improvements of the armillary sphere (discussed later in connection with the Greeks) may be found in this research report in pages 23 through 32. (It's a .pdf file, so you'll need Adobe Reader. The first 8 pages are about the history of the Chinese calendar, while the middle part deals with some of Guo's work in mathematics. You can find a less formidable sample of the latter at this Website for biographies of mathematicians. There you'll also find a more complete account of his life than at Wikipedia, which has only a stub.)
Ecliptic coordinates are shown in this diagram, although it also has the equatorial stuff in it and thus is a little bit complicated.
The Tusi couple is a device created by Nasir al-Din al-Tusi based on a theorem that converts uniform circular motion into linear motion. It was a key ingredient in several models that eliminated the eccentric and/or the equant. An animation shows how it works. Click on the button at lower left that turns on the trail feature, then click the forward button at upper left. In the original version the smaller circle is half the radius of the larger one, while you can change that with the sliders at lower right.
Compare al-Shatir's model for the Moon's motion with Ptolemy's version. As before, click on the trail button before starting. Notice how the distance from Earth varies with Ptolemy's version, then with al-Shatir's. (You can pause the animation after one cycle to see it more easily.) Copernicus made use of essentially the same device as al-Shatir at one point.
Kepler's Laws of Planetary Motion are discussed here. Here's an animation illustrating Kepler's First and Second Laws. You can compare the equant device used by Ptolemy (with the Sun replacing the Earth) with Kepler's Law of Areas using this animation created by Dr. Dennis Duke of FSU. (He also did the ones in the previous item as well as the second one in the item before that.)
Galileo claimed that the apparent motion of sunspots across the Sun's disk was consistent with their being surface markings on the Sun but not consistent with their being the silhouettes of objects passing between the Earth and the Sun. Compare this animation made up of satellite images showing actual sunspots with an animation representing a transit of Mercury. Also, there's an animation of Galileo's drawings from the Galileo Project at Rice University.
Diagrams showing the workings of the Galilean and Keplerian/astronomical refractor are presented on this page. There's also a lot of detail about the fields of view of the two types and some formulae, which you needn't bother with.
Chromatic aberration is shown in this diagram. A partial solution is the achromatic objective, which with two different kinds of glass can bring two colors to a focus at the same point. It reduces, but doesn't completely eliminate, chromatic aberration. (The diagram is slightly inaccurate because it suggests all colors are brought together.) Newton's first published paper in Philosophical Transactions recounts his experiments with prisms which led him to this discovery.
With either lenses or mirrors that have spherical surfaces one can have spherical aberration, where rays that come in to the mirror at different distances from the central axis are brought to a focus at different distances from the center. With the reflector the solution is to use a paraboloidal mirror. (You'll have to scroll down the page a bit.) The mathematical shape of the paraboloidal surface is shown in this diagram.(WARNING: There's some scary-looking stuff on this page about "partial derivatives" and whatnot. Pay it no mind.)
Here is a link to some diagrams showing what images look like as a result of coma with the Newtonian design of reflector. I haven't been able to find any diagrams showing the paths of rays in a paraboloidal mirror setting that illustrate it, at least not yet.
This animation illustrates uniform circular motion. The blue arrow ahead of the moving point represents the point's velocity; the arrows marked v0 and vf are the velocity at the beginning and end of some time interval, and the green arrow marked "-v0" is the negative of v0, essentially subtracting it from vf. The red arrow represents the change in velocity; it points towards the center and marks the direction of the centripetal acceleration.
Diagrams showing the conic sections may be viewed at the top of this page (along with some of the relevant math, which you can skip).
A diagram of tidal forces is this one.
In class I made a passing reference to more about the tides, which I skipped because of lack of time (and also because Newton himself only briefly thought about some of this over the time between the first and second editions of Principia). The topic I left out is tidal friction, which arises because the motion of the waters in response to tidal forces is not perfectly efficient but has some friction associated with it. Consequently the tidal bulges lag the imposed forces, and they end up pointing a little ahead of the Moon instead of directly at it. The reason for this last is that the Earth rotates faster than the Moon revolves around it. The nearer of the two bulges pulls the Moon forward more than the farther one pulls backwards. As a result the Moon gains angular momentum and moves slightly farther away from Earth. The reaction (remember Newton's Third Law of Motion) has the Moon pulling "back" on the tidal bulges, which slows the Earth's rotation down gradually. Even though the Moon's orbital speed decreases as it moves farther away (because of Kepler's Third Law), when we view its motion using the Earth's rotation as our clock and that clock is slowing down the Moon seems to be accelerating; this is called the Moon's secular acceleration ("secular" meaning over a long time span). The history of our ideas about tidal friction is very nicely presented in a short article by Dr. Peter Brosche, who has done research in this field. In his article he makes some general remarks about the development of science which I personally find very trenchant. If you're interested you might take a look. (I had someone ask me about this after class, which suggested the idea of posting this link.) I will warn you that it's somewhat technical and thus a challenging read for a non-scientist. The process described will eventually, over some several billions of years, result in the Earth and Moon turning together, i.e. the day and the month will have the same length. At that point the Moon will be considerably farther away than at present. Long before then we'll stop having total solar eclipses. The solar tides will continue to slow Earth's rotation, and the tidal bulges will be turned the other way. Then the Moon will start to come in and the Earth's rotation will speed up.