Latitude, Longitude and GPS

By Dan Miller and Melinda Chu
Edited by Anna M. Mracek and Ray Arvidson

Latitude and Longitude

Because the earth is nearly spherical (it is a spheroid), a special coordinate system is needed to pinpoint locations on it. This system is a grid of Latitude (east to west) and Longitude (north to south) lines that circle the earth. Latitude and Longitude coordinates allow sailors to reach port, map makers to find the distance between two cities, and Solo Spirit mission controllers to chart the balloon’s path.

What is Latitude?

Latitude lines are the set of circles that are parallel to the equator. The only latitude line that is a Great Circle (circles with their center at the center of the earth) is the equator. The diameters of these circles decrease as the pole is neared.

What is Longitude?

Longitude lines are the set of Great Circles that run through the North and South Poles. All lines of longitude are perpendicular (at ninety degrees) to the equator, and resemble the lines on a basketball. Because the Earth is a spheroid, the longitude lines are closer together at the poles than they are near the equator.

Coordinates:

The latitude and longitude of a specific position can be represented with a pair of numbers similar to the (x, y) pairs that are used in a standard two-dimensional graph. Longitude is measured as degrees east or west of the Prime Meridian, the great circle that passes through Greenwich, England. Latitude is measured in degrees north or south of the equator.

Reading a Map:

The latitude and longitude lines on Mercator projection maps are easy to use. If one finger is placed on the appropriate latitude and one on the appropriate longitude and they are moved into the map in straight lines, the place where they intersect is roughly the place that has the desired latitude and longitude. This is because, on these projections, latitude and longitude lines are straight and intersect at right angles.

How does Mission Control Track the Solo Flight?

Mission Control uses a system of satellites called the Navstar Global Positioning System (GPS). Though it was first developed in the 1970s, it was not fully operational until 1994. It is made up of twenty-four satellites each with three atomic clocks.

How high do the GPS satellites orbit the Earth?

The Satellites circle the globe at a medium altitude of about 11,000 miles (18,000 km) above the earth, in many inclinations. This is so that several satellites will be in the field of view of ground GPS receivers at any given time.

How accurate is the GPS system?

The system works only when at least three satellites are within range of the receiver. Since there are 24 satellites, chances are good--in most places, most of the time--that at least three are within range. The Coarse Acquisition Code (C/A for short) for civilian use is accurate up to 100 feet (30 meters). The Precision Code (P-code) used by U.S. government agencies and other allied governments provides accuracy of up to three feet (0.9 meters).

What is the difference between the C/A code and the P-code?

The main difference between the C/A code and the P-code is that they are broadcast on different frequencies. The Coarse Acquisition Code is broadcast at 1575.42 MHz. The P-code uses 1227.6 MHz broadcasting. Additionally, messages in the Precision Code are usually encrypted in order to protect the information from being intercepted by unwanted eavesdroppers.

How can civilians use the GPS system?

The GPS system is available to civilians. It can be accessed through small receivers (which are already on the market) that enable the GPS system to locate the user very precisely. This system is has already found a number of commercial and scientific uses.



Suggested links:

JPL GPS Data
http://igscb.jpl.nasa.gov/

Sam Wormley's GPS Science Applications and Educational Materials
http://www.cnde.iastate.edu/staff/swormley/gps/science.html



Activities:

Plot the Position of Solo Spirit!

Pin a large Mercator projection world map to a bulletin board or otherwise affix one to a wall or chalkboard.

If using a bulletin board, each day find out the coordinates of the Solo Spirit Balloon and stick a straight pin at the appropriate place on the map. If not using a bulletin board, affix a small sticker (a colored dot works well) to the proper place.

What country or body of water is the balloon over?

What are the coordinates of your hometown?

Look in the back of an Atlas or on a map to find the latitude and longitude for where you live.

Put a special pin or sticker on the world map at the right spot!

Distance between two points on the Earth:
(an exercise for trigonometry students)

The great circle distance between two points on the Earth can be calculated
(approximately) using spherical triangles. (The calculation is approximate because the
Earth is not a perfect sphere; it's an ellipsoid.) In the figure, a spherical triangle is
outlined in blue: it's formed by lines drawn on the surface of a sphere connecting point
A, point B, and point N (the North Pole). Point C is at the center of the sphere.


To find the length of the arc d between points A and B, you can use the law of cosines for the sides of oblique spherical triangles:

cos d = cos (ACN) cos (BCN) + sin(ACN) sin (BCN) cos (ANB)
d = arccos (cos d)

The measure of angle ACN (in degrees) is really 90 minus the latitude of point A, and the measure of angle BCN is 90 minus the
latitude of point B. The measure of angle ANB is the difference in longitude between points A and B.

The resulting value of d will be in degrees, since it is the measure of angle ACB. To determine the length of the arc, first convert d
from degrees to radians. Then multiply the answer by the radius of the Earth, 6378 kilometers or 3963 miles.

This method can be used to compute the approximate distance traveled by Solo Spirit. It is approximate not only because the Earth
is not a perfect sphere, but also because the balloon's path will not always follow a great circle arc.

Mendoza, Argentina the launch site of the balloon, has a location of 38° 53’ S latitude and 68° 49’ W longitude. Using the current
location of Solo Spirit, calculate how far the balloon has traveled, assuming it followed a simple great circle arc. How much has the
balloon's path deviated from this arc? In your calculations, don't forget to convert minutes and seconds into fractions of a degree; 1 degree = 60 minutes = 60x60 seconds.

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