Planetarium Show

Navigating the Night Sky:
Planetarium show for Middle School Children
Post-Show Activity 2
A Sense of Scale

Objectives:

Grade Level

Materials

Background

Another way to give you a sense of the distances between things is to use a proportional (``scaled'') model. In such a model, everything is reduced by the same amount, so all parts of the model relative to each other are of the same proportional size. (In the same way a good trail map you use for hiking or the road map you use for driving is a flat scaled model of the terrain you are moving over.) To create a scale model, divide all of the actual distances or sizes by the same scale factor (in the example below the scale factor is 8,431,254,000), so the scaled distance = (actual distance)/(scale factor).

For our scale model, let us use a yellow mini-basketball about 16.51 centimeters (6.5 inches) across to represent the Sun and then pace out how far the tiny planets would be in this scale model. Since the real Sun is 1,392,000 kilometers (865,000 miles) across, the scale model has all of the planets and distances reduced by an amount equal to (139,200,000,000 / 16.51) = 8,431,254,000 times. The largest planet, Jupiter, would be only 1.7 centimeters across (a dime) and about 92.3 meters away. Our little Earth (a grain of sand) would be closer: ``only'' 17.7 meters (about 18 big steps) away. Our Sun is much larger than the planets, and, yet, it is just a typical star! Here is a scaled model of our solar system:

Scaled Model of the Solar System Object Real Diameter (km) Real Distance (million km) Scaled Size (cm) Scaled Distance (m) Sun 1,392,000 16.51 Mercury 4880 57.910 0.058 (tiny! grain of sand) 6.9 (7 big steps) Venus 12,104 108.16 0.14 (grain of sand) 12.8 (13 big steps) Earth 12,742 149.6 0.15 (grain of sand) 17.7 (18 big steps) Mars 6780 228.0 0.08 (almost 1 mm) 27.0 (27 big steps) Jupiter 139,822 778.4 1.7 (a dime) 92.3 (92 big steps) Saturn 116,464 1,427.0 1.4 (a button) 169.3 (169 big steps) Uranus 50,724 2,869.6 0.6 (button snap) 340.4 (340 big steps) Neptune 49,248 4,496.6 0.6 (button snap) 533.3 (533 big steps) Pluto 2274 5,913.5 0.03 (small piece of dust) 701.4 (701 big steps) Oort Cloud 11,200,000 1,328,400 (1,328 km) Proxima Centauri 375,840 40,493,000 4.5 (handball) 4,802,700 (4,803 km)

The Oort Cloud is a huge spherical cloud of trillions of comets surrounding the Sun that is about 7.5 to 15 trillion kilometers across. In our scale model, the middle of the Oort Cloud would be about the distance between Los Angeles and Denver. Proxima Centauri is the closest star to us outside of the solar system (remember that the Sun is a star too!). Proxima Centauri would be from Los Angeles to beyond the tip of the state of Maine on this scale model (from Los Angeles to New Glasgow, Nova Scotia to be more precise!). In our fastest rocket ships (neglecting the Sun's gravity) it would take almost 70,000 years to reach Proxima Centauri!

Instead of using ridiculously small units like kilometers, astronomers use much larger distance units like an astronomical unit to describe distances between the planets and a light year to describe distances between the stars. An astronomical unit = the average distance between the Earth and the Sun, or about 149.6 million kilometers. For example, Jupiter is (778.4 million km)/(149.6 million km) = 5.203 astronomical units from the Sun. A light year is how far light will travel in one year. The distance D something travels in a given time interval t is found by multiplying the speed v by the time interval. In compact math notation this is: D = v×t. You can find out how many kilometers a light year is by multiplying the speed of light by a time interval of one year: 1 light year = (299,800 kilometers/second) × (31,560,000 seconds/year) = 9,461,000,000,000 kilometers (9.461 trillion kilometers---several tens of thousands of times larger than even the astronomical unit!).

The nearest star is about 4.3 light years away which means that it takes light 4.3 years to travel from Proxima Centauri to Earth. The rest of the stars are further away than that! The speed of light is the fastest speed possible for anything in the universe to travel despite what you may see in science fiction movies or books. It is because of the H-U-G-E distances and l-o-n-g times it would take extraterrestrial spacecraft to travel to the Earth that many astronomers are skeptical about extraterrestrial beings abducting humans.

The Sun is one star among over 200 billion stars gravitationally bound together to make the Milky Way Galaxy. A galaxy is a very large cluster of billions of stars held together by the force of their mutual gravity on each other. That definition is a loaded one that will be unpacked and examined in more detail in later chapters, but for now let us continue on our brief tour of the universe. The Milky Way is a flat galaxy shaped like a pancake with a bulge in the center. Stars and gas are clumped in spiral arms in the flat disk part of the Galaxy. Many stars are also found in between the spiral arms. Our solar system is in one of the spiral arms of the Milky Way and is about 26,000 light years from the center of the galaxy. The entire Milky Way is about 100,000 light years across. In our scaled model with the Sun 16.51 centimeters across, the Milky Way would be about 112 million kilometers across or about 38% of the size of the Earth's orbit around the Sun. Recall that Pluto's orbit is only 1.4 kilometers across on this scale---the Galaxy is MUCH larger than our solar system! Here is an artist's view of our galaxy with the Sun's position marked (note that our entire solar system would be smaller than the smallest dot visible in the picture!):

Let's reduce our scale model even more so that our galaxy is the size of the mini-basketball. The closest other galaxy is a small irregularly-shaped one about 13 centimeters away from the Sun toward the direction of the Milky Way's center. It is about the size of a cooked, fat breakfast sausage link in our scale model. Appropriately, the Milky Way is in the process of gobbling up this galaxy. Two famous satellite galaxies of the Milky Way called the Large Magellanic Cloud and Small Magellanic Cloud are about 30 centimeters and 35 centimeters away, respectively. The Large Magellanic Cloud is about the size of a tennis ball and the Small Magellanic Cloud is about the size of a ping pong ball. The Andromeda Galaxy is the closest large galaxy to the Milky Way: a ball 19 centimeters in diameter (a volleyball) about 4.8 meters away. The Milky Way and the Andromeda Galaxy are at either end of a group of about 30 galaxies gravitationally bound together in the Local Group. The Local Group can be roughly divided into two clumps with each clump having a large spiral in it: the Milky Way and the Andromeda Galaxy. Here are three views of the Local Group, each viewed from a position 90 degrees different from the rest. The Milky Way is the large dot at the intersection of the x,y,z axes and the Andromeda Galaxy is the other large dot.

The closest large cluster of galaxies is called the Virgo cluster (toward the direction of the Virgo constellation). The Virgo cluster has over 1000 galaxies in it and is roughly 50 meters away in our scale model. Notice that compared to their size, the galaxies are relatively close to one another. Stars inside a galaxy are relatively very far apart from one another compared to the sizes of the stars. You will see that the relative closeness of the galaxies to each other has a significant effect on the development of galaxies.

The Local Group and Virgo cluster are part of a larger long, narrow group called the Local SuperCluster, sometimes called the Virgo Supercluster since the Virgo cluster is close to the middle. The Local Group is close to one edge of the Local SuperCluster. In our scale model with the Milky Way the size of a mini-basketball, the Local Supercluster is about 190 meters long and the entire observable universe is about 49.5 kilometers in diameter. Time Now let's try to get a feel for the time scales. I will use another scale model, but instead of reducing distances, I will shrink down time. The scale model is called the ``cosmic calendar'' in which every second in the ``cosmic calendar'' called the ``cosmic calendar'' in which every second in the ``cosmic calendar'' corresponds to 475 real years (so 24 cosmic calendar days = 1 billion real years). If you use the classical number of 15 billion years for the age of the universe, you can squeeze the universe's entire history into one cosmic calendar year (recent measurements place the age closer to 13 billion years). The universe starts in the early morning of January 1 at midnight in the cosmic calendar and our present time is at December 31 at 11:59:59.99999 PM in the cosmic calendar. Here are some important dates in this super-compressed cosmic calendar relevant to us humans: (see also the figure below) Origin of the Universe--Jan. 1 Origin of our galaxy--Jan 24 Solar system origin--Sept. 9 Earth Solidifies--Sept. 14 Life on Earth--Sept. 30 Sexual reproduction advent--Nov. 25 Oxygen atmosphere--Dec. 1 Cambrian explosion (600 mil years ago when most complex organisms appear, fish, trilobites)--Dec. 17 Land plants & insects--Dec. 19, 20 First amphibians--Dec. 22 First reptiles & trees--Dec. 23 First dinosaurs--Dec. 25 KT impact, mammal age, birds--10:00 AM Dec. 30 First primates--Dec. 30 Australopithicenes (Lucy, etc.)--10:00 PM Dec. 31 Homo habilis--11:25 PM Dec. 31 Homo erectus--11:40 PM Dec. 31 Early Homo sapiens--11:25 PM Dec. 31 Neanderthal man--11:57 PM Dec. 31 Cro-Magnon man--11:58:38 PM Homo sapiens sapiens--11:58:57 PM Dec. 31 Human history--11:59:39 PM Ancient Greeks to now--last five seconds Average human life span--0.15 seconds It is rather surprising that we have been able to discover so much about the long term evolution of the universe and the things in it, especially when you consider that we have only been seriously observing the universe for about 100 years, which is only a very slight fraction of the universe's lifetime. About 100 years ago is when photography was first used in astronomy, making truly systematic observation programs possible. How can astronomers say that the Sun will go through a red giant phase in about 5 billion years from now with confidence? Is it hubris to confidently talk about the Earth's formation process 4.6 billion years ago? To give you an idea of the difficulties in studying long timespans consider this analogy: An alien comes to Earth to search for life and to understand how it evolved. ET has a camera and has just 15 seconds to take as many photographs as possible. Fifteen seconds is the same proportion of a human lifetime as the 100 years is to the universe's age (15 seconds/human lifetime = 100 years/universe age). ET returns home and her colleagues try to understand Earth from this 15 second period of snapshots. They won't see any important evolutionary changes. How will they determine the dominant life form? They could use a variety of criteria: 1) Size: leads them to choose whales or elephants; 2) Numbers: choose insects; 3) amount of land space controlled by one species: choose automobiles. Suppose they somehow decide humans are dominant. They now have further problems. There is considerable diversity among the humans (though to ET with 10 tentacles, 200 eyes, and a silicon outer shell, the humans all look alike!). ET and colleagues try to systematically classify the humans. The humans come in a variety of sizes. In a coarse classification scheme, they break the sizes down into small, medium, and large. They also come in variety of optical colors for their outer shell: red, black, brown, yellow, and white. There appears to be 2 separate sexes (ET is both male and female). After some false starts with theories that used hair length and eye color, they are ready to ask themselves, ``Do small, brown, female humans evolve into large, red, male humans?'' ``Do the small stay small and the large stay large?'' ``Why is there a tendency for small humans to be with one or two large humans?'' With the three characteristics [size (3 divisions), color (5 divisions), and sex (2 divisions)], ET has 3×5×2 = 30 different combinations and 30×30 = 900 possible evolutionary schemes to consider! Well, the universe has a lot more characteristics and, therefore, many more combinations to consider!

Procedure

Follow Up

Source:
Some information on this page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.