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."