Every position report, every course drawn on a chart and every heading flown is a statement about the Earth: where a point sits on its surface and which way is which from there. This opening lesson pins both down. It settles what shape the Earth actually is and what shape navigation pretends it is, lays the grid of latitude and longitude over it, and then splits the innocent word north into the three different norths a cockpit actually works with. The magnetic field and the aircraft's disturbance of it were told in the Instrumentation course's magnetism lesson; here the same angles return as the navigator's arithmetic.
The shape of the Earth
The Earth is not a sphere, and not even a tidy mathematical solid. Strip away land, tide and weather and what is left is the geoid: an irregular shape based on the surface of the oceans, influenced only by gravity and centrifugal force. It is the true figure of the Earth, and it is lumpy, because gravity itself varies from place to place. An irregular lump is useless for calculation, so mapping replaces it with a regular stand-in: an ellipsoid, a sphere flattened slightly at the poles, chosen to fit the geoid as closely as possible. A number of different ellipsoids are used for mapping, but WGS-84 (the World Geodetic System 1984) is the reference ellipsoid required for geographical coordinates in aviation: when a chart, a database or a GNSS receiver states a latitude and longitude, WGS-84 is the surface it refers to.
One number about the real Earth carries through the whole subject: the circumference of the Earth is approximately 40,000 km, or approximately 21,600 NM (NM: nautical miles). The second figure is no accident. A full circle holds 360 degrees of 60 minutes each, which is 21,600 minutes of arc, and the nautical mile is built so that one minute of latitude is one nautical mile on the surface. The circle and its own angular measure agree, and the next lesson leans on exactly that agreement for every distance it calculates.
The spinning Earth
The Earth rotates once a day around its spin axis, the line through the north and south geographic poles, turning from west to east. Its yearly journey around the Sun lies in a flat plane named the plane of the ecliptic, and the spin axis does not stand upright in it: the axis is tilted about 23.5 degrees away from the perpendicular to the ecliptic, so it makes an angle of about 66.5 degrees with the plane itself, and it keeps pointing the same way in space all year round.
That fixed tilt is what makes the year interesting. As the Earth moves around its orbit, first one hemisphere and then the other leans toward the Sun. The leaning hemisphere receives its sunlight more steeply and for more hours: the inclination of the spin axis is the cause of the seasons, of the changing insolation, and of the changing duration of daylight through the year (insolation: the intensity of incoming solar radiation). At the equator, days stay near twelve hours all year; the further from the equator, the larger the swing, until inside the polar circles the Sun in midsummer never sets and in midwinter never rises. The Time module at the end of this course turns this picture into sunrise and sunset tables; for now the mechanism is the point: a tilted axis on a moving Earth.
Latitude and longitude
To name a position, navigation lays a grid over the ellipsoid, and geodetic latitude and longitude on the WGS-84 ellipsoid is how a position is defined everywhere in this subject. The grid has two families of lines:
parallels of latitude are circles drawn parallel to the equator, joining all points of equal latitude; the geographic (geodetic) latitude of a place is the angle between the normal (the perpendicular) to the ellipsoid at that place and the plane of the equator, counted from 0° at the equator to 90° north or south at the poles;
meridians are semi-great circles running from pole to pole; the geographic (geodetic) longitude of a place is the angle, measured along the equator, between the prime meridian through Greenwich and the meridian of the place, counted from 0° to 180° east or west.
On a perfect sphere the normal at any point would pass through the centre, and latitude could equally be measured at the centre; on the slightly flattened ellipsoid the normal misses the centre except at the equator and the poles, which is why the definition names the normal and not the centre. For everyday chart work the distinction changes nothing; for the definition question it is the answer. Each meridian, together with the meridian directly opposite it (its anti-meridian), completes a full great circle around the Earth, a fact the great-circles module returns to.
Differences between two positions come with two small rules of arithmetic. The change of latitude between two places is found by subtracting the latitudes when both are in the same hemisphere and adding them when they are in opposite hemispheres: from 52°N to 36°N is 16°, from 20°N to 35°S is 55°. The change of longitude follows the same rule east and west, with one extra clause: if the sum exceeds 180°, subtract it from 360°, because the shorter way round the Earth is the other way. From 170°E to 165°W the add-rule gives 335°, so the change of longitude is 360° minus 335°, which is 25°, crossing the 180° meridian. These two little calculations feed directly into the distance work of the next lesson, where each minute of the answer becomes a nautical mile.