Monday February 7 2011

********* No class was held 2 or 4 February because OU was closed due to winter weather********

Moon and Jupiter tonite

Earthshine This picture of the crescent Moon was taken with a telephoto lens. The sunlit crescent is overexposed to show that the rest of the Moon is NOT completely dark (as you might expect, as this is the NIGHT side of the Moon) because of sunlight reflected from the Earth - Earthshine - which is lighting up the dark side of the Moon. If you were standing on the Moon when this picture was taken, you would have seen an almost "full" Earth. As the Earth is larger than the Moon, and much more reflective, the full Earth as seen from the Moon would be about 100 times brighter than full Moon as seen from Earth.

The star pattern you see is not the Big or Little Dipper (which would be much bigger than the area covered by this photograph) but is a famous cluster of stars called the Pleiades or Seven Sisters.

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Astronomers who finally got it right! This time line shows the dates of the lifetimes of the astronomers who, about 400 years ago, figured out the correct model for the solar system.

**************** Tycho Brahe- Superb Observer ****************

Tycho Brahe solar system model.. Tycho Brahe devised a model of the solar system that is a combination of the geocentric and heliocentric systems. The Earth was at the center, with the Sun orbiting the Earth. The other planets orbited the Sun, rather than the Earth. This goofy looking model was soon forgotten, but Tycho was an important figure in figuring out the right model. Tycho was a excellent observer of the positions of planets. Tycho's careful observations of the position of the planets over two decades were used by Kepler to derive Keplers 3 Laws of Planetary Motion.

Tycho This old artwork shows a montage of Tycho and one of his measuring instruments. He measured the positions of the planets using instruments that were essentially building-sized protractors. (You all remember getting the little plastic protractors to measure angles in school, right?)

************* Kepler and Ellipses *************

While Copernicus made the biggest breakthrough in our understanding of the solar system- realizing that all the planets orbited the Sun, not the Earth- Kepler made another monumental breakthrough by realizing that the planets moved on elliptical orbits, rather than circular orbits. This helped allow astronomers to junk the (to us at least) crazy business of epicycles. Once it was realized that the planetary orbits were ellipses, then the future positions of the planets could be predicted much more precisely than for any previous model of the solar system.

Keplers Laws of Planetary Motion Using the excellent body of planetary position data taken by Tycho, along with what can only be described as pure awesome genius, Kepler derived these laws of planetary motion. They throw out ALL the main ideas of the ancient Greeks- the planets orbit the Sun, not the Earth, the planets move on elliptical paths, not circles, there are no epicycles, and the planets change their speed as they go around the Sun.

Drawing an ellipse.. (a) You can draw an ellipse with two thumbtacks (the two foci) and a loop of string. If you keep the string tight and pull the pencil around the foci, you get an ellipse.

(b) Keplers first law of planetary motion is that each planet orbits the Sun in an ellipse, with the Sun at one of the foci of the ellipse, NOT at the center of the ellipse.

(c) The long axis of the ellipse is called the major axis. Half of the major axis is the "semimajor axis" and is usually given the symbol a, as shown in diagram.

Ellipse of varying shapes (eccentricity). Every circle in the universe has the same exact shape, only the size differs. Ellipses, on the other hand, can have widely varying "sqaushed-ness" (doubt that thats a real word). If the size of the ellipse is large compared to the distance between the foci, the ellipse is almost circular (see B). If the size of the ellipse is only a little larger than the distance between the foci, we get a "cigar shaped" ellipse (see C).

(A) An ellipse, showing foci, major axis, and semimajor axis.

(B) An ellipse where the distance between the foci is small compared to the length of the semimajor axis. This ellipse is not too much different in shape from a circle. This ellipse has a low eccentricity.

(C) This ellipse has a higher ratio of the distance between foci compared to the semimajor axis than the ellipse in B. This ellipse is much more "out of round" than the previous one, and has a higher eccentricity.

Kepler's second law Keplers second law (the "equal area" law) states that the area swept out by the line between planet and Sun is equal for equal time. The planet would take the same amount of TIME to go from A to B as from B to C, etc. For example, the area of the cross-hatched region between points A, B and Sun would be equal to the cross-hatched area between point H, I and the Sun. As the distance between A and B along the orbit is larger than the distance between H and I along the orbit, but the time the same, the planet must move faster between A and B than between H and I.

***************** Galileo turns the telescope to the sky **********

While Galileo did not invent the telescope, he was the first to use it to study the lights in the sky. The two most important things he learned about the sky were that Jupiter had its own family of orbiting objects and that Venus exhibited phases somewhat like the Moon (but with an important difference).

Moons of Jupiter

Moon shadow on Jupiter

Galileo was the first to see that the planet Jupiter had 4 smaller objects orbiting it. This may not seem like a big deal now, but to Galileo it was a shocking revelation - Ptolemy and Aristotle had said that the *Earth* was the center of all motion. Here were objects that clearly were orbiting a body other than the Earth!

The first image is picture of Jupiter and its 4 big moons taken with a small telescope- this is probably similiar to what Galileo saw. (Jupiter is now known to have dozens of orbiting moons, but most require a very large telescope to see.) The moons orbit Jupiter with orbital periods of about 2 days to 2 weeks. The moons present a constantly changing pattern that keep backyard astronomers amused. Sometimes a moon will go in front of or behind Jupiter or cast its shadow on Jupiter. (like in second image).

Phases of Venus in geocentric and heliocentric models.. In the geocentric model, Venus is always between Earth and Sun. It is always seen as a near crescent, as we are seeing mostly the nightside of Venus at all times. In the heliocentric system, Venus goes through a complete range of phases, from thin crescent when it is near Earth to full when on other side of Sun from Earth. Moreover, the angular size of Venus is related to its phase in this model. The "crescent Venus" only occurs when Venus is close to us, and the "full" Venus only when Venus far from us (on other side of Sun from us.) So Venus should look larger when a crecent than when it is full if the heliocentric model is correct.

Observed phases of Venus. These are what the planets look like through a small telescope when they are closest to Earth (and look biggest to us) and when they are farthest away and look smallest. Venus shows the largest change in size. Note that Venus appears much larger when a crescent than when near full. This is easy to understand in the Copernican system (see previous viewgraph) but impossible to explain in the Ptolemaic system. Galileo was the first to see this, as it requires a telescope to see the different phases of Venus.

Photos of Venus's phases These are photos of Venus as it goes through its phases. All were taken with the same telescope, so the different size of images reflects the different Earth-Venus distance. Note that the greater the fraction of the disk we see lit up, the smaller (farther away) Venus looks. The last image (that looks like an annular solar eclipse!) is an image of Venus when it was almost exactly between us and the Sun (but not directly in front of the Sun). Although we are looking entirely at the night side of Venus, we see a ring of light that is due to light bent through the atmosphere of Venus. (This is what the Earth might look like if you stood on the Moon during a lunar eclipse!)

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Sagittarius the Archer This is a constellation visible low in the south in the summer (summer in northern hemisphere). In January (winter) we can NOT see Sagittarius in the night sky becuase the Sun is in the direction of Sagittarius. See Fig 3-1 on page 24 in book (which I don't have a digital version of). In January, *IF* you could see the stars in the daytime, you would see the Sun "in" Sagittarius, as shown in the inset in Fig 3-1 labeled "View from Earth on January 1".

The "Teapot" Sagittarius looks like a teapot to many people. Note the line marked "ecliptic". This is the path of the Sun across the sky. The Sun is on the ecliptic near Sagittarius in December.