Lines of longitude (or meridians) run north and south
perpendicular to the equator (and all other parallels) and meet at both
poles. The location of a given meridian is designated as the angular distance
between the meridian and the prime meridian, which is a line of
longitude running through Greenwich, England. This angular distance ranges
from zero degrees at the prime meridian to 180 degrees on the opposite
side of the globe. Therefore, longitude indicates how far a place is located
to the east or west of the prime meridian.
Together, parallels and meridians comprise a coordinated grid system,
called the graticule, which makes it possible to locate any spot
on the globe. In locating a particular place on earth, the latitude is
always stated first, in degrees, minutes, and seconds (depending on the
accuracy required), and followed by a designation of N (for north) or S
(for south) relative to the equator. Next the longitude is given in degrees,
minutes, and seconds, followed by E (for east) or W (for west) relative
to the prime meridian.
Do Exercise A
The shortest distance between two points is a straight line, but on the surface of a globe the shortest distance is an arc known as a great circle. If you were to plot the route of a great circle on most maps, it would not appear to be a direct route. This is due to the distortion caused by showing (or projecting) the curved surface of the globe onto a flat surface.
Perhaps the most widely used map is the Mercator cylindrical projection. The Mercator map is very useful for navigation because a straight line on the map corresponds to a compass heading. If you look carefully at the map below, both parallels and meridians are straight lines and cross at right angles. The meridians are equally spaced, but parallels are not. This is because the Mercator projection is constructed by straightening the lines of longitude, and by increasing the space between latitude equal to the space of longitudinal widening. This projection is most accurate within 15 degrees of the equator. Distortion is so severe near the pole that the northern and southern limits of the map are fixed at the 84th parallel. The Mercator projection has given many people a distorted perception of the size of the continents. Greenland, for example, appears larger than South America, when actually Greenland is only one eighth of the size of South America.
Mercator projection from www.utexas.edu Dept. of Geography Map Projection
project
Because lines of longitude merge at the poles, the distance represented by one degree of longitude is greatest at the equator and decreases as latitude increases. For example, at the equator a degree of longitude is about 111 kilometers (or 69 miles), while at 60 degrees latitude, a degree of longitude is only about 56 kilometers (or 35 miles). At the poles, the meridians intersect, so a degree of longitude is zero kilometers (that's because there are no degrees of longitude at the poles). Nevertheless, we can easily determine the distance between two places on the globe even if their latitude is not the same.
Do Exercise B
The Meridional Parts Calculator
We keep track of time on a daily basis by marking successive transits of the sun across our meridian (line of longitude). We do the same for two successive transits of the Tropic of Cancer and call it a solar year. We also mark days and years by the transit of a spot on the celestial sphere over a fixed location, with a slightly different result from solar time; This is known as sidereal time (from the Latin sidereus, meaning star) .
Before the advent of rapid travel and instant communication, people all over the world used local time. That is, when the sun crosses your meridian it is noon, and the rest of the day is measured from that point. That system worked just fine until the late eighteen hundreds when it became very confusing to deal with train schedules as a different schedule was necessary for every town. The railroads dealt with the problem by using what they called "railroad time", which was determined by the location of their headquarters. Some cities switched from local time to railroad time and may therefore have varied from neighboring towns by hours (and minutes). If a city had two rail lines, things could get very confusing, with some people going by the time of one rail line, some by the time of another rail line, and still others by local time. Noon whistles at factories may have sounded at all different times.
The situation became intolerable and it was decided and generally agreed on to divide the planet into twenty-four time zones, each exactly an hour apart. Here in the U.S., the lines between the zones were drawn in less populated areas and along state lines where possible. Now, regardless of where you are located within a zone, ignoring local time, the time between adjacent zones is always exactly an hour apart. There are still some countries and parts of countries that do not follow this program exactly; the nearest is Newfoundland in eastern Canada, which is off by one half hour.
Generally speaking, you can determine a location's time zone by its longitude since the 360 degrees of longitude are divided into 24 time zones of 15 degrees each. Every fifteen degrees of longitude marks the center of a zone which extends seven and one-half degrees in both directions. The starting point is zero degrees longitude, the prime meridian. Each zone (every fifteen degrees) east is one hour later, and each zone west is one hour earlier. Look at the time zone map at the back of this exercise and see that at one particular instant, it is an hour later in each zone to the east. If you count all the way around the earth this way, when you get back to where you began you will find that it is one day later. Since it cannot be two different days in one place at the same time we must correct this anomaly. That is the purpose of the International Date Line. The International Date Line runs down the middle of the time zone on the other side of the world from the prime meridian, and so it corresponds to 180 degrees longitude, east and west. Like the other zones, the time zone of the International Date Line spans fifteen degrees and is one hour different from the adjacent zones. Each half of this zone, however, is a different day. When crossing the Date Line from west to east, you subtract a day (it's a day earlier to the east of the Date Line); when crossing the Date Line from east to west, you add a day (it's a day later to the west of the Date Line). This confuses many people, so think about the times around the world at any one instant. If you look to zones to the west, you must subtract one hour for each zone. By the time you've counted all of the zones, you'll have subtracted 24 hours. Thus, you must add a day in order to keep it from being two days at once!
In the summer when we have many hours of daylight, there are several hours of sunlight early in the morning when they are of no real use to many of us. Many people would prefer that it remains light later in the evening so they have devised daylight-saving time, which in effect adds an hour of light to the evening. Here is how it works: At two A.M. on the first Sunday in April, we set our clocks forward one hour. The next morning when we awake at eight o'clock the sun is actually at the same spot in the sky as it was at seven o'clock the day before. If the sun set at eight P.M. the day before, after setting our clocks ahead, it will set an hour later giving us an extra hour of evening light. On the last Sunday in October, we reverse the process and turn our clocks back an hour. In order to help us remember, we say "spring forward, fall back".
Do Exercise C
4. Global Positioning Systems (GPS)
Onboard each satellite are atomic clocks that keep precise time. Each satellite broadcasts its location and time information as a code on two microwave carrier signals (L1 frequency of 1575.42 MHz and L2 frequency of 1227.60 MHz).
The basis of GPS positioning is that your location can be determined if you know the distance to four different satellites. This technique is called triangulating or ranging. The GPS receiver measures the distance to the satellites using the travel time of a coded radio signal and the speed of light. Because your handheld GPS unit does not contain an atomic clock to precisely measure time differences, it contains a directory, called an almanac, of the projected position of each of the satellites in the orbital planes. The GPS receiver uses this information to calculate the time differences and thus distance to each satellite.
Do Exercise D