The Earth, Latitude, Longitude & Distance

A. 75 deg S, 30 deg W

Same-name values subtract, opposite names add. Latitude: 45 N to 30 S crosses the equator: 75 deg S. Longitude: 010 E to 020 W crosses Greenwich: 30 deg W.

A. 135 NM and 155 SM

km / 1.852 = NM: 250 / 1.852 = 135 NM. km / 1.609 = SM: 250 / 1.609 = 155 SM.

A. 21600 NM

The circumference of the earth is 360 x 60 = 21,600 NM.

C. Rhumb lines

A parallel of latitude cuts every meridian at 90 deg, so it is a rhumb line; only the equator is also a great circle.

A. GC routes

The shortest distance between two points on the earth is along the great circle.

B. 1852 metres

ICAO fixes the nautical mile at exactly 1852 m (about 6076 ft) - the mean length of one minute of arc of a meridian. 1609 m is the statute mile.

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

A. 04°00'N 029°58'W

South and north legs cancel. East leg at 6 deg S: 600/cos6 = 603.3 NM east; west leg at 4 deg N: 600/cos4 = 601.5 NM west. Net 1.8 NM east, so longitude is 030 deg 00 W less 1.8 = 029 deg 58 W.

B. 0 to 180 deg east or west of the prime meridian

Longitude is the angle at the earth's axis between the prime (Greenwich) meridian and the meridian of the place, 0-180 deg E or W. Latitude is 0-90 deg N or S.

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

B. 45 deg N and S

Geodetic (the local vertical) and geocentric (line to the centre) latitude are equal at the equator and poles, where the vertical passes through the centre; the difference peaks (about 11.6') at 45 deg.

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

C. rhumb line

A rhumb line keeps a constant true direction because it crosses every meridian at the same angle. A great circle (except a meridian or the equator) crosses each meridian at a different angle.

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

A. 300 NM

Departure = dlong (minutes) x cos lat = 600 x cos 60 = 300 NM.

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

B. 03°50'S

685 km = 369.9 NM = 6 deg 10 min of latitude. 02 20 N less 6 10 = 03 50 S.

A. north pole

At the south pole every direction is north.

A. 6108 ft (approx)

A minute of latitude is longest at the poles, about 1,861.6 m = 6,108 ft (6,046 ft at the equator).

A. the shortest distance between 2 points

A great circle is the shortest path between two points on the surface of a sphere (its plane passes through the centre of the earth).

A. oblate spheroid

The earth is an oblate spheroid.

C. 2 HR 30 MIN

d.long = 40 deg; distance = 40 x 60 x cos 60 = 1,200 NM; time = 1,200 / 480 = 2.5 h.

B. 60 deg 00'N 002 deg 24'W

165 km = 89.1 NM. dlong = 89.1 / cos 60 = 178' = 2 deg 58'. 005 22 W - 2 58 = 002 deg 24'W.

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

B. 31,160 ft

9.5 km x 3,281 ft/km = 31,170 ft.

C. rhumb line and a semi great circle

A meridian runs pole to pole: half of a great circle (its plane contains the earth's axis) and a line of constant direction (000/180), so a rhumb line too.

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

B. 60 NM

One minute of latitude = 1 NM, so one degree = 60 NM (about 111 km - a distractor here, it is not in NM).

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

C. a line of constant direction

Same angle with every meridian = same true track all the way, which is why it is easy to fly. It is generally NOT the shortest route (that is the great circle), and meridians and the equator are both.

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

A. 3360 NM (about 6220 km)

dlong is exactly 180, so the great circle runs over the North Pole: (90 - 62) x 2 = 56 deg = 3360 NM (6220 km). Along the parallel it would be 10,800 x cos 62 = 5070 NM.

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

B. 150 deg E

The anti-meridian is the other half of the same great circle: 180 - 30 = 150, on the opposite side - East.

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

A. 20 deg 15'S, 1215 NM

Across the equator, add: 12 30 + 07 45 = 20 deg 15', = 1215 NM. Direction is towards B, i.e. south.

B. 60 deg N 000 deg 00'

dlong = departure / cos lat = 300 / 0.5 = 600' = 10 deg; 010 W + 10 deg east = 000.

A. 10,800 NM

A parallel shrinks with the cosine of latitude: 21,600 x cos 60 = 10,800 NM.

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

B. 02°00'S

445 km/h x 3 h = 1,335 km = 721 NM = 12 deg 01 min. 10 deg N less 12 01 = 02 deg 01 min S, i.e. about 02 00 S.

A. 057

Convergency = dlong x sin mean lat = 12 x sin 54 = 9.7 deg. In the northern hemisphere an easterly great circle track increases: 047 + 10 = 057.

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

A. poles, equator

A great circle curves towards the nearer pole; a rhumb line on a Mercator-type diagram lies on the equator side of it.

A. 6356.9

Semi-minor axis = a (1 - f) = 6378.4 x (1 - 1/297) = 6356.9 km.

A. about 12,700 km (6,880 NM)

The mean diameter of the earth is about 12,740 km, i.e. about 6,880 NM. 6,370 km is the radius and 40,000 km (21,600 NM) is the circumference.

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

C. S17°50' W177°43.5'

Antipodes: latitude same, opposite name (S17 50); longitude 180 - 002 16.5 = 177 43.5 on the other side (W).

C. Meters, Kilometers and Nautical miles

ICAO Annex 5 lists metre, kilometre and nautical mile for distances; statute miles and feet (for distance) are not used.

A. metres and feet

ICAO (Annex 5): altitude, elevation and height in metres (feet as the alternative non-SI unit). Horizontal distance uses NM and km.

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

C. 35.0 Nautical mile

65 km / 1.852 = 35.1 NM; the latitude does not matter for a distance already in km.

A. 45°

A minute of latitude equals 1 NM (1852 m) at about 45 deg latitude, where the earth radius of curvature gives exactly that.

D. 2482 NM

One is south, one north of the equator: ADD them. 17 23 + 23 59 = 41 deg 22' = 41 x 60 + 22 = 2482 NM.

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

C. 093 48.5'W

d.long = 6 / cos 58 42 = 11.5 min, so longitude is 094 00 W less 11.5 = 093 48.5 W.

A. 7008 nm

Great circle: cos d = sin 41.92 sin 21.28 + cos 41.92 cos 21.28 cos 180.0 -> d = 116.8 deg = 7,008 NM.

B. 451 kt

Each parallel's length is proportional to cos lat: 240 x cos 20 / cos 60 = 240 x 0.94 / 0.5 = 451 kt.

C. considered a perfect sphere (though it is really an oblate spheroid)

The real earth is slightly flattened at the poles (about 1/298), but for nearly all navigation sums it is treated as a sphere, so 1' of latitude = 1 NM everywhere.

Our independent check found that more than one option can be argued for, as worded in the recall. The key gives the answer most references support.

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

A. 03 deg 30'S, 003 deg 28'E

Latitude: 47 26 - 43 56 = 3 deg 30', towards the south. Longitude: 002 16 W to 001 12 E crosses Greenwich, so add: 3 deg 28', towards the east.

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

B. 75° N or S

Distance = 540 x 10.4 = 5,616 NM = 21,600 x cos lat, so cos lat = 0.26 and the latitude is 75 deg.

B. 090°15'S

From 00 15 N to 90 00 S: 15 + 90 deg = 90 deg 15 min, southwards.

B. N40° 00' E064° 20'.

120 kt x 6 h = 720 NM west along the 40 N parallel. d.long = 720 / cos 40 = 940 min = 15 deg 40 min. 080 E less 15 40 = 064 20 E.

A. 5280 ft and 0.869 NM

1 SM = 5280 ft = 1609 m; 1 NM = 6076 ft = 1852 m, so 1 SM = 0.869 NM and 1 NM = 1.15 SM.

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

A. 70 S 050 W

The two vertices of a great circle are antipodal: opposite latitude, longitude differing by 180 deg (130 E -> 050 W).

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

A. 87.9 cm

One inch is exactly 2.54 cm: 34.6 x 2.54 = 87.9 cm.

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

A. 26 deg 36' N/S

cos lat = departure / dlong = 448 / 501 = 0.894, lat = 26.6 deg = 26 deg 36' (N or S - the data cannot tell).

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

A. the equator

The equator's plane passes through the earth's centre (great circle) and it crosses every meridian at 90 deg (rhumb line). Meridians are also both. Other parallels are rhumb lines but small circles.

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

B. a rhumb line and a small circle

Its plane does not pass through the earth's centre, so it is a small circle; it crosses every meridian at 90 deg, so it is a rhumb line.

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

A. 92.5 cm

1 inch = 2.54 cm: 36.4 x 2.54 = 92.5 cm.

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

A. 3600 NM and 5400 NM

Over the pole: (90 - 60) x 2 = 60 deg of a meridian = 3600 NM. Along the parallel: 180 x 60 x cos 60 = 5400 NM. With dlong 180 the great circle runs up one meridian and down its anti-meridian.

B. anticlockwise, west to east

The earth turns west to east (anticlockwise from above the North Pole), which is why the sun rises in the east and local time is ahead east of Greenwich.

A. 50 deg

Crossing the 180 deg meridian: 180 - 150 = 30 deg to the date line, plus 180 - 160 = 20 deg beyond it = 50 deg east. (Crossing Greenwich you add the two longitudes; crossing 180 you add their differences from 180.)