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.

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?