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Space Math: Kepler -- Earth-like Planets by the Score! (Part 1)
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Space Math: Kepler -- Earth-like Planets by the Score! (Part 1)

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Topic: Math

Grade Level: 5-8

Body:

Mission:

Science Education Standards: Physical Science -- Content Standard B: Motions and Forces

Earth and Space Science -- Content Standard D: Earth in the Solar System

Short Description: Students use recent Kepler satellite data summarized in tabular form to estimate the number of planets in the Milky Way galaxy that are about the same size as our Earth, and located in their habitable zones were liquid water may exist.

Source: Space Math (GSFC)


Illustration of a another solar system.

NASA's Kepler Space Observatory recently announced the results of its continuing survey of 156,453 stars in the search for planet transits. Their survey, in progress for just under one year, has now turned up 1,235 transits from among this sample of stars, of which 33 were eliminated because they were too big to be true planets. About 30 percent of the remaining candidates belong to multiple-planet systems in which several planets orbit the same star. Among the other important findings are the numbers of planet candidates among the various planet types summarized as follows: Earth-sized = 68; superEarths = 288; Neptune-sized = 662; Jupiter-sized=165; superJovians=19.

Problem 1 - Create a histogram that shows the number of candidate planets among the 5 different size classes.



Problem 2 - What percentage of all the planets detected by Kepler were found to be Earth-sized?



Problem 3 - About how many stars would you have to search to detect one Earth-sized planet using the Kepler transit method?



Problem 4 - Extrapolating from the Kepler findings, which was based on a search of 156,000 stars, about how many Earth-sized planets would you expect to find if the Milky Way contains about 40 billion stars similar to the ones surveyed by NASA's Kepler Space Observatory?


Answer Key

Problem 1 - Create a histogram that shows the number of candidate planets among the 5 different size classes. Answer:

Bar graph demonstrating the number exoplanets of different sizes.

Problem 2 - What percentage of all the planets detected by Kepler were found to be Earth-sized? Answer: P = 100% x (68/1202) = 5.7 %

Problem 3 - About how many stars would you have to search to detect one Earth-sized planet using the Kepler transit method? Answer: Students may simply scale the results for 68 Earth-like planets in a sample of 156,453 stars to get N = (1/68) x 156,453 stars to get about 2,301 stars.

Problem 4 - Extrapolating from the Kepler findings, which was based on a search of 156,453 stars, about how many Earth-sized planets would you expect to find if the Milky Way contains about 40 billion stars similar to the ones surveyed by Kepler? Answer: There are 40 billion candidate stars in the Milky Way, so re-scaling the survey to the larger sample size we get about (40 billion/156,453) x 68 planets or about 17 million Earth-sized planets.

Note: The Kepler survey has not been conducted long enough to detect planets much beyond the orbit of Venus in our own solar system, so in time many more earth-sized candidates farther away from their stars will be reported in the years to come. This means that there may well be considerably more than 17 million Earth-sized planets orbiting stars in the Milky Way similar to our own sun.

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Last Updated: 25 Jul 2012