Monday, September 1, 2014

Tropical Depression Five (2014)

Storm Active: September 1-

A tropical wave formed over the Central Atlantic around August 23 and began to produced disorganized shower activity as it moved westward. Atmospheric conditions remained hostile for development along the path of the system for nearly a week as it moved generally westward into the Caribbean. Even as upper-level winds improved on August 30, the tropical wave began to interact with the Yucatan Peninsula, inhibiting further development. Convection increased the next day even as the center of the developing low pressure center moved over land. By September 1, the broad low pressure system had moved west-northwestward into the Bay of Campeche, where a tighter circulation appeared. Though the center had primarily left the deep convection behind over the Yucatan, the system was organized enough by that afternoon to be classified Tropical Depression Five.

As of 8:00 pm EDT, September 1, 2014, Tropical Depression Five had maximum winds of 30 mph, a minimum pressure of 1008 mb, and was moving to the west-northwest at 12 mph. Tropical storm warnings are in effect for portions of the Mexican coast near the northwestern Bay of Campeche.

Sunday, August 24, 2014

Hurricane Cristobal (2014)

Storm Active: August 23-29

On August 16, some scattered thunderstorms developed in association with a broad low pressure system situated over the central tropical Atlantic, about halfway between the western coast of Africa and the Caribbean. No further organization occurred until around August 19, when convection became a little more concentrated in association with the system. As the low approached the Leeward Islands on August 21, it remained poorly defined, but began to generate gale force winds. Land interaction limited development over the next day while the low continued west-northwest just to the north of Puerto Rico and Hispaniola. However, on August 23, the system slowed in forward speed and turned northwest towards the Bahamas. That afternoon, though the circulation remained somewhat broad, banding on the north and east sides of the circulation improved to the point that advisories were initiated on Tropical Depression Four.

Some wind shear was affecting the system, but ocean waters near the Bahamas were very warm, and deep convection gradually increased near the center of circulation. By the morning of August 24, the depression had strengthened into Tropical Storm Cristobal. Over the next day, the system moved slowly northward, bringing sustained heavy rain to portions of the Bahamas. Though shear from the north exposed the circulation of Cristobal during the early morning of August 25, the center reformed southeast of its former position, bringing it closer to the convective canopy, and allowing modest strengthening through that morning.

During that day, the system meandered slowly to the north and east, moving away from the Bahamas. Meanwhile, though thunderstorm activity developed closer to the center, Cristobal's overall satellite presentation remind disorganized. The tropical storm was interacting with a frontal boundary, giving the associated convection a more linear than circular pattern. Despite this, winds increased that night and Cristobal became a category 1 hurricane. The system acquired a faster and more definite northward motion on August 26. Atmospheric conditions became more favorable over the next day, allowing Cristobal to develop a more organized, albeit asymmetric, structure. By the morning of August 27, the cyclone had developed a partial eyewall in the northwest semicircle. Though shower activity to the south and east was still scarce, small intensification accompanied this improvement in structure.

Around noontime, Cristobal passed well to the west of Bermuda, bringing scattered showers, gusty winds, and dangerous ocean conditions to the island. Influenced by mid-latitude winds, the system then began its turn towards the northeast, accelerating rapidly. At the same time, the cyclone assumed a more symmetrical appearance. As the hurricane raced to the north and east over the next day, it acquired an eyewall and even an intermittent eye feature during the afternoon and evening of August 28. Cristobal reached its peak intensity that night above 40°N, with 85 mph winds and a minimum pressure of 970 mb.

That evening, however, the system moved over much cooler water, and began extratropical transition as it moved northeast past Nova Scotia with a forward speed of nearly 50 mph. By the morning of August 29, all remaining convection was displaced well to the north of the center. Further, the wind field had broadened, indicating that the cyclone was no longer tropical.

Friday, August 1, 2014

Hurricane Bertha (2014)

Storm Active: July 31-August 6

On July 24, a tropical wave entered the east Atlantic. By July 27, a large area of disorganized shower activity had developed in the vicinity of the system. Convection continued to increase over the next two days, and a circulation became evident in the southeastern portion of the tropical wave early on July 29. Later that day, the low began a turn toward the west-northwest, and entered a drier air mass. Thunderstorm activity decreased markedly that night and into July 30. However, the circulation itself continued to become better defined and the low deepened into July 31. By this time, gale force winds were occurring in portions of the circulation, and only a lack of convection prevented the classification of the system as a tropical storm, since shower activity remained confined to the south and east of the center. Hurricane hunter aircraft which investigated the system noted winds up to 45 mph that afternoon near the center of circulation, even though these areas were devoid of thunderstorms. Finally, that evening, an area of convection appeared and persisted near the system's center, and advisories were initiated on Tropical Storm Bertha.

Even as Bertha entered a more moist and unstable atmosphere, promoting convective development, higher wind shear began to affect the system, restricting thunderstorm activity to the eastern half of the circulation. For a period on August 1, the center became completely exposed due to incoming shear, as Bertha's quick motion towards the west-northwest made it even more difficult for the cyclone to maintain convective coverage. Amidst these fluctuations, however, the circulation remained intact, and the storm entered the Caribbean Sea that afternoon. On August 2, heavy rain bands just north of Bertha affected Puerto Rico and the neighboring islands as the center passed to the south.

As interaction with land began that day, Bertha became even less organized, and a closed circulation was nearly undetectable, even on Doppler radar imagery. During the late afternoon, the system passed over the eastern Dominican Republic, bringing localized heavy rain and gusty winds. By this time, the cyclone had navigated around the southern edge of a ridge to its north, and therefore turned towards the northwest.

On August 3, Bertha brushed the easternmost Bahamas before moving away from land, and in addition away from hostile wind shear. For the first time since its formation, the tropical storm was able to develop healthy outflow and a central dense overcast near the center. When this occurred late that night, Bertha intensified rapidly: its central pressure dropped from 1012 to 999 mb in 12 hours, and winds approached hurricane strength. During the morning of August 4, through Bertha appeared quite disorganized on satellite imagery, a more intense eyewall and slight hints of an eye feature appeared at the center of circulation, even though there was no convection north of the eyewall! However poor the visual presentation, aerial data indicated that the cyclone now had hurricane force winds. Bertha thus reached its peak intensity as a category 1 hurricane with winds of 80 mph and a central pressure of 998 mb.

The system began to accelerate northward and north-northeastward that evening, and began to weaken as an oncoming frontal boundary greatly increased wind shear. By the morning of August 5, the center of circulation was intermittently exposed as thunderstorm activity was repeatedly displaced, and Bertha quickly lost strength, again becoming a tropical storm. Over the following day, the system weakened further and accelerated to the northeast away from the east coast of the United States. The system became extratropical on August 6.



Hurricane Bertha reached category 1 hurricane status (shown above) without much convective organization.



Bertha curved around the edge of a subtropical ridge and therefore missed landfall on the U.S. East Coast.

Tuesday, July 22, 2014

Tropical Depression Two (2014)

Storm Active: July 21-23

On July 16, a tropical wave emerged off of the coast of Africa. A few days later, the system began to show signs of development, the first tropical wave of the season to do so. On July 20, shower and thunderstorm activity increased in association with a low pressure center forming along the wave. Despite being over the open central Atlantic, where sea surface temperatures were hardly sufficient for convective development, the low continued to organize the next day as concentrated thunderstorms appeared about the center. By the afternoon of July 21, it became evident that the low had acquired a closed circulation, and advisories were initiated on Tropical Depression Two.

On July 22, as the system proceeded westward under the influence of a subtropical ridge, dry air began to affect the system from the north, limiting the small amount of deep convection associated with Two primarily to the southern and western quadrants. The depression became slightly more organized that evening as thunderstorm activity increased briefly in coverage and intensity. However, by the morning of July 23, wind shear had also begun to increase, and the circulation started to lose definition due to the hostile atmospheric conditions. A few hours later, it became evident that the circulation was no longer closed, indicating that Tropical Depression Two had degenerated into a trough of low pressure.



As evident in this satellite image, Tropical Depression Two experienced an invasion of dry air from the north throughout its short lifetime.



Tropical Depression Two degenerated into a tropical wave before reaching the Caribbean.

Sources: nhc.noaa.gov, http://commons.wikimedia.org/wiki/File:02-L_2014_track.png#mediaviewer/File:02-L_2014_track.png

Tuesday, July 1, 2014

Hurricane Arthur (2014)

Storm Active: June 30-July 5

On June 25, a frontal boundary oriented east to west over the northern United States began to push southward. Around June 27, a low pressure center formed along the front over North Carolina. Over the next day, the low drifted southeastward over South Carolina and emerged off of the coast early on June 28. Immediately, convection increased in association with the system.

In a region of weak steering currents, the low drifted slowly to the south, bringing rain showers to the northern Bahamas and eastern Florida by June 29. However, wind shear out of the north also increased that day, inhibiting the development of shower activity near the low's center. Despite this lack of convection, the low itself deepened significantly by June 30. Late in the day, upper-level winds once again became more favorable as wind shear dropped to near 10 kt. At this time, reconnaissance aircraft indicated that the system was just below the threshold of becoming a tropical cyclone. By just before midnight, organization had increased sufficiently to classify the system as Tropical Depression One, the first tropical cyclone of the 2014 Altantic Hurricane Season.

Tropical Depression One slowed and became nearly stationary off of the central Florida coast during the morning of July 1. Meanwhile, through the center of circulation remained on the northern edge of thunderstorm activity, banding and convective organization improved and the cyclone strengthened into Tropical Storm Arthur. Though the tropical storm reamined quite close to the U.S. East Coast, most of the deep convection was confined to the southern and eastern parts of the circulation, sparing land areas of the heaviest rain. Banding slowly improved throughout the day, indicating gradual strengthening By that evening, Arthur had begun a definite northward motion ahead of a trough moving into the southeastern United States. Central deep convection remained inconsistent into the morning of July 2, but the cyclone deepened and showed hints of an eye, and Arthur had soon intensified into a strong tropical storm.

Arthur persisted in its northerly motion throughout the day and most of the night, and meanwhile continued to strengthen. An eye feature made a brief appearance on visible satellite imagery during the afternoon of July 2, and the storm continued to gain in organization through the morning of July 3, even despite some ingestion of dry air from the north. By this time, rain bands had begun to sweep over the coasts of the Carolinas. Later in the morning, Arthur finally began to take its long anticipated eastward turn ahead of a front approaching the U.S. east coast and began to accelerate north-northeast.

That afternoon, Arthur developed a well-defined eye apparent on both visible and infrared imagery, indicating that another phase of strengthening was beginning. By the evening, the cyclone was upgraded to a category 2 hurricane. At 11:15 pm EDT on July 3, Hurricane Arthur made landfall near Cape Lookout, North Carolina, reaching its peak intensity of 100 mph winds and a minimum pressure of 973 mb, already stronger than any cyclone of the 2013 Atlantic hurricane season. Around 5:00 am on July 4, the center of circulation passed over the northern Outer Banks and emerged into the Atlantic. Meanwhile, the system's outer bands affected the coastal areas of Virginia, Maryland, Delaware, and New Jersey.

Increasing wind shear and colder waters began to weaken Arthur that morning, even as its windfield expanded, indicating that the extratropical transition had begun. Late on July 4, Arthur made its closest approach to Cape Cod as a minimal category 1 hurricane, bringing heavy rainfall and some tropical storm force winds to the region. By this time, Arthur was accelerating rapidly to the northeast and losing tropical characteristics. Early on June 5, the Arthur made landfall in southern Nova Scotia as the remaining deep convection became separated from the low-level center. The cyclone became post-tropical shortly afterward. The remnants of Arthur continued north and northeast over Newfoundland and into the North Atlantic near Greenland.



Hurricane Arthur was the first hurricane to make landfall in the United States since 2012.



Arthur took a rather unexpected shift to the west before landfall, bringing it inland over the Outer Banks of North Carolina.

Thursday, May 22, 2014

Professor Quibb's Picks - 2014

My personal predictions for the 2014 Atlantic hurricane season is (written May 22, 2014)

13 cyclones attaining tropical depression status,
12 cyclones attaining tropical storm status,
4 cyclones attaining hurricane status, and
1 cyclone attaining major hurricane status.

These predictions are near normal for the tropical depression and tropical storm categories, and below normal for the hurricane and major hurricane categories. The last 15 years have for the most part seen exceptionally high tropical cyclone activity due to the "warm" phase of the Altantic Multi-Decadal Oscillation (AMO). This oscillation (involving anomalies in sea surface temperatures) could explain the high tropical cyclone activity in the 1950's, the low activity in the 1980's, and the high activity in the 2000's. The current warm phase is expected to last at least several more years, likely keeping the number of tropical cyclones close to average even during seasons in which conditions are not generally favorable, such as this coming season.

ENSO oscillation forecasts indicate that an El Nino is likely to develop during the 2014 hurricane season, particularly in the late summer. Since an El Nino event is associated with a strong jet stream across the U.S. and higher wind shear, the development of such an event is likely to supress hurricane activity. Since the event is predicted to develop near the peak of the season, hurricanes and major hurricanes (which form more often near the peak of the season) are less likely.

In a manner similar to last season, the ocean temperatures of the east Atlantic are predicted to be below average for much of this season. This too discourages the formation of major hurricanes, since powerful tropical cyclones most often have their origins in the east Atlantic. During August 2013, a large quantity of Saharan dust was blown westward over the eastern Atlantic, cooling the water and disrupting cyclone formation. Though such events are difficult to forecast, above average trade winds could result in a similar event this season, further reducing eastern Atlantic activity.

Below, my anticipated risk factors for four major regions of the Atlantic basin are listed. The risk index runs from 1 meaning very low potential to 5 being very high potential (with 3 about average).

U.S. East Coast: 3
Though the season as a whole is expected to be inactive, any cyclones which do develop are likely to curve northward due to the position of the Bermuda high pressure system farther to the east during an El Nino. Thus the possibility exists for a grazing blow to coastal areas, especially Cape Hattaras.

U.S. Gulf Coast/Northern Mexico: 2
The Gulf of Mexico (particularly its northwestern section) have recorded persistently low sea surface temperature this year compared to the rest of the Atlantic basin. This factor, combined with the strong upper-level winds and powerful frontal boundaries passing over the U.S. Gulf coast, will likely destroy cyclones approaching the region.

Yucatan Peninsula and Central America: 2
This season, the upper atmospheric conditions favor cyclones paths which curve to the north, due to the eastward position of the Bermuda High pressure region. Usually, cyclones must take a more westward track without curavture in order to affect Central American regions and the Yucatan Peninsula. Any tropical systems reaching land therefore are likely to be weak tropical storms. In fact, this region is more at risk from Eastern Pacific tropical cylones than Atlantic ones.

Caribbean Islands: 2
During an El Nino season, Caribbean summers tend to be dry, due to a dry air mass situated over much of the region. In addition, persistent wind shear also pervades the Caribbean during an El Nino. The combination of these two factors can halt tropical cyclone development for weeks on end, ensuring that any storms that do develop pass to the north. The largest risk to the Caribbean Islands is for a cyclone to pass just to the north.

Overall, the 2014 Atlantic Hurricane Season is expected to be below average, particularly in intense cyclones, and the risk to most landmasses is smaller than normal. However, as history has repeatedly demonstrated, even quiet seasons may have devastating storms, such as Hurricane Andrew of 1992. Only 7 tropical storms formed that year, but one, Andrew, made landfall in Florida as a category 5 hurricane, only the third Atlantic hurricane to make landfall at such an intensity in recorded history. During any season, hurricane preparedness is a must.

Wednesday, May 14, 2014

Hurricane Names List-2014

For the North Atlantic Basin, the list for naming tropical cyclones in 2014 is as follows:

Arthur
Bertha
Cristobal
Dolly
Edouard
Fay
Gonzalo
Hanna
Isaias
Josephine
Kyle
Laura
Marco
Nana
Omar
Paulette
Rene
Sally
Teddy
Vicky
Wilfred

This list is the same as the 2008 list with the exception of Gonzalo, Isaias, and Paulette, which replaced Gustav, Ike, and Paloma, respectively. These names were retired after the 2008 season.

Wednesday, April 30, 2014

MAVEN

MAVEN (Mars Atmosphere and Volatile EvolutioN) is a NASA space mission primarily focused on studying the Martian atmosphere. Previous Mars missions have already given us hints into Mars's past, including numerous signs of past liquid water and various geographical and chemical signatures of a planet that was habitable many, many years ago. MAVEN will approach the problem of elucidating Mars's past from a different angle, by examination of its upper atmosphere.

Before MAVEN, our hypothesis as to the demise of Mars's habitability was as follows: several billion years ago, when the Solar System and its planets were still young, Mars had, like Earth, a molten core.



Earth's molten core consists of metals such as iron that conduct electricity. The circulation of these metals throughout the core, induced by the rotation of the Earth, generates a magnetic field (as in the illustration above). This magnetic field, in turn, protects us from the charged solar wind by deflecting it towards the poles. Mars is theorized to have had a similar core and magnetic field. However, being farther from the Sun and smaller, Mars's core cooled over time, and eventually solidified. The planet's magnetic field then weakened, and solar wind blew away a majority of Mars's atmosphere, leaving it with a rarefied layer of mostly carbon dioxide. Such a thin atmosphere would have been inhospitable for liquid water, and thus any bodies of water dried up, likely killing any life, if it had developed there.

MAVEN's observations will probably not alter this basic understanding, but will provide much more detailed information. For example, by observing how solar wind interacts with Mars's current atmosphere, the spacecraft will provide data concerning the exact mechanisms involved in atmospheric loss. To this end, MAVEN carries several instruments that measure solar wind and its impact on Mars. Also, by observing the current rate of gas loss, the mission will allow scientists to extrapolate backward and infer a more precise timeline of Mars's climate evolution. In order to accomplish this goal, MAVEN includes instruments that detect gaseous ions escaping from the Martian atmosphere. These are the "volatiles" to which the name refers. Finally, the probe also has a device known as a mass spectrometer, which can measure the abundance of different isotopes of certain chemical elements. Since heavier isotopes are less likely to be ejected from Mars simply due to their slightly greater mass, the ratio of isotope abundance in Mars's atmosphere versus that in Earth's, for example, can indicate exactly how much has been lost and thus how dense the atmosphere was in the past.

Artist's rendering of MAVEN

MAVEN launched on November 18, 2013. After about a ten month cruise, the probe will enter orbit of Mars in September of 2014. A few weeks after, the spacecraft will assume its science orbit, a highly elliptical orbit. The low point of its orbit brings MAVEN within 100 miles of the surface, allowing it to easily sample the atmosphere, and the high point brings it to more than 3000 miles from Mars's surface, so that the spacecraft can also take global observations. The science phase is planned to last about a year.

Sources: http://www.nasa.gov/mission_pages/maven/main/index.html#.Uf03vZIsmG0, http://www.nasa.gov/sites/default/files/files/MAVENFactSheet_Final20130610.pdf, http://lasp.colorado.edu/home/maven/science/, http://www.ipgp.fr/~aubert/Julien_Aubert,_Geodynamo,_IPG_Paris/Home.html

Wednesday, April 23, 2014

Eclipses and Saros Cycles 3

This is the third part of a three part post. To begin viewing the first, click here.

The previous post revealed the primary astronomical tool for predicting eclipses, the saros cycle. According to this cycle, the Moon has the same apparent size, inclination to the Earth's orbit, and angle to the Earth-Sun line in the Earth's orbital plane every 6585.32 days. Therefore, if an eclipse occurs on a given date, another very similar eclipse will occur about 18 years later with respect to the above parameters. During an eclipse, the angle of the Earth-Sun line to the Earth-Moon line will either be 0° (for a solar eclipse) or 180° (for a lunar eclipse), and the Moon will be at the same angle after a saros cycle, so two eclipses separated by a saros cycle must either both be solar or both be lunar. Similarly, during an eclipse, the Moon is either passing through the Earth's orbital plane at the ascending node or the descending node, and the eclipse after a saros cycle has passed will involve the Moon at the same node. Finally, the apparent size of the Moon will be the same for eclipses separated by a saros cycle.

However, many other conditions are not invariant before and after the length of time of a saros cycle. For example, since the decimal part of the length of the saros cycle is .32 days, two eclipses separated by a saros cycle will not be at the same time of day on Earth. In fact, the second eclipse will occur about 8 hours later than the first (.32 days is approximately 8 hours). This also guarantees that the eclipse will not occur in the same place on the Earth's surface. Futhermore, since the saros cycle is about 18 years and 11 days, the Earth will also be in two different places on its orbit around the Sun when the two eclipses occur.

In addition, 6585.32 days is not exactly an integral multiple of each of the synodic, draconic, and anomalistic months. For instance, 242 draconic months is about 6585.35 days (using the more precise value of 27.21222 days for the draconic month), which, although very close to the length of 223 synodic months, 6585.32 days, is not equal to it. As a result, even as as 223 synodic months pass from one eclipse and the Moon returns to its position along the Earth-Sun axis, the period of 242 draconic months is not quite complete, so the Moon will not have quite reached its node. Thus, over time, the eclipses separated by saros cycles shift until, eventually, the necessary conditions no longer align, and eclipses cease. Any given saros series will therefore only have a certain number of eclipses before the alignment ends.



The above image illustrates the progress of a saros series of lunar eclipses, where the gray bullseye represents the Earth's shadow (recall that if the Moon passes through the light gray, or partial shadow, of the Earth, the eclipse is partial, and if it passes entirely into the dark gray area, the total shadow, the eclipse is total). This series of eclipses is also at the descending node. Therefore, we can see that, before the saros series begins, the Moon has already passed the descending node at the time of the correct angular alignment of the Moon, Earth, and Sun. Thus the Moon is "too low" to be hit by Earth's shadow (blue-gray Moon). However, after a saros cycle has passed, the angular alignment is once again correct, but a full draconic month has not yet passed, so the Moon is a little less past its descending node than before.

Eventually, the draconic month has drifted backward enough so that the passage through the descending node does coincide with the correct arrangement of the Moon, Earth, and Sun in the orbital plane, and the path of the Moon does take it through the Earth's shadow. At this point, partial and then total eclipses will occur. However, over time, the Moon's progress in the draconic month will again fall behind, and at the time of correct angular orientation, the Moon will have not yet reached the descending node. At this point (the pink Moon), eclipses will cease and the saros series ends.



A similar phenomenon occurs with solar eclipses. In the above diagram, a few total solar eclipse paths across the Earth are shown, all from the same saros series (though there are many others), and again at the Moon's descending node. Note that each eclipse is indicated by a path along the Earth's surface. The paths are the areas which experience totality some time during the eclipse. The path of the eclipse moves from west to east, even though the part of the Earth facing the Sun moves from east to west along the globe. This is because the Moon's velocity, and thus the velocity of its shadow, is greater from west to east then the area that of the point on the Earth's surface moving from east to west.

As mentioned above, successive eclipses in a saros cycle are separated (in time of day) by about 8 hours, approximately a third of a day. Thus the second eclipse takes place about 120° west of the first. Thus two eclipses in a saros series three saros cycles apart will be at about the same longitude. But for the above series, which take place at the Moon's descending node, eclipses later in the series are not as far along with respect to the draconic month as those at the beginning. Thus, just as for lunar eclipses, the eclipses in a series at the descending node shift "upward", and in the solar case, this has the effect of shifting the totality path north for each successive saros cycle. Thus the first eclipses in the same saros series as above, are only partial, and can only be seen near the south pole. Eventually, as the series progresses, the Moon's shadow intersects the Earth, again beginning at low latitudes. As in the figure, the path shifts north until the eclipses can only be seen near the north pole, and then not at all. The down-to-up or south-to-north pattern for saros series reverses for series at the ascending node.

Saros series are numbered, with separate numberings for lunar and solar eclipse series. For lunar eclipses, those at the descending node are given odd numbers and those at the ascending node even numbers. The situation is reversed for solar eclipses. The saros series, further, are ordered in number by starting date. Contemporary series which are currently producing total eclipses are in the low to mid 100's. For example, the solar eclipse on August 21, 2017 belongs to solar saros 145. Solar and lunar saros series each include around 70 eclipse events, spanning a period of roughly 1200 years. Of course, these series overlap, so any given year, eclipses occur from different saros series. For example, the year 2012 had solar eclipses from series 128 and 133, while it had lunar eclipses from series 140 and 145.

In conclusion, saros series are the most important tool in the categorization of eclipses, and have allowed us to identify when eclipses have occurred thousands of years into the past, and to predict when the will occur thousands of years into the future.

Sources: http://en.wikipedia.org/wiki/Saros_(astronomy), http://www.cropcircleconnector.com/inter2012/italy/bracciano-earthquake7.jpg, http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0304-1-08-eclipse/Path%20of%20Totality.htm, http://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html#section106

Tuesday, April 15, 2014

Eclipses and Saros Cycles 2

This is the second part of a post concerning eclipses and saros cycles. For the first, see here.

To understand how solar eclipses are predicted, we first must define some terminology relating to various types of "months". These months are not calendar months, but rather are time intervals related to the moon's orbit.

Synodic Month (29.53 days): This is the most common period referenced in the context of the moon. It measures the time it takes for the Moon to complete a revolution with respect to the line between the Earth and the Sun, or the time between two full moons or two new moons. However, this month is not equal to the period of the Moon's orbit, because the line between the Earth and the Sun shifts, as the Earth itself revolves.



The above image shows the position of the Earth and the Moon relative to the Sun at two successive new moons. Note the angle between the line connecting the Earth and Sun and the line marking the point at which the Moon has completed exactly one orbit around the Earth. Such an orbit takes 27.32 days.

Draconic Month (27.21 days): This "month" is the average time between successive crossings of the ascending node by the Moon on its orbit. The nodes of an orbit are the orbit's intersection with some plane of reference. In the context of eclipses, we are concerned with the intersection of the Moon's orbit around the Earth with the plane containing the Earth's orbit and the Sun. Since the Moon's orbit is inclined to this plane, there are only two points of intersection (see diagram below).



The two nodes of the Moon's orbit are the ascending node, at which point the Moon crosses from below the plane of the Earth's orbit to above (where the area "above" the plane is the space beyond the Earth's north pole), and the descending node, where the opposite occurs. Since, due to the effect of the Sun's gravity, the nodes of the Moon's orbit shift with time against the Moon's direction of orbit, the draconic month (time between crossing ascending node twice) is slightly shorter than the orbital period of the Moon (27.32 days). The draconic month is important for the prediction of eclipses because eclipses can only occur when the Moon is in the plane of the Earth's orbit and the Sun, i.e., when the Moon is at an ascending or descending node.

Anomalistic Month (27.55 days): The Moon's orbit, just like the Earth's and that of other celestial bodies, is not a perfect circle. Thus the Moon's distance from Earth varies. The farthest point of the Moon's orbit from the Earth is known as the apogee (deriving from Ancient Greek "from" and "earth", the second of which also gives us geography, geocentric, etc.), and the closest point the perigee (with "peri" meaning "around").

Diagram of the Moon's orbit (elongation exaggerated)

The anomalistic month measures the time it takes for the Moon to travel from one apogee (or perigee) to the next. Note that this length of time is slightly longer than a lunar orbital period, because the apogee and perigee move along the lunar orbit in the same direction as the Moon's motion, so it takes longer for the Moon to "catch up" to its apogee than for the Moon to simply complete an orbit. The anomalistic month is important for eclipse prediction, because although it does not affect the apparent position of the Moon in the sky, whether the Moon is closer to apogee or perigee does affect its apparent size, and thus can affect the type and duration of an eclipse.

Apparent size of the Moon at apogee and perigee.

Note that the apparent size of the Sun varies too, as the Earth's orbit is also elliptical, but the variation occurs at only a fraction of the magnitude (about 3% variation versus the Moon's 12%). Therefore, we focus on the Moon's apparent angular diameter as the determining factor.

In summary, progress through the synodic month indicates the Moon's position relative to the Earth-Sun line (in the Earth-Sun orbital plane), progress through the draconic month indicates how far the Moon is from the Earth-Sun orbital plane, and progress through the anomalistic month indicates the Moon's apparent size. It so happens that the length of time equal to 223 synodic months is about the same as that of 242 draconic months and 239 anomalistic months, all of which equal approximately 6585.32 days. The reason this is significant is that after this period of time passes, a whole number multiple of each of the three "months" will have passed, and the Moon will be in almost exactly the same position relative to the Sun, the same apparent size, and the same inclination from the Earth-Sun orbital plane. Thus if an eclipse occurs at a given date, a nearly identical eclipse will occur again 6585.32 days later! A period of 6585.32 days, about 18 years, is known as a saros cycle.

The sequence of eclipses produced beginning at a given date and including all the eclipses separated from the first by some number of saros cycles is known as a saros series. Eclipses, both lunar and solar, are classified by saros series. The next post explores the details and applications of saros cycles and series.

Sources: http://www.hermit.org/eclipse/Graphics/diagrams/Rotations3.png, http://en.wikipedia.org/wiki/Saros_(astronomy), http://www.hermit.org/eclipse/Graphics/diagrams/Draconic.png, http://www.metahistory.org/images/moonorbit.gif, http://www.astro.virginia.edu/class/whittle/astr1230/im/moon_sidereal.gif