"A Study of the Effects of Sunrise and Sunset on the Ionosphere as"
A Study of the Effects of Sunrise and Sunset on the Ionosphere as Observed by VLF Wave Behavior By Leandra Merola South Side High School Rockville Centre, New York Merola, Leandra Abstract The purpose of this study was to observe solar activity and sudden ionospheric disturbances (SIDs) by monitoring the strength of VLF (very low frequency) radio waves. Specifically I studied how sunrise and sunset affected VLF radio waves. To accomplish this it was necessary to accurately record ionospheric disturbances and relate them to solar activity. The sun releases electromagnetic radiation, which is absorbed by the atmosphere around the Earth. This radiation has the potential to disturb or ionize the thermosphere, the outer most layer of the atmosphere, and this then affects radio waves, including VLF waves, that are reflected by the ionosphere. To conduct my study, I built an antenna that captured very low frequency radio waves that are reflected by the ionosphere. The antenna was attached to a VLF radio reciever, obtained from the Solar Center at Stanford University in California. The specific VLF waves observed in this study are used to communicate with U.S. submarines. The data that I collected was recorded by a computer and converted into graphs that illustrate disturbances in the ionosphere. The results of this study showed that radiation from the sun disturbs VLF waves that are reflected by the ionosphere. I was then able to conclude that the ionosphere was also affected by solar radiation. I also found that sunrise and sunset drastically change the signal strength of VLF radio waves because of the dramatic variation in the ionizing of the ionosphere. 2 Merola, Leandra Introduction The purpose of this project was to investigate the effects of sun-induced ionospheric disturbances on Very Low Frequency (VLF) radio waves. The ionosphere reflects transmitted VLF radio waves back to Earth. The strength of these radio waves depends on how much or how little the ionosphere is ionized. Solar radiation contributes to ionization of the atmosphere, which can alter the strength of the transmitted VLF radio waves. This project explores how the ionosphere and VLF radio waves react to the solar radiation, especially in different geographic locations on Earth. The project also looks specifically at the impact of solar radiation on the ionosphere at local sunrise and sunset. The sun emits electromagnetic radiation that ranges from gamma rays to radio waves. This energy can be directly from the sun in the form of thermal energy or the energy can be in the form of solar flares. “A solar flare is an explosion on the sun that happens when energy stored in twisted magnetic fields is suddenly released” (http://www.spaceweather.com/, 2006). According to Davies (1990) solar flares emit radiation in various ranges of wavelengths from long radio waves to short X-rays and can last from a few minutes to several hours. This radiation, depending on the strength of the solar flare and the angle to the Earth, affects the Earth’s atmosphere. The ionosphere is located approximately 80 km and higher above the Figure 1: Earth and is the outer-most layer of the atmosphere (Fig 1, Layers of the http://www.haarp.alaska.edu/haarp/ion1.html). The ionosphere is made up of Ionosphere many gases including nitrogen and oxygen. It is called the ionosphere 3 Merola, Leandra because the small fraction of the solar energy at UV and smaller wavelengths is energetic enough to strip electrons off molecules in the air. When this ionizing radiation enters the atmosphere, it collides, primarily, with oxygen molecules. The shortest energy waves that come from the sun are partly absorbed by the oxygen molecules; it is these waves that ionize the particles (http://www.haarp.alaska.edu/haarp/ion1.html, 2006). The ionosphere is broken up into several layers, all of which are ionized at all times except for the D layer, the layer closest to the Earth (Fig 1), which disappears at night because the neutral density below about 200 km is high enough that electrons recombine with oxygen in a few hours or less (Khanal, 2004). Ionization in the E region decreases a little during the night, but the D layer does not reappear until the sun rises at that altitude again. Figure 2: Radio Waves are Reflected by the Ionosphere (http://www.haarp.alaska.edu/haarp/ion1.html) VLF (very low frequency) radio waves are used primarily by the military to communicate with submarines, but they are also used as avalanche beacons and for wireless heart rate monitors. VLF waves have a frequency somewhere between 3 and 30 kHz and a wavelength between 100 and 10 km. These radio waves are used to communicate with submarines because at this frequency, they can penetrate water roughly 10 to 40 meters (Radio Waves, 2006). VLF waves are useful because not only do they travel along the ground but the ionosphere also reflects them. Because of this quality they are ideal for communicating around the world. They 4 Merola, Leandra are also ideal for monitoring the ionosphere. VLF waves bounce off the ionosphere, so if anything happens to the ionosphere the radio wave will also be affected. Solar activity, such as solar flares, the ionosphere and VLF radio waves are all interrelated. Solar flares affect the ionosphere, which then affects the VLF radio waves that bounce off the ionosphere. There are two major types of radiation that affect the ionosphere, solar flares and simple background cosmic radiation. The cosmic radiation is not as strong as the solar flares but it is constantly there whereas solar flares are only discrete events during the daytime when the sun is facing a certain location, but they come in powerful bursts. During the night VLF waves have to travel 90 km, to the E layer in the ionosphere before returning to Earth. During the day the D layer is partially ionized so the VLF radio wave must first travel through the D layer, losing some of its energy along the way. The signal strength of the VLF wave will be stronger at night than in the daytime (Khanal, 2004). However, if there is any kind of solar activity the radio waves will not have to travel as far because the increased radiation will ionize the D layer and the D layer, instead of the E layer, will reflect the VLF radio waves. Therefore the signal strength fluctuates as the reflection fluctuates because of the amount of absorption. More than ever, people rely on radio wave technology such as GPS systems and communication devices. However, there are many studies that show that radio wave technology is subject to disruption. In a study cited by Contreira et al. (2004) showed that AM radio waves faded when there was a solar flare. Contreira et al. (2004) also showed that the AM radio signal was not as strong during the day because the energy from the sun was ionizing the ionosphere, which results in the absorption of some of the AM radio waves. Although VLF waves respond differently to solar activity, my study shows that radio wave technology is affected by disturbances in the ionosphere and this disturbance can affect everyday life. When using VLF 5 Merola, Leandra radio waves for communication, solar activity will affect the strength of the receiving signal. Therefore the purpose of this study was to investigate how VLF radio waves are impacted by the radiation given off by the sun at various times. To monitor solar flare activity using VLF radio waves, Stanford University set up a program that distributes inexpensive ionospheric monitors to students around the world (http://solar-center.stanford.edu/SID/, 2006). These monitors, with the help of an antenna, record VLF radio waves that are emitted from a specific VLF transmitter station. By tracking the strength of the radio waves over a period of time it is possible to draw conclusions about the characteristics of the ionosphere, because the radio waves and the ionosphere are so closely related. When there is a fluctuation in the signal strength during the day, it is known as a Sudden Ionospheric Disturbance or a SID. A SID is a change in the level of ionized particles in the ionosphere, which cause the VLF waves to be reflected either more or less. To find out what caused the SID, there is data from the GOES satellite that monitors the sun directly and records solar flares. This data can be found on http://www.sec.noaa.gov/ftpdir/warehouse/2006/2006_plots/xray/. If the SID occurs at the same time as a solar flare, which can be found by using data from the GOES satellite, then there is a direct correlation between the sun, the ionosphere and VLF radio waves. Therefore the sun and solar flares affect VLF radio waves. The SID monitor can be useful because it allows indirect observation of the ionosphere and the Sun. The SID monitor also allows data to be collected from many different locations. This can be useful not only in understanding the ionosphere but also in understanding the impact on radio wave technology that relies on the ionosphere. It is important to study the ionosphere and radio wave technology that relies on the ionosphere because the ionosphere will not remain constant in its level of ionization for a long time. When 6 Merola, Leandra the ionization does change we should be aware of the fact that radio waves will also change because the ionization level in the atmosphere impacts them. Presently, there has been a very low level of SID activity in the ionosphere because the sun is relatively calm. If the characteristics of the ionosphere change because solar activity increases then VLF radio waves will no longer work the way they were supposed to. Therefore today VLF waves work fine; however, if there is a solar flare tomorrow then the VLF radio waves will work in unexpected ways. Although there is a known 11-year cycle for solar activity corresponding to the sun’s magnetic field reversal, it is not possible to predict, with a high level of accuracy, when individual solar flares will occur. This makes us vulnerable to potential unexpected negative effects on important technological tools that rely on the ionosphere and the level of ionization. Currently the sun is at its lowest point of the 11-year cycle so there are not a great number of solar flares, or SIDs. However, it is predicted that in the next five or six years there will be a 30 to 50 percent increase in solar activity compared to the last solar maximum (Leary, 2006). It is important to take advantage of the present lull in the solar activity to explore the sun’s baseline effect on the ionosphere and VLF waves when it is not highly active. If we can understand what is happening in the ionosphere when there is no solar activity it could be easier to solve the issues of the accuracy of technology so that we will be prepared when the solar activity is more frequent. For example, more than ever we are using GPS or global positioning systems, however, one study showed that disturbances in the ionosphere cause GPS satellite signals to fade (Peter, 2003). Aguire, (2005) confirms that more and more scientists and amateurs from around the world are recording SIDs and noticing how they affect radio communications. In the near future, because of solar disturbances, there will be a decrease in the accuracy of technology that is dependant on radio waves that are reflected by the ionosphere. 7 Merola, Leandra For this project a SID monitor was used in a suburban area on Long Island, New York to record VLF radio waves from a US Navy transmitter in North Dakota and track changes in the ionosphere. Data was collected and compared to data recorded in Boston, Massachusetts and Logan, Utah by the same type of device monitoring the same transmitter. Logan is south of the transmitter, but at nearly the same latitude as Long Island. I have examined the variation of VLF intensity at my receiver nearly every day since April 2006. The signal varies in a characteristic way at each station at sunrise and sunset due to variations in the ionosphere. In particular, variations at sunrise and sunset are not mirror images of each other. A typical signal over 24 hours is shown in Fig 4, in which the characteristic events during sunrise and sunset are identified. I tabulated these times during sunrise and sunset at the location of my receiver and compared them to the times of sunrise and sunset at the transmitter and to the times of the sunrise and sunset spikes and dips. This data is shown in Figures 5 and Table 1. By studying what is happening in the ionosphere at a specific moment, the conclusion is that the ionosphere is affected by the sun and specifically by the angle of the sun in relationship to a certain location. The sun similarly affects the VLF radio waves that are reflected by the ionosphere. Procedure A Sudden Ionospheric Disturbance (SID) monitor was obtained from Stanford University’s Solar Center (http://solar-center.stanford.edu/SID/). The monitor was made available to educators, high schools and research institutions. The program’s goals are to distribute SID monitors to people around the world, have them track SIDs and share the data collected through their website. 8 Merola, Leandra Monitor The particular monitor used, which is connected to an antenna which I made, records VLF radio waves transmitted from a military radio station in LaMoure, North Dakota (Latitude 46.37N, Longitude 98.33). The monitor was programmed by Stanford University, to receive radio waves with a wavelength of 25.2 kHz, which LaMoure transmits. The device was connected to a computer in Rockville Centre where it runs continuously, measuring the signal strength every 5 seconds. The setup was located in Rockville Centre, New York (Latitude 40.67N, Longitude 73.64W). The VLF radio waves were recorded by the computer, which transferred the raw analog data into digital values. The program measures the radio wave’s strength in voltage and takes a point of data every five seconds. Figure 3: Construction of Antenna A B C Antenna Construction (Figure 3, A-C) The monitor was connected to an antenna, which I altered from the original plans included with the kit from the Stanford Solar Center. I used a square structure for the base og the 9 Merola, Leandra antenna that I built which was sturdier than the one recommended by Stanford University. The base of the antenna was constructed of PVC pipe (diameter = ¾”) (Fig 3, A). Eight, 4” pieces of 9 PVC were connected into a square using elbows and T’s. I then used 8 pieces that were 4 32 " long to divide the square into quadrants using T’s and a cross joint. Two inch pieces were used 9 to build vertically and 4 32 " pieces to build parallel to the ground. This raised the base and added another dimension. To make the base sturdier I added another level by building up with 6 9 ¼” pieces and across with 4 32 " pieces. To attach the two appendages I used a 2” piece of PVC. I then attached the antenna, which was made in the shape of an “X,” of 1”x 2” pine attached to the base using another piece of PVC 25” long (Fig 3, C). After the frame of the antenna was built, with help from my classmates, I wrapped 24-gauge wire around the mast 50 times (Fig 3, B). Once the coil antenna was built I placed it outside and positioned it so that the plane of the wire was perpendicular to the expected transmission source (Fig 3, C). I connected the antenna to the SID monitor and then calibrated the monitor. Connection with the Computer The monitor was attached to my computer using an available serial port. The computer recorded the data that the monitor collected and stored the information in a file. The computer recorded a data point every 5 seconds in 24 hour blocks. Excel Graphs and comparing Data The raw data was recorded and stored as voltage versus time values in a .csv formatted file. I then convert the raw data into graphs, which were easier to use to make comparisons. To change a csv (comma separated value) file, which is the format the program automatically uses, into a excel file I clicked on the file and used Excel’s chart wizard. Once the data was represented as a line graph (Fig 4), I looked for the phenomenon called the sunrise/sunset effect. 10 Merola, Leandra Around sunrise and sunset the graphs have large spikes because of the sudden change in ionization. The phenomenon is a good indicator of accurate data because it is a phenomenon that has shown up on previous data from SID monitors. After I was sure I could see the sunrise/sunset effect, I looked for SIDs, which are changes in the voltage over time on the daytime part of my graph (Fig 4). If I had any sort of spike, like the one in Fig. 4, then I would check it against solar flare activity using graphs from the GOES satellite, which can be found on http://www.sec.noaa.gov/ftpdir/warehouse/2006/2006_plots/xray/, to see if there was a correlation between a spike on the graph and the spikes on the graphs from the GOES satellite (Fig 5). The GOES satellite orbits the Earth outside of the atmosphere and captures data from the sun. The satellite records solar flare activity. This includes the time at which solar flares occur, how long they last and the intensity of the solar flare. By comparing this information with the graphs from the SID monitor, I was able to determine whether or not the SID is induced by a solar flare. I also studied the sunrise/sunset effect to find out what was happening that was different during sunrise and sunset. Finally, I used my graphs to compare them with other data from scientists from two locations in the United States. I compared data with a scientist in Utah and a professor in Boston, Massachusetts and I looked for any similarities and differences between our graphs, especially those differences during sunrise and sunset. 11 -5 -4 -3 -2 -1 0 1 2 3 4 5 7/4/2006 0:00 7/4/2006 0:40 7/4/2006 1:21 Sunset Results Spike (A) 7/4/2006 2:02 7/4/2006 2:43 7/4/2006 3:24 7/4/2006 4:05 7/4/2006 4:46 7/4/2006 5:27 7/4/2006 6:08 7/4/2006 6:49 7/4/2006 7:30 7/4/2006 8:11 7/4/2006 8:52 SID (D) 7/4/2006 9:32 7/4/2006 10:13 7/4/2006 10:54 (B) 7/4/2006 11:35 12 7/4/2006 12:16 Hours (UTC) 7/4/2006 12:57 Sunrise Dip 7/4/2006 13:38 Crazy4horses168@aol.com 7/4/2006 14:19 Recovery (C) 7/4/2006 15:00 SID Project NML_S-0021 SSHS 2006-07-04 Figure 4: Sample Data from July 4th 7/4/2006 15:41 Solar Flare 7/4/2006 16:22 Figure 5: Solar Flare Data from GOES Satellite 7/4/2006 17:03 7/4/2006 17:43 7/4/2006 18:24 7/4/2006 19:05 7/4/2006 19:46 7/4/2006 20:27 7/4/2006 21:08 7/4/2006 21:49 The graphs from my SID monitor created a definite daily pattern. Each graph showed that after local sunset there was an increase in the signal strength or spike (A) as seen in Fig. 4. 7/4/2006 22:30 Merola, Leandra 7/4/2006 23:11 7/4/2006 23:52 Merola, Leandra During the nighttime the signal was high, but the signal strength also varied from night to night. There was, however, a definite dip, or decrease in signal strength, before sunrise (B), which is followed by a recovery (C) and a more subtle decrease in signal strength as seen in Fig. 4. After local sunrise the graph leveled out and remained at a relative constant unless there was a SID (D). These trends were repeated almost everyday and an example of an everyday graph can be found in Fig. 4. Because there were so few SIDs I focused on sunrise and sunset and how they affect the ionosphere. To find patterns in my data, during sunrise and sunset, I took a week of data in July and compared the local sunrise time, the sunrise time by the transmitter, the times of the sunrise Table 1: Sunrise and Sunset Times Local sunrise Date (UTC) NML sunrise First spike Recovery Local sunset NML sunset Spike 7/2/2006 10:27 11:44 8:59 9:52 1:29 3:29 2:59 7/3/2006 10:27 11:45 9:02 9:52 1:29 3:29 3:01 7/4/2006 10:28 11:46 9:07 9:44 1:29 3:28 2:59 7/5/2006 10:28 11:46 8:59 9:52 1:28 3:28 2:55 7/6/2006 10:29 11:47 8:57 9:54 1:28 3:28 2:53 7/7/2006 10:30 11:48 9:10 9:44 1:28 3:27 2:56 7/8/2006 10:30 11:49 9:08 9:55 1:28 3:27 2:57 Average 10:28 11:46 9:03 9:50 1:28 3:28 2:57 13 Merola, Leandra Sunrise and Sunset Effect 14:24 12:00 9:36 NML sunrise Local sunrise Time (UTC) Recovery 7:12 Sunrise spike NML sunset Sunset spike 4:48 Local sunset 2:24 0:00 0 1 2 3 4 5 6 7 8 9 Days Figure 6: Sunrise and Sunset Effect Graph Deleted: ¶ spike and recovery, the local sunset time, the sunset time by the transmitter and the time of the sunset spike. By using Table 1 and Fig. 6 we can clearly see the order of the events. Fig. 6 shows that the sunrise spike on my graphs happen before the sun rises over the location of the receiver or the transmitter. Fig. 6 also shows that the sunset spike occurs after sunset at the location of the receiver and before sunset at the location of the transmitter. This means that the ionosphere is ionized before the sun rises and after the sun sets because there is a change in signal strength which means that there is a change in the level of ionization. Once I knew what types of patterns my graphs formed, I compared my own graphs with graphs from other receivers using the same type of transmitter. I found that my graphs were 14 Merola, Leandra similar to those graphs created from receivers at a similar longitude. On the other hand, my graphs were different from those graphs created from receivers with a very different longitude. These similarities and differences can be seen in Fig. 6. Local Sunset for Rockville Sunset Spike for Sunrise Dip for Centre Rockville Centre Rockville Centre and and Boston and Boston Logan Boston __ = Rockville Rockville Centre Centre __ = Logan __ = Boston Local Sunrise for Boston Rockville Centre and Boston Figure 7: Graph of Data from Rockville Centre, NY; Logan, UT; Boston MA for July 10th 2006 Deleted: ¶ Stanford University has hosted this project along with many other projects using SID monitors (Fig 7). In order to look at data more carefully, Stanford set up a website where people with SID monitors can share their data. This graph, from the Stanford University website, shows how similar the Rockville Centre and the Boston graphs are. They have similar sunrise and sunset spikes and the daytime values are almost exactly the same. The Logan graph is different because there is a decrease in the signal strength before sunset and the sunrise spike and recovery are larger and more spread out over a period of time. 15 Merola, Leandra Discussion The goal of this project was to use VLF radio waves as a tool to monitor the ionosphere and to observe how radiation from the sun affects the strength of VLF radio waves. Because there was not a lot of solar activity in the form of solar flares, I concentrated my analysis on how sunrise and sunset affect the ionosphere and VLF radio waves that are reflected by the ionosphere. By graphing the sunrise and sunset times and the times of the various peaks on a graph, I was able to determine the order of events that affect the ionosphere and VLF radio waves. I found that the sun rises in the ionosphere first. This causes the ionosphere above the receiver and transmitter to be ionized before the sun even rises at the location of the receiver, assuming that, like my set up, the receiver is east of the transmitter. When radiation from the sun comes around the Earth, which acts like a shield during the night, the radiation again ionizes the ionosphere. This sudden ionization causes the signal strength of the VLF radio waves to decrease in a short period of time. As seen in Fig. 7 when the sun first starts to ionize the part of Figure 7: Diagram of the Sun’s Radiation and the Ionosphere Transmitter Logan Rockville Centre Earth Sun Ionosphere Not Drawn to Scale 16 Merola, Leandra the ionosphere observation, it is from the underside of the atmosphere. This was an interesting find because for the most part the ionosphere is always ionized from above. With this piece of information I concluded that the second sunrise spike or the recovery is due to the fact that the sun’s rays of radiation have moved past the ionosphere directly above the transmitter and receiver and the sun is slowly starting to ionize the ionosphere from above. Once the sun is ionizing the ionosphere from above, the curve on the graph is relatively constant due to the constant bombardment of radiation from the sun. The sunset effect can be similarly explained. The sun sets at the location of the receiver first. The Earth then blocks the rays of radiation as the sun sets on the ionosphere. As soon as the radiation cannot reach the ionosphere, the signal strength increases drastically in a short period of time. The sun then sets at the location of the transmitter because the transmitter is west of the receiver. When comparing my data with other data from across the United States, I noticed that while all the graphs were similar in shape they had some differences. One major cause of these differences could be the calibration of the individual monitor. When setting up a monitor you must calibrate it for +- 5V and even the slightest difference in calibration can cause differences in the results. For example, in Fig. 6, the Logan graph has a much higher daytime reading. This could be due to differences in calibration or the variation in local wave strength because Logan is west of the transmitter and the wave propagation from east to west could be different from the west to east observations. This difference in signal strength, while noticeable, is unimportant because it is the change in signal strength, not the actual reading, that matters. I also noticed, when comparing the graphs, that latitudinal differences do not affect the results as much as longitudinal differences do. Boston and Rockville Centre have similar 17 Merola, Leandra longitudes but different latitudes and the graphs are very similar, in fact the sunrise and sunset spikes shown in Fig. 6 match up almost perfectly. However, because Rockville Centre and Logan have very different longitudes, even though their latitudes are similar, their graphs are very different. For example, Fig. 6 shows that the Logan graph has an entirely different sunset spike and a delayed sunrise spike. This is because Logan is west of the transmitter and the sunset effect is the same as the sunrise effect except backwards. In Rockville Centre and Boston the sun sets over the receiver and then in the ionosphere and finally at the transmitter. However, in Logan, the sun sets at the transmitter first. The sun then ionizes the ionosphere from the underside one last time, which causes the signal strength to decrease. The sun then sets in the ionosphere over Logan and causes the signal strength to increase rapidly and finally the sun sets in Logan. Therefore, longitudinal differences play a major role in the differences of the VLF radio wave strength, especially because of the relationship to the transmitter. After analyzing data from these multiple sources, I can conclude that the angle of the sun has an effect on VLF radio waves strength and the ionosphere. My project has shown how many of the interesting characteristics of VLF radio waves depend on the behaviors of the ionosphere, which rely on the sun’s radiation. However, there is still a lot out there that is not known about VLF radio waves and their relationship with the ionosphere. As further research it would be interesting to study why the signal strength at night is not constant. It would also be interesting to study how solar flares affect VLF radio waves in different locations around the world, especially since the solar activity will soon be increasing. I hope that his project can be the jumping off point for other fascinating studies about radio wave technology and their relationship with the ionosphere and the sun. 18 Merola, Leandra References (2006). Index of /ftpdir/warehouse/2006/2006_plots/xray . Retrieved November 13, 2006, from GOES Solar Flare Graphs Web site: http://www.sec.noaa.gov/ftpdir/warehouse/2006/2006_plots/xray/ About the Ionosphere, 21 Jan. 2003. HAARP. (Nov 22, 2005) URL: http://www.haarp.alaska.edu/haarp/ion1.html Aguirre, E. L. (2005 May). Amateurs detect effects on earth. Sky and Telescope, 109, Retrieved August 8 2006, from http://proquest.umi.com/pqdweb Contreira, D., Rodrigues F. S., Makita K., and Brum, C. G. (2004). An experiment to study solar flare effects on radio-communication signals. Advances in Space Research, 36(12), 2455-2459. Davies, Kenneth (1990). Ionospheric Radio. London: Peter Peregrinus Ltd. Khanal, S. (2004). Retrieved October 17, 2006, from The Effect of Solar Flares on the VLF Radio Waves Transmitted in the Ionosphere Web site: http://solar-center.stanford.edu/SID/docs/effect-of-flares.ppt Leary, W. E. (2006, March 6). Scientists say next solar cycle will be stronger but delayed. New York Times. Peter N., (2003, March 3). In Iraq, solar storms play havoc with communication. Christian Science Monitor, p. 15. Radio Waves. (2006). In Wikipedia [Web]. Wikipedia Foundation, Inc.. Retrieved Oct. 14, 2006, from http://en.wikipedia.org/wiki/Radio_spectrum Space Weather Monitors Stanford SOLAR Center. (2006). Retrieved December 5, 2005, from http://solar-center.stanford.edu/SID/ 19