Thursday, January 3, 2008

Coordinate System of the Earth and Celestial Sphere.

Latitude and Longitude together are used as a geometric coordinates system to locate places on the surface of the earth. It is like the Cartesian coordinate system, which is used to locate points on a plane where the X-axis (Horizontal lines) and the Y-axis (Vertical lines) cross. In a Cartesian coordinates, a point on a plane whose coordinates are (3, 4), is 3 units to the right of the Y-axis and 4 units up from the X-axis. Latitude and longitude coordinate system is similar to the Cartesian coordinate system, except that the earth, which the latitude and longitude system is used to locate places on its surface, is spherical in shape. However, the principles are the same for the most part.

Latitude lines run horizontally east-west, parallel to one another. Latitude gives location to places north or south of the equator, which is an imaginary line that divides the earth into northern and southern hemispheres. Latitude is measured in degrees from 0°, at the equator, to 90° at the north and south poles. Each degree of latitude is approximately 111km (69 mi) apart, but the slight flattening at the poles causes the length of a degree of latitude to vary from the equator to the poles.

On the other hand, Longitude lines, which are also called the meridian, run vertically from north to south on the sphere. They converge at the poles and are widest at the equator, about 111 km (69 miles) apart. Just like the length of a degree of latitude decreases from the equator to the poles, the length between the lines of longitude also decreases from the equator to the poles. Zero degrees longitude is located at Greenwich, England. The degrees of longitude continue 180 degrees east and 180 degrees west of Greenwich and they meet and form the International Date Line in the Pacific Ocean. Greenwich, the site of the British Royal Greenwich Observatory, was established as the site of the Prime Meridian by an international conference in 1884. Therefore the meridian is an artificial line and any government or region can create their own meridian and hence a different time keeping.

This coordinate system can then be used to precisely locate places on the surface of the earth. For example, Banjul, the capital of the Gambia is located a few degrees north of the equator and about fifteen degrees west of the longitude zero degrees (that is about one hour behind, and about 111km due west of, Greenwich in London). Each degree of latitude and longitude are divided into minutes and second for more precise location of places and time zones.
Furthermore, this coordinate system of latitude and longitude is used to find great circle distances between any two places on the surface of the earth. Like flat plane geometry, the great circle distance is calculated using spherical geometry because the earth is spherical in shape. In flat plane geometry, the shortest distance between any two points is a straight line and in spherical geometry, the shortest possible distance between any two points is the great circle distance. A great circle of the earth is any line that passes through its center, dividing it into two equal hemispheres. This means that a great circle is equal to the circumference of the earth. The equator of the earth is the only great circle among the lines of latitude and all the lines of longitude, including the meridian are all great circles of the earth. Other than locations on the equator or on due north or south, the great circle distances on a flat map seem to be curved. The great circle distance between places located on the northern or southern hemispheres seem to curve towards the north or south poles, respectively.

Therefore, to find the shortest possible distance between two locations on the surface of the earth must follow the great circle linking the two points. For example, to find the distance between Banjul International Airport in The Gambia and John F Kenney International Airport in New York, I would need a set of coordinates (latitude and longitude) for the two places to calculate the smaller arc of the great circle. Banjul Airport is located at 13° 20’ 19” N and 16° 39’ 17” W; JFK is located at 40° 38’ 36” N and 73° 47’ 22” W. Approximately, Banjul is located at 13.34° North (0.2328 rad) and 16.66° west (0.2908 rad); and JFK is located at 40.64° North (0.7093 rad) and 73.64° west (1.2853 rad). Now I can use the great circle formula to find the shortest distance between Banjul and New York. From this calculation, I found out that the shortest distance between Banjul Airport and JFK about 6280 Kilometers. The calculation is as follows:
Great Circle Distance between Banjul International Airport and JFK in New York City is as follows using the great circle distant formulae.

Distance=0.9852929*6,372.795km

Distance=6279.069km.

This is the shortest possible distance between Banjul International Airport and JFK in New York City. Great circle distance is useful for airlines, shipping routes, and other purposes for navigation on the surface of the earth.

Celestial coordinate system is similar to the spherical geometry. This system is based on the motions of the earth around the sun, our star. The days, months and years on the earth are base on the activities of the earth (rotating and orbiting) around the sun. 24-hour day is called the solar day because it’s based on the time it takes for the sun to make one complete circuit around the local sky. This is slightly (about 4 minutes) longer than a sidereal day which is based on the time it takes a distant start to complete one circuit around the local sky. This is possible because, while the earth rotates on its axis at an average speed of about 1,000 km per hour, it is at the same orbiting around the sun at an average speed of about 100,000 km per hour. Therefore, for the original opposite sides of the earth to meet the sun again, the earth must complete slightly more than one full rotation on its axis. On the other hand, stars in our local sky are too far away for us to notice their movement; as a result, they seem to be fixed at one position. Solar day is not exactly 24 hours; it varies slightly between 25 seconds longer or shorter. The average day for the year is about 24 hours.

A Sidereal month is about 27 days while synodic month, the meeting of the sun and moon in the sky, occurs about every 29 days. The difference is still due to the motions of the earth around the sun; the moon must complete more than one full rotation around the earth before it can meet the sun in our local sky. In the same way, our year, which is the tropical year, is also longer than the sidereal year. The tropical year or calendar year is based on seasons, starting with spring equinox of one year to next spring equinox. Our year is marked with four distinct seasons in most parts of the world due to the sun’s movement in our local sky, which is in an ecliptic to the celestial sphere. The sun crosses the celestial equator on the southern side at spring equinox, which means spring on the northern hemisphere and fall in the southern hemisphere.

The illusionary celestial sphere is very important in locating objects in the sky. The celestial coordinate systems works like the latitude and longitude, and Cartesian coordinate systems. The north and south celestial poles represent the geological north and south poles, the celestial equator represent the equator of the earth, and Declination (dec) and Right Ascension (RA) represent latitude and longitude respectively. Therefore, the lines of declination are parallel to the equator and the celestial equator has a declination of zero degree, just like the equator of the earth has zero degree of latitude. While latitude is measured in positive numbers from zero to 90 degrees, north or south from the equator, declination is measured differently. The north celestial has a declination of +90 degrees, the celestial equator has a declination of zero degrees, and the south celestial pole has a declination of -90 degrees.

Right Ascension, on the other hand is also closely related to longitude in its applications. Like longitude, Right Ascension lines run from the north celestial pole to the south celestial pole. It is measured in hours, minutes and seconds east of the spring equinox. Greenwich is the similitude of Spring Equinox—zero degrees of Longitude and Right Ascension. Let’s say an object in our celestial sphere has a declination of 60 degrees and Right Ascension of 5 hours, its means that the object is located 60 degrees north of the celestial equator and each day the object crosses the meridian 5 hours of sidereal time after spring equinox. Another example, if a star has a declination of zero degrees and Right Ascension of zero hours, the star would rise due east, reach the meridian at spring equinox, and set due west. Stars with declination of more than zero degrees rises north of due east and sent south of due west, and the stars with less than zero degrees rise south of due east and sets north of due west. Stars with a declination of more than +90 degrees are circumpolar, meaning they do not rise or set, and stars with lest than -90 degrees never rise above the horizon.

Unlike the stars, which appear fixed at one place, the sun’s motion in our sky is apparent. Due to the tilting of the earth on its axis during its orbit around the sun, the sun appears to move in an ecliptic in the celestial sphere. The sun completes a full revolution around the celestial sphere in one year. At the spring equinox, the sun has a declination of zero degrees and RA of zero hours. For the next three months, the declination steadily increases to 23.5 degrees and Right Ascension steadily increase to 6 hours on Summer Solstice (June 21). The next three months, the declination of the sun decrease to zero and Right Ascension increase to 12 hours on Fall Equinox (Sept 21). This means that the sun rises due east and set due west at spring equinox, rises north of due east and sets south of due west at Summer Solstice, rises due east and sets due west at fall equinox, and rises south of due east and sets north of due west at winter solstice. It also means that day light is longer at spring and fall equinoxes and shorter during the solstices.

Now how can I determine my latitude and longitude in the celestial sphere? The secret is finding either the celestial north or south poles. An observer’s latitude is equal to the altitude of the celestial pole in the sky. If you know a star’s declination to be 20 degrees north and it appears in your sky at altitude of 70 degrees south, it means the celestial equator crosses your meridian at an altitude of 50 degrees south (70°-20°=50°), and your altitude is 40 degrees north (90° minus 50°). During the day, altitude can be found from the altitude of the sun, by knowing the date and the sun’s declination on that date. For example, on December 21, if the sun crosses the meridian in the south at altitude 75 degrees, therefore, the celestial equator crosses the meridian at an altitude of 51.5 degrees (75° minus 23.5°) and the latitude of the observer is 38.5 degrees north. To find your longitude using the position of an object in the sky is to compare the objects current position to its known longitude to determine how far it has moved and compare this time with the Greenwich Time to know the local time.

By ML Touray

Global Warming: Is it a Real Threat to Our Survival?

It is indisputably true that human activities play an important part in virtually all natural systems on Earth. Human beings are the main catalyst of change in the environment at local and even global scale. Massive population growth and tremendous scientific and technological advancement over the past century have indeed brought about fundamental changes in the way people interact with the natural system. Our energy consumption, which is mainly derived from burning fossil fuel, has increased greatly due to the industrial revolution and other related human developments.

Preponderant of credible and leading scientists and local and international scientific organizations conclude that coal plants, automobiles and other human activities emit faster and more carbon dioxide and other greenhouse gases into the atmosphere than the natural system can recycle. They argue that since these gases are responsible for warming our planet (earth), therefore, artificial increase in their quantity and composition could leads to radical changes in global temperature. The proponents of the theory of global warming argue that urgent remedial actions must be taken otherwise within the next few centuries; the earth’s temperature might increase radically to forbid life, as we know it.

This is how the green house effect works. It is a well-known fact that the atmosphere surrounds the earth. It consists of different layers, each containing different gases and pressures for different uses for habitability of the earth. The greenhouse gases—carbon dioxide, methane nitrous oxide, ozone, and others--are responsible for warming our planet. The “greenhouse effect” occurs when sunlight penetrates the earth’s atmosphere (Perkins, p3). Some of the radiation is absorbed by the atmosphere, some is reflected away, and about half is absorbed by the earth’s surface (land and sea). The greenhouse gases absorb the infrared radiation from the earth and re-radiate both upwards to space and downward to earth. This process keeps the earth surface about thirty-three degrees Celsius (59 Fahrenheit degrees) warmer than it would otherwise be (U.S. Climate Action Report 2002). This process is natural and does not pretense any threat to our survival. In fact, this process makes life possible on earth.

The concern is about the excess greenhouse gases that are produced due to human activity. Most atmospheric scientists have concluded that excess greenhouse gas emission due to human activity is causing global warming at an unprecedented scale. Global warming is defined by Encyclopedia Britannica Online as follows: “An increase in global average temperature resulting from an increase in the amount of Carbon dioxide, Methane, and certain other trace gases in the atmosphere.” Carbon dioxide, which is mainly produced by burning fossil fuel (coal, oil, and natural gas), is the main concern because its production has increased rapidly over the past century.

Mark Hertsgaard reports that atmospheric composition of carbon dioxide and other greenhouse gases has increased greatly and it is expected to increase even more rapidly during the twenty-first century. According to Hertsgaard, global average temperature has increased during the 20th century. Globally, it is very likely that 1990s was the warmest decade and 2005 was the warmest year in instrumental record, according to Sid Perkins, the author of the article “An Ounce of Prevention.” He reports that tidal gauge data show that global average sea level has risen during the past century and precipitation and rainfall has increased in some regions and reduced in others.

Bivens reports that in 1988 the United Nations commissioned an Intergovernmental Panel on Climate Change (IPCC) consisting of 200 credible and leading scientists to assess, the scientific basis, possible effects, and mitigation of human induced climate change. Its third assessment report of 2001, led to negotiation of the Kyoto Protocol on environmental protection, which aims at reducing global greenhouse gas emission by 5 percent below pre-industrial revolution numbers.

According to Bivens, the IPCC, which is the main authority on global climate change, predicts severe consequences if the current trend of greenhouse gas production and emission continues without curbing. Global average temperature is projected to increase by 1.4 to 5.8 Celsius degrees and the Northern Hemisphere snow cover and sea ice extent are projected to decrease further by the end of the century if the current trend continues, he cites the IPCC report.

These changes might seem insignificant but when they apply to global average then smallish numbers have large significance. The difference between an ice age and an interglacial period might be only a few degrees Celsius. Not because we would be a little bit warmer but that degree of average temperature change has large consequences for things like sea level rise and possibly many other climate variables. Hertsgaard cites the U.S. Climate Action Report which reports that ‘not only is global warming real, but its consequences—heat waves, water shortages, rising sea levels, loss of beaches and marshes, more frequent and violent weather—will be punishing for Americans.’

Unlike weather, which is concern with instantaneous state of the atmosphere, climate deals with longer time scale, with averages and other statistics over space and time? It implies that the climate is more complex, multifaceted, and difficult to predict precisely. Therefore, a smallish change in one or more parts of the equation could lead to significant climate change. For example, suppose that the earth get warmer as projected. Then ice and snow cover melts and the darker substances—land and sea—are exposed. Therefore, in response to the warming, the world has become a little bit darker and hence less reflective, so it absorbs more sun light. This chain of responsive reactions would in fact lead to more global warming. It is a positive feedback, where an action leads to more actions of itself. The process is like having a thermostat in a house set so that when the house warms up, it turned on the furnace and warms it up still more.

According to environmental activists and leading scientists, possible effects of global warming are indeed gloomy and need urgent attention from every individual person. They argue that there is not only ample scientific evidence to support the facts about global warming, but also there are fundamental ecological changes presently occurring in our world. In recent memory, humankind has witnessed severe droughts in many regions of the globe and its impact on food security, access to water, hunger, disease and even loss of lives. Heavy downpour of rain in some regions has caused severe flooding, avalanche, and mudslide resulting in destruction of properties and lives. A modest rise in sea level would threaten the very existence of coastal towns globally which are gradually being consumed by water. Hence, oceans are expanding and land is diminishing.

The ability of human systems to adapt to and cope with climate change depends on such factors as wealth, technology, education, information, skills, infrastructure, access to resources and management capabilities. There is a potential adaptability variance within the world communities. The developed nations are more endowed with these attributes and capabilities than the developing nations, particularly the least developed nations that are generally poorest in this regards. As a result, they have less capacity to adapt and are more vulnerable to climate change, just as they are more vulnerable to other stresses. In recent memory, the world has witnessed droughts and famine in many developing countries especially sub-Saharan African countries resulting to hunger, starvation, disease and death.

On the contrary, developing nations emit the least amount of greenhouse gases into the atmosphere. The EPA reports on its website that total emission of carbon dioxide by the United States alone is more than that of one hundred and fifty developing nations combined, as well as more than Japan, China, India combined. It implies that world’s poorest are paying the bitter price of climate change whereas their contribution to the adverse change is at best minimal. Some environmental activists capitalize on morality and fairness to argue for action to combat global warming.

The Bush Administration’s position on global warming is not only explained by its refusal to ratify the Kyoto Protocol but also the administration’s 2002 report on global warming. The administration’s 2002 environmental report contradict credible models and statistics on climate change. The report brush out many possible effects of global warming as mere guesswork of environmental extremists The Bush administration argues that implementation of the Kyoto protocol would slow down economic growth and development at home and that developing nations would not be bound by the same greenhouse production obligation as the largest emitters. This argument is contradicted by Matt Bivens, in his article where he argued that the entire energy need of the United States could be provided by wind and solar energy at a lower economic and environmental cost than the current energy sources—coal, oil and, natural gases and also that the united state is largest emitter.

Notwithstanding these facts and arguments, Bevins reports, the energy industry and its lobbyists have employed propaganda machinery to misinform the public about the causes and effects of climate change. A few of the opponents still question whether temperatures have actually been rising at all. Others acknowledged the change but argue that the changes could be because of the natural system and that the proponents of global warming most not overlook the period in climate studies. They also try to discredit climate models that are used to predict future climate. They argue that models are limited to human knowledge of the atmospheric system and therefore cannot be accurate to predict future climate. However, it most be understood that such models are used by metrologies today to forecast weather and they have been precise in forecasting weather. Therefore, climate models cannot be totally disregarded without further studies. Some even suggest that continued warming of the planet could be beneficial to some parts or regions of the world.

In recent years, the United States has been bombarded with several massive natural disasters that could be attributable to climate change. Sid Perkins reports that scientists have concluded from historical records that the total power released by storms had dramatically increased—“more that doubling in the Atlantic in the past 35 years mainly due to rise in water temperature.”

What does this mean for the residents of the United States coastal regions? There could be more powerful and frequent hurricanes resulting in heavy damages, and lose of lives. According to the U.S. Climate Action Report, “The 2005 Atlantic hurricane season is the busiest on record and extends the active hurricane cycle that began in 1995—a trend likely to continue for years to come.” The season has most named storms, most hurricanes, most category five storms, and most expensive hurricane on records. It was the most devastating hurricane season the country has experienced in modern times, the report says. For example, according to the report, Hurricane Katrina has cause a damage of at least eighty billion Dollars and claims the live of at least one thousand and three hundred peoples. That is not all, hurricane Katrina has resulted into one of the largest oil, and hazardous material spill in history, which is expected to cause serious environmental degradation and human effects within the years to come.

From the above, one could safely conclude that global warming is a real threat to our very existence on the earth, if the statistics and sources can be trusted. The alternatives are either to reduce emission or find a way to store green house gases after they are produced into something that would prevent them from polluting the atmosphere. According to Bivens, the technology exists that can collect and store carbon dioxide produced by power plants, factories and other large stationary sources and prevent them from polluting the atmosphere. A transition to renewable energy sources such as nuclear power (though controversial for reasons of safety and high cost waste disposal, releases no carbon dioxide), solar power, wind power and hydrogen fuel cell would greatly reduce green house emission. Another way to reduce emission is by aforestation because the many plants would be effective in breaking up carbon dioxide during photosynthesis, by releasing oxygen into the atmosphere and turning carbon into plant tissue. Since climate issues are global, existing global concerted efforts in mitigating climate change need to be strengthened by further negotiations between all the parties. Individual persons must be reoriented about global warming so they can make informed decisions in its alleviation. Everyone can help reduce greenhouse gas emission when he or she buys an energy efficient appliance, energy efficient car, adding insulation to a house, residing close to work, commutes by public transport.