**Shape of the Earth**

The sperical shape of the Earth changes over time:

- The Earth isn't, in fact, spherical. It nearly is, but not quite. The centrifugal "force" generated by the Earth's slow rotation causes the equator to bulge just a little bit (about 20km) compared to the poles.

*Note: I know that centrifugal "force" isn't a force at all, but in terms of everyday experience it is an easily understood concept. The niceties of inertial pseudo-forces and rotating reference frames can come later.*Superimposed on this ellipsoidal shape are some smaller dents and bulges caused by the uneven distribution of mass in the crust and the mantle of the Earth. These are typically only a few metres in height, but may extend over tens to thousands of km in width.

- The shape of the Earth changes on a daily basis! Just as there is a tide in the oceans, so also is there a solid body tide within the rock beneath your feet. The Earth's surface rises and falls a few centimetres every day, under the tidal influence of the Moon and Sun.

**Earth's Rotation**

The Earth is rotating around an axis (called its rotational axis). The Earth's axis is tipped over about 23.5° from vertical.

Earth's rotational axis points in the same direction relative to the stars, so that the North Pole points towards the star Polaris. Think of the Earth as a spinning top, tipped over to one side. Over very long time periods (thousands of years) the direction of Earth's axis slowly changes due to precession.

The Earth rotates around once in 24 hours - that's a rate of 1000 miles per hour. The time it takes for the Earth to rotate completely around once is what we call a day. It's Earth's rotation that gives us night and day. The polar spin axis of the Earth is not fixed in space. Instead, the Earth slowly processes like a spinning top, but it takes around 24,000 years for each slow "wobble".

**Latitude and Longitude**

Maps and globes usually have lines on them to help locate places on Earth. These lines are called latitude and longitude lines. These lines are not actually on the planet, but are imaginary lines used to help us find our way around the curved surface of Earth. The imaginary lines circling the globe in an east-west direction are called the lines of latitude (or parallels, as they are parallel to the equator).

They are used to measure distances north and south of the equator. The lines circling the globe in a north-south direction are called lines of longitude (or meridians). They are used to measure distances east and west. Lines of latitude and longitude crisscross to form a grid. The location of any point on the surface of Earth can be de scribed by two coordinates: its latitude and its longitude.

#### Latitude

Latitude measures how far north or south a point lies from the equator. The equator is at 0 degrees (0°) latitude, and it divides Earth into its northern and southern hemispheres. It is the starting point for measuring distances in degrees north or south of the equator.

Values for latitude range from 0° to 90° North for locations north of the equator, and from 0° to 90° South for locations south of the equator. Notice on the figure that the lines of latitude run in the east-west direction and are parallel to the equator. Any other location directly east or west of you lies at the same latitude that you do.

#### Longitude

The lines circling the globe in a north-south direction are called lines of longitude (or meridians). Greenwich, England (near London) was selected to be zero degrees longitude in 1884, because it was the home of the most advanced observatory at that time.

The “Prime Meridian” runs from measuring east and west longitudes. Locations with 0º longitude lie exactly on the Prime Meridian.

Longitude measures how far east or west a point lies from the Prime Meridian. Values for longitude range from 0º to 180º E for locations east of the Prime Meridian, and 0º to 180º W for locations west of the Prime Meridian. 180º E and 180º W are the same longitude line.

**Meridians are Longitude Lines and Parallels are Latitude Lines**

Parallels of Longitude and Meridians of Latitude, provides a system of geometrical coordinates used in designating the location of places on the surface of the earth. (For the use of these terms in astronomy, see Coordinate System; Ecliptic.) Latitude, which gives the location of a place north or south of the equator, is expressed by angular measurements ranging from 0° at the equator to 90° at the poles. Longitude, the location of a place east or west of a north-south line called the prime meridian, is measured in angles ranging from 0° at the prime meridian to 180° at the International Date Line.

Midway between the poles, the equator, a great circle, divides the earth into northern and southern hemispheres. Parallel to the equator and north and south of it are a succession of imaginary circles that become smaller and smaller the closer they are to the poles. This series of east-west-running circles, known as the parallels of latitude, is crossed at right angles by a series of half-circles extending north and south from one pole to the other, called the meridians of longitude.

Although the equator was an obvious choice as the prime parallel, being the largest, no one meridian was uniquely qualified as prime. Until a single prime meridian could be agreed upon, each nation was free to choose its own, with the result that many 19th-century maps of the world lacked a standardized grid. The problem was resolved in 1884, when an international prime meridian, passing through London's Greenwich Observatory, was officially designated. A metallic marker there indicates its exact location.

Degrees of latitude are equally spaced, but the slight flattening at the poles causes the length of a degree of latitude to vary from 110.57 km at the equator to 111.70 km at the poles. At the equator, meridians of longitude 1 degree apart are separated by a distance of 111.32 km; at the poles, meridians converge.

Each degree of latitude and longitude is divided into 60 minutes, and each minute divided into 60 seconds, thereby allowing the assignment of a precise numerical location to any place on earth.

**Commonly Used Terms**

**Equator:** The line which encircles the Earth at an equal distance from the North and South Poles.

**Geographic Coordinates:** Coordinate values given as latitude and longitude.

**Great Circle:** A circle formed on the surface of a sphere by a plane that passes through the centre of the sphere. The Equator, each meridian, and each other full circumference of the Earth forms a great circle. The arc of a great circle shows the shortest distance between points on the surface of the Earth.

**Meridian:** A great circle on the surface of the Earth, passing through the geographical poles and some third point on the Earth's surface. All points on a given meridian have the same longitude.

**Parallel:** A circle or approximation of a circle on the surface of the Earth, parallel to the Equator and connecting points of equal latitude.

**Prime Meridian:** The meridian of longitude 0 degrees, used as the origin for the measurement of longitude. The meridian of Greenwich, England, is the internationally accepted prime meridian in most cases.

**Great Circles**

A great circle is the shortest path between two points along the surface of a sphere. The precise definition of a great circle is the intersection of the surface with a plane passing through the centre of the planet. Thus, great circles always bisect the sphere. The equator and all meridians are great circles. All great circles other than these do not have a constant azimuth, the spherical analogue of slope; they cross successive meridians at different angles. A great circle are the shortest path between points is not always apparent from maps, because very few map projections (the Gnomonic is one of them) represent arbitrary great circles as straight lines.

Because they define paths that minimize distance between two (or three) points, great circles are examples of geodesics. In general, a geodesic is the straightest possible path constrained to lie on a curved surface, independent of the choice of a coordinate system. The term comes from the Greek geo-, earth, plus daiesthai, to divide, which is also the root word of geodesy, the science of describing the size and shape of the Earth mathematically.

**Rhumb Lines**

A rhumb line is a curve that crosses each meridian at the same angle. This curve is also referred to as a loxodrome (from the Greek loxos, slanted, and drome, path). Although a great circle is a shortest path, it is difficult to navigate because your bearing (or azimuth) continuously changes as you proceed. Following a rhumb line covers more distance than following a geodesic, but it is easier to navigate.

All parallels, including the equator, are rhumb lines, since they cross all meridians at 90º. Additionally, all meridians are rhumb lines, in addition to being great circles. A rhumb line always spirals toward one of the poles, unless its azimuth is true east, west, north, or south, in which case the rhumb line closes on itself to form a parallel of latitude (small circle) or a pair of antipodal meridians.

The following figure depicts a great circle and one possible rhumb line connecting two distant locations. Descriptions and examples of how to calculate points along great circles and rhumb lines appear below.

**Small Circles**

In addition to rhumb lines and great circles, one other smooth curve is significant in geography and the Mapping Toolbox: the small circle. Parallels of latitude are all small circles (which also happen to be rhumb lines). The general definition of a small circle is the intersection of a plane with the surface of a sphere. On ellipsoids, this only yields true small circles when the defining plane is parallel to the equator. In the Mapping Toolbox, this definition includes planes passing through the centre of the planet, so the set of all small circles includes all great circles as limiting cases. This usage is not universal.

Small circles are most easily defined by distance from a point. All points 45 nm (nautical miles) distant from (45ºN, 60ºE) would be the description of one small circle. If degrees of arc length are used as a distance measurement, then (on a sphere) a great circle is the set of all points 90º distant from a particular centre point.

For true small circles, the distance must be defined in a great circle sense, the shortest distance between two points on the surface of a sphere. However, the Mapping Toolbox also can calculate loxodromic small circles, for which distances are measured in a rhumb line sense (along lines of constant azimuth). Do not confuse such figures with true small circles.

**True North and Magnetic North**

#### True North

True North is an imaginary straight line between you and the geographic North Pole (that theoretical dot at the top of the globe). This straight line is a great circle that passes through you and both the North and South Poles. It is called a Meridian of Longitude as previously shown.

#### Magnetic North

The Magnetic North Pole, that spot the needle or card on your compass points towards, is not located at the geographic North Pole. If you live in the Western Hemisphere, Magnetic North is actually located south of the geographic North Pole. As a result, and depending on where you are, there is almost always an angular difference between True North and the direction your compass is pointing (Magnetic North).

This angular difference is called Variation. To find out how much variation there is for your area; look at a World Aeronautical Chart.

**Terrestrial Magnetism, Magnetic Variation and the Change in Variation with Time**

#### Terrestrial Magnetism

The Earth's magnetic field is generated within its molten iron core through a combination of thermal movement, the Earth's daily rotation, and electrical forces within the core. These elements form a dynamo that sustains a magnetic field that is similar to that of a bar magnet slightly inclined to a line that joins the North and South Geographic Poles. A compass placed in this magnetic field thus does not point due north, declination measures the angle between the compass reading at any point on the Earth's surface and true north (measured in degrees). The geomagnetic reference model is the basis for establishing the declination and its variation across the surface of the globe.

#### Variations in the Earth's Magnetic Field

The intensity and structure of the Earth's magnetic field are always changing, slowly but erratically, reflecting the influence of the flow of thermal currents within the iron core. This variation is reflected in part by the wandering of the North and South Geomagnetic Poles. Because a wide range of commercial and military navigation and attitude/heading systems are dependent on models of the magnetic field, these models need to be updated periodically. The magnetic field's strength and direction and their rates of change are predicted every 5 years for a 5-year period.

Charts of secular variation document the predicted yearly changes in each of the components of the magnetic field, providing the information necessary to update the field strength and direction information during the 5 year periods that separate publication of new models. Older models continue to be of use for such necessary processes as the establishment of property boundaries. Compass readings for points located in the past were likely to have been made using a geomagnetic model with a declination value different from that in use today. Re-surveying boundaries requires access to the geomagnetic model in use at the time of the original survey.

**Latitude and a Nautical Mile**

#### Nautical Mile

A unit of length used in sea and air navigation, based on the length of one minute of arc of a great circle. A nautical mile is used internationally and is equal to 1,852 meters.

#### Knot

The derived unit of speed is the knot, defined as one nautical mile per hour. Both nautical miles and knots are widely used around the world for maritime and aviation purposes.

#### Latitude Degrees, Minutes and Nautical Miles

Each parallel is named with the number of degrees it represents from the equator (which is designated 0 degrees) Thus south of the equator we begin at zero, continuing to the south pole which is 90 degrees south. Some southern hemisphere places: Melbourne 38 degrees south, Brisbane 27 degrees south, and the Darwin at 12 degrees south.

Each degree of latitude is further divided into 60 minutes of latitude. Each minute is again divided into 60 seconds of latitude. In navigation we usually deal with whole degrees, minutes, and tenths of a minute. More on that later. Each minute of latitude is equal to one nautical mile. Now let's do the math: 90 degrees of latitude from the equator to the north pole. So 90 degrees times 60 minutes equals 5400 miles. This is the distance from the equator to the south pole.

#### Describing Co-ordinates

The most common way to locate points on the surface of the Earth is by standard, geographic coordinates called latitude and longitude. These coordinate values are measured in degrees, and represent angular distances calculated from the centre of the earth.

It's conventional when describing co-ordinates to enter latitude first, or to place it directly above longitude. There's no need to attach the prefixes "lat" and "long" or "L" or "Lo" although you may do so. The descriptors N, S, E or W indicate clearly north or south of the equator and east or west of the prime meridian.

For example, using the format, degrees, minutes and seconds to express the position of Brisbane Airport can be described as:

S 27° 23.0

E 153° 07.1