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Module 8
 Applications of Angular Measure

Exploring the Transit of Venus in 2012
 Objectives: Students will learn about the Transit of Venus through reading a NASA press release and viewing a NASA eClips video that describes several ways to observe transits. Then students will study angular measurement by learning about parallax and how astronomers use this geometric effect to determine the distance to Venus during a Transit of Venus.

Mathematics Skill or Topic Area:

Applications of Angular Measure

Next Gen Science Standards: PS3: Energy; ETS 1: Engineering Design

Common Core ELA for Science: RST.6-8.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions; RST.6-8.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.6-8.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

Common Core Math Standard: CC.7.G.2 Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides.

Video Engagement: Transits Discover how scientists used the last Venus transit and a geometric technique called parallax to verify the distance between the sun and Earth. Find out what scientists hope to learn the next time Venus transits the face of the sun in June 2012 (5 minutes). View Program

 Engage your students with a press release: Venus Transit: A Celestial Rarity NASA joined the world in viewing a rare celestial event, one not seen by any person now alive. The planet Venus appeared to cross in front of the Sun as seen from Earth. The last "Venus transit" occurred more than a century ago, in 1882, and was used to compute the distance from the Earth to the Sun. Scientists with NASA's Kepler mission hope to discover Earth-like planets outside our solar system by searching for transits of other stars by planets that might be orbiting them. The Venus transit was visible over about 75 percent of the Earth, and ended at sunrise over central and eastern North America. The event was over by the time the Sun rises over the West Coast of North America (but viewers in Alaska could see the beginning of the transit and, for Northern Alaskans, the entire transit, because the Sun does not go below the horizon). If people missed the June 8 Venus transit, they will have another chance in 2012 (June 6). After that, there will not be another Venus transit until 2117 (December 11). During the 19th century, Venus transits were essential for astronomers to fathom the scale of the heavens, because they were used to give a relatively accurate distance from the Earth to the Sun. So critical was this measurement that, beginning in 1761, leading nations sent expeditions to remote corners of the globe to time exactly when Venus appeared to begin its transit of the Sun. The precise timing of the transit depended on location because different places on the globe saw the event from different angles. The times were compared and the distance to the Sun calculated using the known distances between expedition locations on the Earth and trigonometry. The transit phenomenon has relevance to the future of astronomy as well. There is evidence for more than 100 extrasolar planets (planets outside our solar system) around other nearby stars. However, current techniques can only detect large planets, gas giants like Jupiter. But a star might have a planet that appears to pass in front of it by chance alignment with the Earth, and planets similar in size to the Earth could be detected if they transit their parent star. Press release date line - June 10, 2004 Press release location: [ Click Here ]

Explore math connections with

SpaceMath@NASA

Problem I - Angular Size and Similar Triangles - - A critical concept in astronomy is angular size, measured in degrees, minutes or arc-seconds. This is a review of the basic properties of similar triangles for a fixed angle. Topics include geometry, similar triangles and proportions. [Open PDF]

Problem II - The Last Total Solar Eclipse--Ever! - Students explore the geometry required for a total solar eclipse, and estimate how many years into the future the last total solar eclipse will occur as the moon slowly recedes from Earth by 3 centimeters/year. Topics include angular measure and rates of change. [Open PDF]

Write your own problem - Using information found in the Math Connection problems, the press release or the video program, create your own math problem that involves angle measure or parallax. Explain why you set the problem up this way, and how you might find its answer.