## Time and Seasons

The **second** is the fundamental unit of time. Atomic clocks define the second: It is 9,192,631,770 periods of the light emitted in the transition between two energy levels in the caesium-133 atom.

A **day** is defined as the time interval between two successive upper transits of a given celestial reference point. An **upper transit** occurs when a celestial reference point or body crosses the celestial meridian moving westward. The **celestial meridian** is the imaginary line drawn through the north point of the horizon, the zenith, and the south point of the horizon.

The **Vernal equinox** is a point in space used as the zero point for **Sidereal Time**, and the sidereal day is arbitrarily divided into 24 sidereal hours of equal length, each of which consists of 60 sidereal minutes with 60 sidereal seconds per minute. **Local Sidereal Time** is 0^{h} 0^{m} 0^{s} when the vernal equinox lies on the celestial meridian and 1^{h} when the vernal equinox is 15° west of the celestial meridian.

Local sidereal time is defined as the **hour angle** of the vernal equinox. The hour angle is how far west (positive) or east (negative) of the meridian the celestial object is.

**Apparent Solar Time** is the hour angle of the sun plus 12^{h}, so local apparent noon always occurs at 12^{h} and marks the start of the **apparent solar day**. Due to the eccentricity of the Earth’s orbit and the inclination of the equatorial plane to the ecliptic, the length of the apparent solar day is not constant.

The Earth’s orbital speed reaches a maximum at perihelion (≈ January 2^{nd}) and a minimum at aphelion (≈ July 3^{rd}). The apparent solar day is longer at perihelion than at aphelion.

To avoid the variability of solar time, we define the **mean solar day** as the hour angle of a fictitious point (the **mean sun**) that moves eastward along the **celestial equator** at the average angular rate of the true sun.

The mean solar day begins at midnight and its length is 1/365.2564 of a sidereal day. The difference between apparent solar time and mean solar time is called the **equation of time**: the mean sun may lag or lead the true sun by as much as 16 minutes. The mean solar day is about 4 minutes longer than a sidereal day. The length of the sidereal day is 23^{h} 56^{m} 4.09^{s} in mean solar time and so a star appears to rise about 4 minutes earlier each night.

Standard time at Greenwich is referred to as **Greenwich Mean Time** (GMT) or equivalently **Coordinated Universal Time** (UTC). The Earth’s rotation rate is subject to small unpredictable variations and so UT is often replaced with **Ephemeris Time** (ET) in celestial mechanics.

The **Year** is the time it takes the Earth to orbit the sun. With respect to the stars, the Earth’s orbit takes **one sidereal year** of 365.2564 mean solar days. Whereas the **tropical year** (the year of the seasons) of 365.2422 mean solar days, is the period with respect to the vernal equinox that precesses about 50″ westward along the ecliptic each year.

Planetary perturbations cause the Earth’s perihelion to precess in the direction of the vernal equinox. We call the time between successive perihelion passages the **anomalistic year **of 365.2596 mean solar days. Is too

The Earth’s seasons arise because the equatorial plane is inclined about 23.5° to the ecliptic. The eccentricity of the Earth’s orbit is too small (*e* ≈ 0.017) to greatly affect the seasons.

When the sun is at the vernal equinox (≈ March 22^{nd}) or the **autumnal equinox** (≈ September 23^{rd}) its declination is 0° and there are 12 hours of day and 12 hours of night at all points on the Earth’s surface. The Noon altitude of the sun is 90° (**Zenith**) at the equator and 0° at the poles.

At the **summer solstice** (≈ June 22^{nd}) the sun attains its greatest declination +23.5° and passes directly overhead at noon for all observers at latitude 23.5° North (the **Tropic of Cancer**). On this date (the first day of summer) the days are the longest in the northern hemisphere. At the same time winter begins in the southern hemisphere and the days are the shortest there.

The situation is reversed at the **winter solstice** (≈ December 22^{nd}) when the sun’s declination is -23.5°. The sun then passes overhead for all observers at latitude 23.5° South (the **Tropic of Capricorn**).

Latitude 66.5° North is called the **Arctic Circle** and 66.5° South is the **Antarctic Circle**.