HJB --- GMA --- UFF

Latitude and Longitude:
Representing Points on the Earth's Surface

Rogério Vaz de Almeida Jr,   Jonas Hurrelmann,   Konrad Polthier   and   Humberto José Bortolossi

Clique aqui para ver esta página em português.

The Java Applet

This Java applet is part of an undergraduate project sponsored by PIBIC/CNPq and PROPP/UFF (Fluminense Federal University in Niterói, RJ). Additional features were programmed and gently provided by Jonas Hurrelmann and Konrad Polthier from Freie Universität in Germany. The software helps the understanding of the concepts of latitude and longitude and it allows the visualization of geographical elements over the Earth's surface like meridians, parallels, poles, political divisions and the location of many countries' capitals. Moreover, for each country, there is a corresponding link to Wikepedia (a free encyclopedia), allowing quick access to useful informations about the country: its history, economy, politics, geography, demographics, etc. Some countries were not included in the applet because they have a very small surface.

If you have some suggestion or if you wish to see some funcionality added to the program, please, contact us. The e-mail address is at the bottom of this web page.


To run this applet, you need the version 1.4 or higher of the Java Runtime Environment installed in your computer. A version for Microsoft Windows may be downloaded here (file j2re1.4.exe with 10 Mb).

The applet takes some time to be loaded in the first time. Please, be patient. If the applet doesn't start, you may need to change the Java settings in your browser. For the Windows XP, access the option “Java Plug-in” available in the “Control Panel”. Choose the tab “Advanced” and add the parameter --Xmx128M to the text field “Java Runtime Parameters”.

To rotate the globe, press the left button mouse over its surface, keep the button pressed and, then, drag the mouse.

To zoom in or to zoom out the globe, keep the key “s” pressed, click with the left button mouse over the figure and, then, drag the mouse.

To mark a point on the Earth's surface, keep the key “i” pressed, press the left button over the globe and, then, drag the mouse. The latitude and longitude of this point will be displayed in the tab “position” on the right side of the applet. In this same tab, there is a tool that computes the distance between capitals. The corresponding geodesical arc is drawn on the globe's surface.

If the globe appears flatted, please, press the “Refresh” button of your browser.
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You may use the applet offline downloading the file (2.8 Mb). The source code of the program is also available in this file.

This applet was developed with the graphical library JAVAVIEW.

Geographical Coordinates: Latitude and Longitude

If we want to locate points over the Earth's surface, we may imagine it divided by imaginary lines. These lines form a grid over the Earth's surface and, from which, it's possible to define the geographical coordinates system known as latitude and longitude.


The latitude of a point on the Earth's surface is the angle (measured in degrees) between the plane of the equator and the straight line segment that joins the point to the center of the globe. On the applet belows, keep the key “i” pressed, press the left button over the globe and, then, drag the mouse. The latitude and longitude of the “white point” will be displayed in the tab “position” on the right side of the applet.

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The equator corresponds the great circle perpendicular to the Earth's axis, determining the division of the Earth in two hemispheres: North and South. The latitude changes from 0º to 90ºN (North: above the equator) or from 0º to 90ºS (South: below the equator). The parallels are circles parallels to the equator and they determine the latitude of a place. Points at the same parallel have the same latitude. The North Pole has latitude 90ºN and the South Pole has latitude 90ºS. Every point on the equator has latitude 0º.

There are other parallels of interest: the Tropic of Cancer (with latitude 23.5ºN), the Tropic of Capricorn (with latitude 23.5ºS), the Arctic Circle (with latitude 66.5ºN) and the Antarctic Circle (with latitude 66.5ºS). The Arctic and Antarctic Circles have an interesting property. During the summer solstice, the Sun raylights fall perpendicularly at the Tropic of Cancer. Therefore, places with latitude between 66.5ºS and 90ºS (region limited by the Antarctic Circle) have 24 hours of darkness. On the other hand, places with latitude between 66.5ºN and 90ºN (region limited by the Arctic Circle) have 24 hours of daylight. This situation inverts when winter solstice occurs.

The latitude of a point can be also defined as being the difference between the angle made by the sunlights at the point in question and the angle made by the sun of the same day at the equator.

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The longitude of any point on the Earth's surface is the measure of the angle (in degrees) between the planes that contain the point, the Earth's axis and the Greenwich Meridian (adopted as reference).

The meridians are half circles with ends at the poles and they are perpendicular to the parallels. The Greenwich meridian divides the Earth in two parts, East and West, and it receives this name because it passes throught the Greenwich Observatory (a town near London). The longitude changes from 0º to 180º East (when the point in question is in the east side of the Greenwich meridian) and West (when the point in question is in the west side of Greenwich meridian).

Before Greenwich, other meridians were taken as reference: Mecca, Jerusalem, Rome, Paris and Copenhagen. When, in 1767, the Royal Observatory in England published the most comprehensive tables of lunar positions available, sailors over the world found themselves calculating their longitude easier setting their chronometers from Greenwich. This practice become official in 1884 when the International Meridian Conference established the prime meridian at Greenwich.

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Time Zones

It's natural to divide the Earth's globe (360 degrees) in 24 parts (each one with 15 degrees) corresponding to the 24 hours of a day. Nevertheless, the measure of time is made dividing the Earth in 25 sectors called time zones.

The time zone number 0 (zero) has 15 degrees of longitude, having Greenwich as its central meridian. The next 22 times zones have 15 degrees of longitude too and they are located around the time zone number 0, 11 in the left and 11 in the west. These 23 time zones sum up 345 degrees of longitude. The remaining 15 degrees are divided in the last two time zones, each one with 7.5 degrees. They are separated by the meridian with 180º of longitude.

The brazilian territory has 4 time zones and, since it is totally on the west hemisphere, all of them have negative time zones when compared to Greenwich.

Geographical and Spherical Coordinates

Using simple trigonometry, it is easy to deduce that a point with latitude φ and longitude θ on a sphere with radius r has coordinates:

(x, y, z) = (r cos(θ) cos(φ), r sin(θ) cos(φ), r sin(φ)).

It is important to notice the similarities between geographical and spherical coordinates (studied in the calculus courses). While geographical coordinates use φ to indicate angles with respect to the plane of the equator, in spherical coordinates, φ indicates the angle between the point on the globe surface and its axis. Thus, the cartesian coordinates of a point with spherical coordinates (θ, φ, ρ) are:

(x, y, z) = (ρ cos(θ) sin(φ), ρ sin(θ) sin(φ), ρ cos(φ)).