Time, the Sun & Twilight

C. 1800 ft/min

Height to lose 27,000 ft. Time available = 85 / 340 h = 15 min. ROD = 27,000 / 15 = 1800 ft/min. ROD = height / time, and time = distance / GS.

The question was recalled without its options; these options were written to it.

A. Beginning of July

Aphelion, when the earth is furthest from the sun, is in early July.

A. 0-6 degrees

Civil twilight covers the time when the centre of the sun is between 0 and 6 deg below the horizon.

C. November and February.

The equation of time is greatest (about 14-16 min) in early November and mid-February.

B. inclination of the polar axis with the ecliptic plane

Seasons exist because the earth's polar axis is inclined about 23.5 deg to the plane of its orbit (the ecliptic).

A. Beginning of January

Perihelion, when the earth is closest to the sun, is in early January (aphelion in early July).

B. 23.5 deg

The earth's equatorial plane is inclined about 23.5 deg to the plane of the ecliptic.

C. the inclination of the ecliptic to the equator

Because the equator is tilted 23.5 deg to the ecliptic, the sun's declination swings between 23.5 N and S, and with it the share of each parallel that is in daylight. Rotation gives day and night, but not their changing length.

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C. 2 h 05 min

500 / 240 = 2.083 h = 2 h 05 min.

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B. 21 June

At the summer solstice (about 21 June) the sun's declination is 23.5 N, so northern parallels have their largest share of daylight. 22 December is the longest day in the southern hemisphere.

D. 23 deg

The sun is overhead at most at 23.5 deg (tropic).

A. LMT 1130, ST 1100

Arc to time: 15 deg = 1 h, 1 deg = 4 min. 22 30 E = 1 h 30 min ahead: LMT 1130. Standard time is set by the state, here UTC + 1 = 1100. Memory aid: longitude east, UTC least - so east of Greenwich the local time is ahead and you add.

C. 480 kt

Same time, so speed is proportional to the length of the path. The 60 deg parallel is cos 60 = half the equator: 240 / 0.5 = 480 kt.

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A. Between Sunset and when the centre of the sun is 6° below the true horizon.

Civil twilight lasts from sunset until the centre of the sun is 6 deg below the true horizon.

A. day gained, date lost

Crossing the International Date Line from west to east the calendar date goes back one day - you gain a day and lose a date.

D. All the above

The inclination of the earth's axis to the ecliptic causes the seasons and the varying length of daylight through the year; it stays constant.

A. 23.5

The sun is vertically overhead at most at the latitude of the tropics, 23.5 deg.

A. GD = AD x GS / TAS

Same time in the air: GD / GS = AD / TAS. In still air GS = TAS, so the ground distance equals the air distance.

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C. 424 kt

GS is proportional to the length of the parallel: 300 / cos 45 = 300 / 0.707 = 424 kt.

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B. it is the time set by the legal authorities for a country or part of a country

Standard time is the time set by the legal authority of a country or part of it.

A. 0230 on 3 December

1830 + 8 h = 2630, i.e. 0230 the next day. (0207 would be LMT, using the longitude: 7 h 37 min.)

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B. 1800

60 deg = 4 h. East is ahead: 1400 + 4 = 1800 LMT. ("Longitude east, UTC least; longitude west, UTC best.")

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A. 4 h 59 min

Climb covers 42 NM, descent 42.5 NM, leaving 715.5 NM of cruise: 715.5 / 180 = 3 h 58.5 min. Add the 1 h of climb and descent: 4 h 59 min.

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A. 1028

75 30 E = 5 h 02 min of time. East of Greenwich LMT is ahead of UTC, so UTC = 1530 - 0502 = 1028.

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B. varies through the year

The apparent solar day is not a constant length: it changes through the year (equation of time).

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C. 66°

The highest latitude at which the sun rises and sets every day is 66 deg (about 66.5).

C. are given in LMT.

The Air Almanac lists sunrise, sunset and twilight as LMT (for sea level). To get UTC or standard time you convert the LMT using the longitude afterwards.

B. the spring and autumn equinoxes

At the equinoxes the sun crosses the equator and its declination changes fastest (about 0.4 deg a day); at the solstices it is at its turning point and hardly changes - so day length is almost constant for a few days.

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A. 2000 on 5 May

LMT on the Greenwich meridian is UTC. 180 deg E is 12 h ahead: 0800 + 12 = 2000, same date.

A. Because the Earth's spin axis is inclined to the plane of its orbit around the Sun.

Seasons result from the inclination of the earth axis to its orbital plane.

D. 365 days 5 hours48 minutes 45 seconds

The correct answer is: 365 days 5 hours48 minutes 45 seconds.

B. Spring (Vernal) Equinox and Autumn Equinox)

Day length changes fastest at the equinoxes, when the sun's declination changes at its greatest rate.

A. 259 kt

300 x cos 45 / cos 35 = 300 x 0.707 / 0.819 = 259 kt. The higher latitude has the shorter circle, so the lower speed.

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A. 1218

010 24 E = 41.6 min of time, so UTC = 1200 - 0042 = 1118 (about). Standard time = UTC + 1 = 1218.

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C. The center of Sun is 6° below the celestial horizon

Morning civil twilight begins when the centre of the sun is 6 deg below the horizon.

B. 80°05'

5 h = 75 deg, 20 min = 5 deg, 20 s = 5 arc minutes: 80 deg 05 min.

B. 82 30'

5 h 30 min x 15 deg/h = 82 deg 30 min.

A. July

Aphelion is in early July.

C. Never

Delhi is at 28.6 N, north of the tropic (23.5 N), so the sun is never overhead there.

C. 1738:40 previous day

95 20 W = 6 h 21 min 20 s. West of Greenwich LMT is behind UTC: 0000 - 6:21:20 = 17:38:40 on the previous day.

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C. a fixed (distant) star

A sidereal day is one rotation relative to the stars: about 23 h 56 min, about 4 minutes shorter than the solar day.

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A. 24 minutes

The correct answer is: 24 minutes.

B. two successive identical phases as seen from the earth (new moon to new moon, about 29.5 days)

Synodic = relative to the sun (phase to phase, 29.5 days); sidereal month = relative to the stars (27.3 days).

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A. 1555 UTC

Latest landing 1810 - 0015 = 1755; minus 2 h flight time = 1555 UTC. Work backwards from the limit, in one time system.

B. 253 kt

420 x cos 53 = 420 x 0.602 = 253 kt.

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A. 1546

dlong = 30 deg 45' = 2 h 03 min of time. A is west of B, so its LMT is earlier: 1749 - 0203 = 1546.

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B. 820 kt

Speed ratio = cos 45 / cos 75 = 0.707 / 0.259: 300 x 2.73 = 820 kt. North or south does not matter - only the latitude.

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B. 66.5 deg

The axis makes 66.5 deg with the orbital plane - equivalently the equator is tilted 23.5 deg to the ecliptic. That tilt, not the elliptical orbit, causes the seasons.

A. the date goes back one day

Going east you move into the zone 24 h behind: the date decreases by one (you "gain" a day), while LMT runs on continuously.

B. 1333 UTC

Planned time for 70 NM = 23.3 min; actual 20.3 min, so GS = 70 / 20.3 x 60 = 207 kt. Remaining 250 NM at 207 kt = 72.5 min: 1200 + 20.3 + 72.5 = about 1333.

B. 12 deg below the horizon

Civil twilight: sunset to 6 deg below. Nautical: 6 to 12 deg. Astronomical: 12 to 18 deg. Aviation uses civil twilight.

A. about 20 minutes longer

Sidereal year = 365.256 days (orbit relative to the stars); tropical year = 365.242 days (equinox to equinox) - shorter by about 20 min because of the precession of the equinoxes.

B. an amount fixed by the government of the state, usually a whole or half hour

Standard time is legal time set by each state (India: IST = UTC + 5:30, kept on 82 deg 30' E). LMT is the one that follows the exact longitude (4 min per degree).

A. 180 kt

Time 62 min. GS = 186 / 62 x 60 = 180 kt.