Analemma picture

Analemma in Athens (lat=38 , lon=23)

10:00 UTC+2, 12:28 UTC + 2 and 15:00 UTC + 2

Analemma on the Globe

Close-up

Motion of the Sun The daily motion of the Sun is

westward The yearly motion of the Sun is

eastward with respect to the stars

The true Sun The true Sun is the usual sun True noon is when the Sun crosses

the meridian True time is time measured by the

true Sun, i.e., sundial time The true day is the time from one

true noon to the next

The mean Sun The mean Sun is a virtual body that

moves along the celestial equator at constant speed and meets the true Sun at the vernal equinox

The mean Sun crosses the meridian at mean noon, i.e. 12pm

The mean day is the time from one mean noon to the next

The mean Sun 2 (Local) mean time is UTC adjusted

for longitude (Local) mean time is time by the

mean sun (depends on longitude and the EoT)

Standard time is the official time, including time zone and DST 

Mean time and true time Make sure you understand the

difference between “true time” and “time of true noon”

Look at the following table:True time of true noon = True time of mean noon =Mean time of true noon =Mean time of mean noon =

Mean time and true time 2 Two of these are easy. True time of

true noon = Mean time of mean noon = 12

Suppose the true Sun if 15 min early. In that case true time of mean noon = 12:15 whilemean time of true noon = 11:45

Equation of time Equation of time = true time –

mean time If evaluate both times at mean

noon, we get 12:15 - 12 = 0:15

If we evaluate at true noon, we get12 - 11:45 = 0:15

Equation of time 2 So if the true Sun is ahead, then: 1. EoT is positive 2. True time is later than mean

time 3. The mean time of true noon is

earlier than the mean time of mean noon

Equation of time 3 true time = mean time + EoT Used to be

mean time = true time + EoT Now we know mean time, but not

true time The EoT is positive when the true

Sun is fast

When is the true day longest? The length of the true day depends

on the speed of the eastward (yearly) motion of the Sun

When the Sun moves quickly eastward, the westward motion is slower, and the true day is longer

Why does the eastward motion change? The are two reasons One is the obliquity of the Earth’s

axis One is the eccentricity, i.e., the

orbit of the Earth is an ellipse, not a circle

We will consider them one at the time

Obliquity The ecliptic is not parallel to the

celestial equator At the time of the solstices it is

parallel to the celestial equator At the time of the equinoxes it is

tilted to the celestial equator This makes the eastward motion

faster around the solstices

Obliquity 2

Obliquity 3 This can also be seen as follows

Obliquity 4 Remember that when the true Sun

is behind in the annual motion, it is ahead in the Sky

Obliquity 5 Early February is the time when

the true Sun is the furthest behind. It is also the time when it goes from moving faster backwards to moving slower backwards.

Eccentricity When the Earth is at perihelion

near January 4, the Earth will revolve faster, and the eastward motion of the Sun with respect to the stars is faster

This makes the true day longer around perihelion

Eccentricity 2 The EoT is the cumulative effect When the Sun moves

fastest/slowest eastward, the graph is steepest down/up

Combined effect The obliquity gives two fast

periods The eccentricity gives one fast

period The combined effect is one very

fast period in December-January and one medium fast period in June-July

Combined effect 2

Combined effect 3

Extremes of equation of time maximum value (16m 25s) around

November 3 (I will usually round this to 17m or 15m)

minimum value (-14m 15s) around February 11 (I will usually round this to -14m or 15m)

Setting analemma

Rising and setting analemma

Rising analemma at the Equator

Earliest and latest sunrise in Singapore Singapore is at latitude 1N The sunrise time varies between 6:46

a.m. and 7:17 a.m., with the earliest sunrise on November 1 and the latest on February 9

In the same way, the sunset time varies between 6:50 p.m. and 7:21 p.m., with the earliest sunset on November 5 and the latest on February 13

Earliest and latest sunrise in Singapore 2 Singapore is at longitude about

103.75°E, so on average, the Sun will cross the meridian at 13:05

In Early November the Sun will therefore cross around 12:48 and in mid February around 13:19

Earliest and latest sunrise in Singapore 3 Because of refraction and the fact that

sunrise and sunset are determined by the upper limb of the Sun and not the center of the Sun, the length of the day on the Equator is about 12h 8m

At latitude 1N, the length of the day will vary by about 9 min, between 12h 3m and 12h 12m

Earliest and latest sunrise in Singapore 4 In both early November and mid

February, the length of the day will be about 12h 04m, so if the Sun crosses the meridian at 13:19, the sunrise will be at 7:17 a.m. and the sunset at 7:21 p.m.

If the Sun crosses the meridian at 12:48, the sunrise will be at 6:46 a.m. and the sunset will be 6:50 p.m.

Flowering time for plants in Singapore

Some plants flower when the time of sunrise changes most rapidly

Not based on earliest sunrise or longest day

Rising analemma at 5N

Penang, Malaysia is at 5N

Rising analemma at 12N

Bangkok is at 13N. There is a 50 days period between August 22 and October 10 when the variation in the sunrise in within an interval of 20 seconds!

Rising analemma at 25N

Rising analemma at 40N

Beijing is at 40N

Rising analemma at 60N

Oslo, Norway is at 60N

Rising southern analemma

Setting northern analemma

Setting southern analemma