Astronomy behind navigational time
Aviation time starts with repeatable motion in the sky. Rotation defines the day, revolution defines the year, and the Sun provides the link between time and longitude.
The solar system in outline
The solar system contains the Sun, eight major planets, their natural satellites and smaller bodies. In order from the Sun, the planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. Each planet follows its own orbit and completes it in its own period. For navigation, the essential body is Earth and the apparent daily motion of the Sun and stars across the sky.
Rotation and revolution
Earth rotates eastwards about its geographic axis. Seen from above the North Celestial Pole, the rotation is anticlockwise. This makes the Sun and stars appear to move westwards across the sky. One rotation, measured against a selected celestial reference, defines a day. Earth also revolves anticlockwise around the Sun when viewed from the North Celestial Pole. One orbital cycle defines a year.
The celestial reference picture
The celestial sphere is an imaginary sphere centred on Earth. The extension of Earth's equatorial plane forms the celestial equator, also called the equinoctial. The extension of the rotation axis meets the sphere at the celestial poles. A body's declination is its angular distance north or south of the celestial equator, making declination analogous to latitude.
The Moon in the system
The Moon shines by reflected sunlight. Its synodic cycle from one new Moon to the next is about 29.5 days. The illuminated portion appears as new Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, third quarter and waning crescent. Its average daily delay is about 50 minutes, although precise rise and set times come from an almanac.
| Earth motion | Reference | Time idea produced |
|---|---|---|
| Rotation about the axis | Sun or distant star | Solar or sidereal day |
| Revolution around the Sun | Distant star or seasonal cycle | Sidereal or tropical year |
| Eastward rotation through longitude | Meridian and celestial body | Hour angle and local solar time |
Earth's orbit and Kepler's laws
Earth does not move around the Sun at constant speed on a perfect circle. Its elliptical orbit and changing speed help explain why apparent solar time is uneven.
Kepler's first law
Each planet moves in an ellipse with the Sun at one focus. Earth is nearest the Sun at perihelion, which occurs in early January, approximately 4 January in Oxford's treatment. It is farthest away at aphelion in early July, approximately 4 July.
Kepler's second law
The radius vector joining the Sun to a planet sweeps out equal areas in equal times. Because the radius is shorter near perihelion, Earth must move faster there. It moves slowest near aphelion. Equal areas do not mean equal distances travelled along the orbit.
Kepler's third law
The square of a planet's sidereal orbital period is proportional to the cube of its mean distance from the Sun. This compares the periods of different planets. For this chapter, the important practical result is that Earth's orbital period supplies the astronomical year.
Seasons, solstices and declination
The seasons are caused mainly by the inclination of Earth's axis, not by the small annual change in distance from the Sun.
Obliquity of the ecliptic
Earth's axis is inclined about 66.5 degrees to the orbital plane, which is the same as 23.5 degrees from the normal to that plane. The plane of Earth's orbit is the ecliptic. The equatorial plane is the equinoctial. The angle between them, about 23.5 degrees, is the obliquity of the ecliptic.
Oxford gives an Earth to Sun distance of about 91.4 million statute miles at perihelion and 94.6 million statute miles at aphelion. The resulting change in received heat is only about 3 percent and cannot explain the opposite seasons of the two hemispheres.
Solstices and equinoxes
| Approximate date | Sun's declination | Northern Hemisphere | Southern Hemisphere |
|---|---|---|---|
| 21 March | 0 degrees, moving north | Spring equinox | Autumn equinox |
| 21 June | 23.5 degrees north | Summer solstice | Winter solstice |
| 21 September | 0 degrees, moving south | Autumn equinox | Spring equinox |
| 21 December | 23.5 degrees south | Winter solstice | Summer solstice |
Solar declination
The Sun's declination is the angular distance north or south of the celestial equator. Over a year it varies like a sine wave from 23.5 degrees north through zero to 23.5 degrees south and back. When the Sun is vertically overhead, its altitude is 90 degrees and it is at the observer's zenith.
Sidereal, apparent and mean solar days
A day is one rotation of Earth measured against a chosen celestial body. The reference body changes the measured length.
Sidereal day
A sidereal day is the interval between successive transits of a distant star over the same meridian. It is approximately 23 hours 56 minutes of mean solar time and is nearly constant. It is not tied to the normal cycle of daylight and darkness.
Apparent solar day
An apparent solar day is the interval between successive transits of the real Sun over an observer's meridian. During one Earth rotation, Earth also advances along its orbit, so Earth must rotate a little farther before the Sun returns to the meridian. The apparent solar day is therefore longer than the sidereal day.
Its length is not constant because Earth's orbital speed changes and the ecliptic is inclined to the equinoctial. Bali describes an apparent day as varying roughly from 23 hours 59 minutes 24 seconds to 24 hours 00 minutes 30 seconds.
Mean solar and civil day
The mean solar day is the average length of apparent solar days over a year. It is constant at 24 hours and remains related to light and darkness, so it is used as the civil day. A fictitious mean Sun is imagined to move westwards around the celestial equator at constant speed.
The equation of time
A clock based on the constant mean Sun and a sundial based on the real Sun do not normally agree. Their difference is the equation of time.
Definition and sign
Bali states the relationship as Equation of Time = Apparent Solar Time minus Mean Solar Time. It may also be written as sundial time minus clock time. A positive value means the apparent Sun is ahead of the mean Sun. A negative value means it is behind.
Why the difference changes
Two effects combine: the changing orbital speed required by Kepler's second law and the projection of motion along the inclined ecliptic onto the equinoctial. The difference builds and reverses during the year. Apparent and mean solar time agree on several dates, but not at every equinox or solstice.
Maximum differences
Oxford gives the largest difference as about 16 minutes in mid November and a second large difference of about 14 minutes in mid February. In the November example, apparent noon occurs at 1144 mean time and mean noon remains 1200 LMT. In February, apparent noon occurs at 1214 while mean noon is 1200 LMT.
Local mean time and hour angle
Local mean time identifies the position of the mean Sun relative to an observer's meridian. Hour angle expresses the same geometry as an angle measured westwards.
Local Mean Time
Local Mean Time, or LMT, is mean solar time at a particular meridian. Local mean noon is 1200 LMT, when the mean Sun transits the observer's meridian. At local mean midnight it is on the opposite meridian. Places east of Greenwich experience local mean events earlier in universal time than places to the west. Full conversion to UTC and zone time belongs to the next chapter.
Hour angle
The hour angle of a celestial body is the arc of the equinoctial between a datum meridian and the meridian through the body, measured westwards from 0 to 360 degrees. When the datum is Greenwich, it is Greenwich Hour Angle, or GHA. When the datum is the observer's meridian, it is Local Hour Angle, or LHA.
Reading GHA and LHA
A body with GHA 050 degrees is transiting the 050 west meridian. GHA 180 degrees places it on the 180 meridian. GHA 270 degrees west is equivalent to longitude 090 degrees east. LHA is found from GHA and the observer's longitude using algebraic east and west signs, then reduced to the range from 0 to 360 degrees.
| Quantity | Datum | Measured |
|---|---|---|
| GHA | Greenwich meridian | Westwards from 0 to 360 degrees |
| LHA | Observer's local meridian | Westwards from 0 to 360 degrees |
| Declination | Celestial equator | North or south, analogous to latitude |
Sidereal, tropical and calendar years
A year can be referenced to the stars, to the cycle of seasons or to the civil calendar. The definitions are close but not identical.
Sidereal year
The sidereal year is the time Earth takes to complete an orbit measured against a distant star. Oxford gives approximately 365 days 6 hours.
Tropical year
The tropical year is the interval for one cycle of the seasons, such as one March equinox to the next. Oxford gives 365 days 5 hours 48.75 minutes. It is the year that the civil calendar must follow if the seasons are to remain in their usual months.
Calendar and leap year
The ordinary calendar year has 365 days. A leap day is normally inserted every fourth year. The century correction omits the leap day in century years not divisible by 400. Thus 2000 and 2400 are leap years, while 2100, 2200 and 2300 are not.
| Year | Reference | Approximate length |
|---|---|---|
| Sidereal | Distant star | 365 days 6 hours |
| Tropical | Seasonal cycle | 365 days 5 hours 48.75 minutes |
| Calendar | Civil convention | 365 days, or 366 in a leap year |
Putting the time framework together
The definitions form one connected system. Each answers a different question, so substituting one for another creates predictable errors.
Choose the correct reference
| If the problem asks about | Use | Remember |
|---|---|---|
| One rotation relative to a star | Sidereal day | About 23 hours 56 minutes |
| Real Sun crossing a meridian | Apparent solar time | Day length varies |
| Constant civil solar day | Mean solar time | 24 hours |
| Sun's north or south position | Declination | Range about 23.5 degrees north to south |
| Body's westward angular position | GHA or LHA | Measured from 0 to 360 degrees |
| Clock and sundial difference | Equation of time | Apparent minus mean |
Worked chain
At the June solstice, the Sun's declination is about 23.5 degrees north. Suppose a body has GHA 270 degrees. It is transiting the meridian 270 degrees west of Greenwich, which is the same as 090 degrees east. If the apparent Sun crosses an observer's meridian at 1144 mean time, the apparent time is 16 minutes ahead and the equation of time is about plus 16 minutes.
Operational relevance
These ideas support UTC and local time conversion, sunrise and sunset prediction, almanac use and celestial reference geometry. The next chapter turns angular movement into clock time and applies longitude, UTC, zone time and the International Date Line.