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GIZMO - Exploration Guide

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					       Exploration Guide » Solar System Explorer
Mankind first began trying to send a spacecraft to Mars in 1960. Seven tries and nearly five
years later, NASA's Mariner 4 mission performed a close flyby that returned 22 television
images of the surface of Mars. It was no simple achievement.
First, scientists put Mariner 4 into Earth orbit. Then, the rockets of the spacecraft were fired so
that Mariner 4 would leave its Earth orbit and orbit the Sun. This had to be done precisely to
ensure that the orbital path of the spacecraft would exactly intersect with the orbit of Mars.
Unless the timing was perfect, Mariner 4 and Mars would never meet.
While today's technology allows us to send probes to distant planets, the laws that govern the
planetary orbits were first described by Johannes Kepler as early as 1609.
Exploring Our Solar System
In this activity, you will explore the relationships between the shape of a planet's orbit, the
planet's average distance from the Sun, and its motion.

1. In the Gizmo™, click the small o in the zoom controls to the right of the diagram of the
   planets. This will reset the diagram to its initial zoom state. Turn on Show orbital paths and
   click Play (      ). Watch the planets as they orbit the Sun.
       a. At this zoom level, you can see the orbits of the four inner planets—Mercury, Venus,
           Earth, and Mars. Select each planet in the Solar system dropdown menu to highlight
           its orbit in red. Which of the four planets completes an orbit around the Sun in the
           shortest period of time? Which of the four planets is moving most quickly?
       b. From the Solar system dropdown menu, select Mercury. What do you notice about
           the shape of Mercury's orbit? How is this orbit different from the others that you can
           see? Mercury's orbit is a good example of Kepler's First Law, which states that
           planetary orbits are in the shape of an ellipse.
       c. Turn on Additional data and note the Eccentricity of Mercury's orbit. Eccentricity
           refers to how flattened the orbit is. A perfectly circular orbit has an eccentricity of 0. A
           completely flattened ellipse has an eccentricity of 1. Compare the eccentricity value of
           Mercury to that of Venus, Earth and Mars. Which of the four planets has the most
           circular orbit?
       d. Click the small + in the zoom controls to enlarge the graph, and watch Mercury
           closely. Does Mercury move at the same rate throughout its orbit? If not, at what point
           does it move most quickly? This is an example of Kepler's Second Law, which states
           that a planet moves most quickly when it is closest to the Sun in its orbit.
2. When Mercury reaches the point in its orbit that intersects the x-axis, click Pause (         ). Jot
   down the date (shown below the simulation) on a sheet of paper. Then click Play. When
   Mercury has completed one full orbit, click Pause again. Note the new date.
         a. How many days did it take Mercury to make one complete orbit around the Sun?
             This amount of time is referred to as the orbital period of Mercury. Be sure to write
             this value down.
         b. Under Solar system, select Earth. Repeat the process from the previous step. What
             is the orbital period of Earth? The orbital period for each planet is also called the
             planet's year. In fact, Earth takes exactly 365.256 days to orbit the Sun.
         c. Planetary orbits are usually expressed in terms of Earth years. To convert, divide the
             orbital period of Mercury (in Earth days) by 365.256 to get the orbital period in Earth
             years. Compare this number to the value shown in the Additional data chart. Are
             they close?
        d. Based on the axes shown in the Gizmo, what is the radius of Earth's orbit? This
           value is expressed in astronomical units. One astronomical unit (AU) is equal to the
           average distance from Earth to the Sun.
        e. What is the average radius of Mercury's orbit, in astronomical units? Check your
           estimate with the Additional data chart.
        f. Estimate the orbital period and orbital radius of Venus (the second planet from the
           Sun) and then of Mars (the fourth planet from the Sun), and use the corresponding
           Additional data charts to check your answers.
        g. Create a table like the one shown below. Fill in the Orbital Period and Orbital Radius
           values for Venus and Mars. (You will use the remaining two columns later.)




       h. One of the most famous planetary alignments is the transit of Venus, when Venus
           traces a path across the face of the Sun, as seen from Earth. (Usually, due to the
           slight tilt of Venus's orbit relative to the Earth, Venus passes above or below the
           Sun.) A transit was seen in June, 2004, and the next one will occur in the year 2012.
           In what month will this transit occur? Use the Gizmo to find the date of the next
           transit. You can check your answer by doing an internet search on "transit of Venus."
3. Now, you will study the orbits of the outer planets.
       a. Under Solar system, select Jupiter. Click - to zoom out until the orbit of Jupiter
           becomes visible. Estimate the orbital radius of Jupiter.
       b. Click Play, and estimate the orbital period of Jupiter. Check your estimated period
           and radius values with the Additional data chart, and fill in your table with the correct
           values. (Note that you can speed up the simulation with the Slow/Fast slider if you
           like.)
       c. Zoom out further and repeat the data collection process for Saturn, Uranus, and
           Neptune and add these values to your table.
       d. Under Solar system, select Pluto. (Note: Under the new definition of a planet, Pluto
           is considered a "dwarf planet.") Zoom out until the orbit of Pluto becomes visible.
           How is Pluto's orbit different from the orbits of most other planets? What planet is the
           shape of Pluto's orbit most similar to? Notice that there is a period of time during
           which Pluto is actually closer to the Sun than the orbit of Neptune!
       e. Determine the period of Pluto and add that value to your table. (Note - do not record
           the orbital radius of Pluto at this time, you will calculate it later using Kepler's Third
           Law.)
4. You will now see if there is a relationship between the orbital periods and radii you have
   recorded.
       a. Look at the list of orbital periods (represented by the letter T) and orbital radii (r). Do
           you see any relationship between the orbital periods and orbital radii?
b. Square the orbital period (T2) for each planet and record these new values in the
   fourth column of the table. Then cube the orbital radius (r3) for each planet and
   record these values in the fifth column.
c. Compare the list of squared periods and cubed radii. Do you see a relationship now?
   If so, what is it?
d. This relationship, in which the square of the orbital period is proportional to the cube
   of the orbital radius, is Kepler's Third Law of planetary motion. It is normally written:

   T2 = kr3

   The value of k differs depending on the mass of the star at the center of the
   planetary system. In our solar system, when AU are used for distance and Earth
   years are used for time, k is equal to 1.
e. Based on Pluto's period, use Kepler's Third Law to determine the average radius of
   Pluto's orbit. Check your answer using the Gizmo.
f. The most distant large object discovered in our solar system is Sedna, discovered in
   2003. Sedna has an average orbital radius of an astounding 526 AU. According to
   Kepler's Third Law, what is Sedna's period? You can check your answer by doing a
   web search on "Sedna orbital period."

				
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