The Sun's motion, and its effect on time-keeping

In the ecliptic system, the Sun's coordinates are
fairly simple,

because its ecliptic latitude is 0° at all
times,

while its ecliptic longitude constantly increases.

However, the Sun's longitude does *not *increase
at a *steady *speed of exactly 360° a year.

And it's
important to know the Sun's position,

because it's used for
normal time-keeping (*solar* time, rather than *sidereal
*time).

By Kepler's Second Law,

the Earth orbits faster at
perihelion and slower at aphelion.

So the Sun appears to move
fastest along ecliptic in January

and slowest in July.

We can
invent an imaginary Sun (the *dynamical mean Sun*)

which
coincides with the true Sun when the Earth is at perihelion,

but
moves along the ecliptic at a *constant *speed.

The true Sun
appears to move faster than the dynamical mean Sun

when the Earth
is around perihelion,

and slower when the Earth is near aphelion:

one cycle per year.

However, an object moving at a constant speed along
the *ecliptic*

is still moving at a varying speed with
respect to the *equator*,

since the ecliptic is tilted to
the equator.

We invent another imaginary Sun, called simply the
**mean Sun**,

which moves along the *equator* at constant
speed;

the dynamical mean Sun appears to lag behind this

where
the ecliptic is steeply tilted to the equator (around the equinoxes)

and catch up where it's nearly parallel (around the solstices):

two cycles per year.

Combining these two effects gives the total
difference in time between the true Sun and the mean Sun,

which
is called the **equation of time** (the solid black line on the
diagram).

The true Sun is about 14 minutes late, compared to
the mean Sun, around 10th February,

about 4 minutes early around
May 15th,

about 6 minutes late around July 25th,

and about 16
minutes early around November 5th.

The interval between two meridian transits of the
*mean *Sun is the **mean solar day**.

The upper transit
of the mean Sun across the local meridian marks midday, **local mean
time. Greenwich Mean Time** (GMT) is defined as midday

when the mean Sun crosses the meridian of Greenwich.

**Apparent solar time**, as measured by the
the

may differ from GMT for three reasons.

Firstly, because of the equation of time,

Secondly, because of the longitude of the observer

(the further west, the later the Sun will cross the meridian).

Thirdly, because of "Summer Time".

Britain uses GMT as standard time in winter, adding
one hour in summer.

Most other countries adopt their own standard
time,

suitable for their own longitude (large countries may have
several time-zones),

differing from GMT by a set amount.

In practice, the Earth's rotation is not quite
constant.

Time is now regulated by atomic clocks, and called
**Coordinated Universal Time** (UTC),

but this is artificially
kept within 1 second of GMT

by adding a "leap second"
when necessary.

Astronomers also use **Terrestrial Time** (TT,
formerly called Ephemeris Time, ET)

for describing the motions of
solar-system bodies.

The difference TT-UTC is called "delta-T".

At any location, local *mean* time and local
*sidereal *time agree at the autumn equinox.

(Why?
Because, at the autumn equinox,

the Right Ascension of the mean
Sun is 12 hours,

and the mean Sun is on the local meridian at
12h, local mean time.)

But sidereal time runs faster than
solar time, by one day a year,

or approximately 3.94 minutes a
day.

Exercise:

On April 1st, what is the Sun's
approximate ecliptic longitude?

And approximately what is
Greenwich Sidereal Time at midnight on April 1st?

Click here for the answer.

After this digression into the topic of *time*,

we
now return to the *position *of an object in the sky.

There
are various physical factors which may change the apparent position
of an object.

Previous section:
The
relation between ecliptic and equatorial coordinates

Next section: The Moon

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index