Earth & solar system

061 General NavigationChapter 1

The earth’s motion relative to the sun and stars underpins time, seasons, direction definitions, and distance calculations.

Schematic

Earth's axis inclined ~23.5° to the ecliptic — drives seasons and declination (schematic, not to scale).

Solar system

Key fact

The solar system consists of the sun, eight planets, asteroids, and comets — not stars.

Key fact

Kepler’s 1st law: planets move in elliptical orbits with the sun at one focus.

Key fact

Kepler’s 2nd law: the sun–earth radius vector sweeps equal areas in equal time (earth moves faster when closer to the sun).

Key fact

Earth spins anticlockwise when viewed from above the North Pole.

Key fact

Earth orbits the sun in an elliptical path. Perihelion (closest) — early January. Aphelion (furthest) — early July.

Ecliptic, equinoxes & solstice

Definition — Ecliptic

The apparent yearly path of the sun around the earth.

Definition — Plane of ecliptic

Imaginary plane containing the earth’s orbit around the sun.

Definition — Plane of equinoctial

The plane of the equator extended into space.

Key fact

Obliquity of the ecliptic — angle of 23.5° between the plane of the ecliptic and the plane of the equinoctial. The polar axis is inclined 66.5° to the ecliptic.

Key fact

At equinoxes (March spring, September autumn) the sun crosses the equinoctial plane — equal day and night. Rate of change of declination is highest near equinoxes, but latitude has the smallest effect on daylight duration near equinoxes.

Key fact

Summer solstice (June) — sun reaches 23.5°N (Tropic of Cancer). Winter solstice (December) — sun reaches 23.5°S (Tropic of Capricorn).

Key fact

Polar circles at 66.5°N/S — latitude beyond which midnight sun or polar night can occur.

Definition — Apparent sun

The visible sun — always in the plane of the ecliptic. Used for apparent solar time; day length varies through the year.

Definition — Mean sun

A fictitious sun coinciding with the apparent sun at spring equinox, travelling along the celestial equator at uniform speed. Used for constant time measurement.

Key fact

Difference between mean sun and apparent sun is greatest in February and November (“equation of time”).

Declination & daylight

Definition — Declination

Angular distance of the sun north or south of the celestial equator — its position relative to the plane of the equator.

Key fact

When declination is northerly, daylight in the southern hemisphere is shorter than in the northern hemisphere.

Key fact

Midnight sun — sun visible for 24 hours (where latitude and declination allow).

Key fact

Sunset — when the centre of the sun is 6° below the celestial horizon (civil twilight definition). Atmospheric refraction makes sunrise slightly earlier and sunset slightly later.

Exam trap

On the earth’s ellipsoid, one minute of latitude at the equator is less than 1 NM — distance per minute increases toward the poles. One minute along a meridian = 1 NM at 45° latitude.

Shape of the earth

Key fact

The earth is an oblate spheroid — flattened at the poles (compressibility). Equatorial radius ≈ 3444 NM, polar radius ≈ 3433 NM. Polar diameter ≈ 1/300 (0.3%) less than equatorial.

Formula — Compressibility

Compressibility = (Semi-major axis − Semi-minor axis) / Semi-major axis

Semi-minor axis ≈ Semi-major axis ÷ 297

Geocentric vs geodetic latitude

Key fact

Geocentric latitude — measured from the earth’s centre. Geodetic/geographic latitude — measured using the local horizontal and a plumb line (ICAO/aviation method).

Key fact

They are equal at poles and equator. Maximum difference ≈ 11.6′ at 45°N/S.

Days & time

Definition — Sidereal day

Earth rotates 360° relative to the stars (~23 h 56 min). Constant.

Definition — Solar day (apparent)

Period between successive transits of the true sun — 360.9° of rotation (~24 h). Longer than sidereal day because orbital and rotational motion are in the same direction.

Key fact

1200 LMT — mean sun on observer’s meridian (hour angle 000°). 0000 LMT — mean sun on observer’s anti-meridian.

Key fact

UTC = LMT ± (longitude × 4 minutes). Countries west of Greenwich are slow on UTC. Crossing the date line: W→E gain a day, E→W lose a day.

Great circles, rhumb lines & direction

Schematic

Great circle = shortest path (concave to equator). Rhumb line = constant track (concave to nearer pole).

Definition — Great circle

Circle on the earth’s surface whose centre and radius are those of the earth. Shortest distance between two points. Also called orthodrome.

Definition — Small circle

Any circle on the earth’s surface that is not a great circle — does not pass through the earth’s axis.

Definition — Rhumb line

Line cutting all meridians at the same angle — constant direction. Longer than the great circle. Following a non-cardinal rhumb line spirals toward the pole.

Key fact

Meridians join the poles (lines of longitude). Max longitude 180°E/W. Parallels lie east/west. Equator = 0°, max latitude 90°N/S.

Key fact

Vertex — point on a great circle of highest latitude; true track is 090° or 270° there. Vertices are antipodal.

Key fact

A great circle path bends toward the nearer pole. GC distance along a meridian/anti-meridian is always a great circle distance.

Direction definitions

Term	Meaning
Bearing	Direction to/from a point or object
Heading	Direction the aircraft nose points
Track	Actual path over the ground (TMG)
Relative bearing	Clockwise from aircraft nose
True north	Local meridian toward North Pole

Vector notation from notes: -----> heading, ------>> track, ------->>> wind.

Quick revision

Topic	Remember
Obliquity	23.5°
Polar circles	66.5°N/S
Perihelion / Aphelion	Jan / Jul
Sidereal vs solar	Solar day longer
GC vs RL	GC shorter; RL constant track