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Math in the News: Issue 57

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In this issue of Math in the News we investigate the Super Moon phenomenon mathematically. For more math media resources, go to http://www.media4math.com.

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Learn more about the Super Moon phenomenon. Watch this YouTube video. http://youtu.be/kOplwuMTyS4
The Super Moon The Moon’s elliptical orbit around the Earth makes it closer to Earth at its perigee and farthest from Earth at its apogee.
Date Distance (km) 2-Jan 404589 17-Jan 369899 30-Jan 404325 11-Feb 367928 27-Feb 404842 The Super Moon 10-Mar 362408 26-Mar 405744 7-Apr 358324 This table shows the 22-Apr 406431 distance from the Earth to 5-May 356964 the Moon throughout 2012. 19-May 406439 3-Jun 358491 Notice how the distances 15-Jun 405796 vary, reflecting the changes 1-Jul 362366 from apogee to perigee. 13-Jul 404793 29-Jul 367310 10-Aug 404122 23-Aug 369740 7-Sep 404303 18-Sep 365759 4-Oct 405183 16-Oct 360660 1-Nov 406066 14-Nov 357356
Date Distance (km) 2 404589 17 369899 30 404325 42 367928 58 404842 The Super Moon 70 362408 86 405744 98 358324 To graph the data let’s 113 406431 convert the dates to 126 356964 numerical values. January 140 406439 155 358491 1 is assigned 1 and 167 405796 December 31 is assigned 183 362366 360. We can now graph 195 404793 211 367310 this as a scatterplot. 223 404122 236 369740 251 404303 262 365759 278 405183 290 360660 306 406066 319 357356
The Super Moon The graph of the data shows how the distance from the Earth to the Moon is periodic.
Date Distance (km) 2 404589 17 369899 30 404325 42 367928 58 404842 The Super Moon 70 362408 86 405744 98 358324 We can modify the data to 113 406431 make it easier to graph. 126 356964 The average distance from 140 406439 155 358491 the Earth to the Moon is 167 405796 384483 km. Let’s rescale 183 362366 the data using this formula: 195 404793 211 367310 223 404122 236 369740 251 404303 262 365759 278 405183 290 360660 306 406066 319 357356
Date Distance (km) 2 2.0186 17 -1.4504 30 1.9922 42 -1.6475 58 2.0439 70 -2.1995 The Super Moon 86 2.1341 98 -2.6079 113 2.2028 Here is the rescaled data. 126 -2.7439 140 2.2036 155 -2.5912 167 2.1393 183 -2.2037 195 2.039 211 -1.7093 223 1.9719 236 -1.4663 251 1.99 262 -1.8644 278 2.078 290 -2.3743 306 2.1663 319 -2.7047 333 2.1963 347 -2.7319 360 2.1691
3 2 1 0 0 50 0 100 0 150 0 200 0 250 0 300 0 350 0 400 0 -1 1 -2 2 -3 3 The Super Moon Here is the graph of the rescaled data with the Super Moon highlighted.
The Super Moon The reason that a Super Moon is so rare is that the periods for the phases of the Moon and its orbit differ by about two days. These graphs show how they quickly get out of phase, and it takes many periods for them to intersect. Super Moons happen about once a year.
The Super Moon Do you plan on watching the next Super Moon?

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Math in the News: Issue 57

  • 1.
  • 2. Learn more about the Super Moon phenomenon. Watch this YouTube video. http://youtu.be/kOplwuMTyS4
  • 3. The Super Moon The Moon’s elliptical orbit around the Earth makes it closer to Earth at its perigee and farthest from Earth at its apogee.
  • 4. Date Distance (km) 2-Jan 404589 17-Jan 369899 30-Jan 404325 11-Feb 367928 27-Feb 404842 The Super Moon 10-Mar 362408 26-Mar 405744 7-Apr 358324 This table shows the 22-Apr 406431 distance from the Earth to 5-May 356964 the Moon throughout 2012. 19-May 406439 3-Jun 358491 Notice how the distances 15-Jun 405796 vary, reflecting the changes 1-Jul 362366 from apogee to perigee. 13-Jul 404793 29-Jul 367310 10-Aug 404122 23-Aug 369740 7-Sep 404303 18-Sep 365759 4-Oct 405183 16-Oct 360660 1-Nov 406066 14-Nov 357356
  • 5. Date Distance (km) 2 404589 17 369899 30 404325 42 367928 58 404842 The Super Moon 70 362408 86 405744 98 358324 To graph the data let’s 113 406431 convert the dates to 126 356964 numerical values. January 140 406439 155 358491 1 is assigned 1 and 167 405796 December 31 is assigned 183 362366 360. We can now graph 195 404793 211 367310 this as a scatterplot. 223 404122 236 369740 251 404303 262 365759 278 405183 290 360660 306 406066 319 357356
  • 6. The Super Moon The graph of the data shows how the distance from the Earth to the Moon is periodic.
  • 7. Date Distance (km) 2 404589 17 369899 30 404325 42 367928 58 404842 The Super Moon 70 362408 86 405744 98 358324 We can modify the data to 113 406431 make it easier to graph. 126 356964 The average distance from 140 406439 155 358491 the Earth to the Moon is 167 405796 384483 km. Let’s rescale 183 362366 the data using this formula: 195 404793 211 367310 223 404122 236 369740 251 404303 262 365759 278 405183 290 360660 306 406066 319 357356
  • 8. Date Distance (km) 2 2.0186 17 -1.4504 30 1.9922 42 -1.6475 58 2.0439 70 -2.1995 The Super Moon 86 2.1341 98 -2.6079 113 2.2028 Here is the rescaled data. 126 -2.7439 140 2.2036 155 -2.5912 167 2.1393 183 -2.2037 195 2.039 211 -1.7093 223 1.9719 236 -1.4663 251 1.99 262 -1.8644 278 2.078 290 -2.3743 306 2.1663 319 -2.7047 333 2.1963 347 -2.7319 360 2.1691
  • 9. 3 2 1 0 0 50 0 100 0 150 0 200 0 250 0 300 0 350 0 400 0 -1 1 -2 2 -3 3 The Super Moon Here is the graph of the rescaled data with the Super Moon highlighted.
  • 10. The Super Moon The reason that a Super Moon is so rare is that the periods for the phases of the Moon and its orbit differ by about two days. These graphs show how they quickly get out of phase, and it takes many periods for them to intersect. Super Moons happen about once a year.
  • 11. The Super Moon Do you plan on watching the next Super Moon?