Monday 29 August 2011

The first set of images are related to topics discussed last Wednesday.

Kepler's Second Law.

Dominance of Sun's mass in Solar System. Yep, Big Nate is getting it straight. The Sun contains about 713/714 of the total mass in the Solar System, with everything else containing only 1/714 of the total. (I am sure many of you feel just like Big Nate does in the last panel when its 9PM on Wednesday nite! What can I say- I get paid to talk!)

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.

While Copernicus made (or at least is credited with making) 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 allowed astronomers to junk the 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.

Tycho Brahe- Ace observer This old artwork shows a montage of Tycho and one of his pre-telescopic measuring instruments. He measured the angular 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?) These careful measurements of the positions of planets were the basis of Kepler's astounding work in figuring out the 3 Laws of Planetary Motion.

Photos of Venus's phases As discussed earlier, Galileos observations of the phases of Venus put a nail in the coffin of geocentrism. 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!)

Mar's retrograde loops - The Movie.

This is an animation of a retrograde loop of Mars in 1996/1997. Note the date counter in the lower corner.

Mar's retrograde loop - The Photo. If you carefully noted the position of Mars relative to background stars over a period of a few months, you would find that Mars mostly moves eastward relative to the stars, but sometimes it "backs up" , moves to the west for a while, then turns around again and heads to the east.. This motion is called a "retrograde loop".

This is a photo montage of a loop along with the background stars and constellations. The numbers next to the images of Mars are the dates. Mars starts on the western (right hand) edge of the frame on 8/18 (August 18), then moves steadily eastward (to the left) until about 11/10 (November 11). At this point Mars "turns around" and heads towards the west until 1/31 (January 31 of next year), at which time it again "turns around" and starts heading east again until it reaches the left hand edge of the frame in May. The top part of Orion is shown, alongs with a few other constellations. Left of Betelgeuse is Canis Minor (the Little Dog). Canis Major (the Big Dog) is off the picture, below Canis Minor.

Retrograde loops in geocentric system This is how Ptolemy explained the retrograde loops of Mars- with a "wheel on a wheel" - an epicycle.

Retrograde loops in heliocentric model- The Movie Retrograde loops of Mars, Jupiter and Saturn are easily explainable in heliocentric model, occuring when we pass the outer planet as both Earth and the outer planet orbit Sun. Planets closer to the Sun orbit the Sun in a shorter time than planets farther from Sun.


Angles using hand width

Angles using Big Dipper

It is very useful to be able to *estimate* angles on the sky with your naked eye. Here are two "protractors" that are useful. When using your hand as a protractor, make sure you have stretched out your arm as far as you can (without hurting yourself!). If you put your fist 2 inches from your eye, it will subtend an angle larger than 10 degrees!


Here is a very practical application/illustration of Keplers 3rd Law. (Well, the generalization of Keplers 3rd Law - for any massive body, not just Sun, as required for original Keplers 3rd Law - see next to last image from 24 August.) If you put a communication satellite in low Earth orbit (say at Shuttle or Space Station altitude) it would orbit the Earth in about 95 minutes, so would constantly be zipping around in the sky. However, if we are clever, we can put a satellite in an orbit where it orbits the Earth in the same time it takes for the Earth to rotate, so the satellite appears FIXED in the sky! This is called a geosynchronous orbit.

Geosynchronous satellite orbit. A geosynch orbit is one in the Earths equatorial plane at a distance from Earth (determined from Kepler's 3rd law) where the period of revolution is 24 hours, or one day. At this special distance from Earth, a satellite completes one revolution each day, so (from Earth) it appears to be fixed in the sky- it does not rise and set. The satellite and Earth turn at the same angular rate, each completing one "turn" each day. For the satellite to appear fixed in the sky the orbital plane must be in the same plane as the Earth's equator. (You could put a 24 hour period satellite on a orbit that went over the poles, but that would not be fixed on the sky- think about what the sky motion of such a satellite would be.)

The image shows 3 typical satellites at geosynch orbit. The view is tilted - the actual orbits are circular. Note that (unlike many diagrams I use) the size of the orbit is TO SCALE with the size of the Earth.

Because the satellite appears in a fixed spot in the sky, you can point a satellite dish (antenna) at that spot and always be pointed at the satellite. Thus, many communication satellites and broadcasting satellites are located at geosynch. Famous science fiction author Arthur C. Clarke was one of the first to suggest the use of this orbit for communications satellites (back in the 1940s!) and so this region of space is sometimes called the "Clarke Belt".

Geosynchronous satellite.. This is a diagram where the size of the Earth and the distance to the sateliite are to scale (the stick figure person is NOT to scale!). This shows why satellite dishes point south of the equator (in the northern hemisphere). A geosynch orbit is about 6.6 earth radii from the center of the earth, or at a "height" of 5.6 radii above surface.