Notes on Time and Space

A discussion on Time:

The second is the fundamental unit of time. It was originally defined as: - the amount of time required for a 1-m pendulum to swing from one side of arc to the other

Now, it is defined as: 9 192 631 770 cycles of radiation corresponding to the transition between two hyperfine levels in the ground state of Cesium-133

Worth noting: There are approx 365 1/4 mean solar days in one solar year (watch time). The mean solar day is the average length of a solar day, 24 hours.

Solar year - the time between 2 vernal equinoxes. This is actually the tropical year, which is growing shorter by 0.5 sec/century. 1900 is the standard tropical year.

Sidereal time - time by the stars

Sidereal year - the amount of time for the Sun to return to a given position among stars

Calendars:

Julian - 365 days with an extra day every 4 years (leap year).
This was still a bit imprecise - consider that in 1988, the year was 365 d, 5 h, 48 min, 43.5 s. By 1582, the Julian calendar was out of phase with Easter by nearly 10 days. So, Pope Gregory XIII adopted a new calendar; 10 days were dropped from that year.

Gregorian calendar -
Years evenly divible by 4 are leap years. Every 4th century year is a leap year (2000, 2400; NOT 1600, 1700, 1800, 1900, 2100)

Daylight savings time
http://en.wikipedia.org/wiki/Daylight_saving_time
http://www.timeanddate.com/time/dst/

Changed a few years back. Now: DST Starts at 2 AM, second Sunday in March - set clocks AHEAD 1 hour
DST Ends at 2 AM, second Sunday in November - set clocks back

We are EST, Eastern Standard Time. During DST, we become EDT (Eastern daylight time).

Greenwich Mean Time (GMT) - 5 hours ahead of EST. Roughly the same as Universal Time (UT).

Universal time (UT)
Basically the mean solar time as measured on the Greenwich meridian, thus, 5 hours ahead of us. Formally, UT is defined by a mathematical formula as a function of sidereal time and is thus determined by observations of stars.

Sidereal time
In 365 1/4 solar days, Earth makes 366 1/4 rotations on its own axis. So, there are 366 1/4 sidereal days in a solar year. Each sidereal day is shorter by about 4 minutes than a solar day. UT and GST agree at one instant every year (at the autumnal equinox, around Sep 22). Thereafter, the difference between them grows, in the sense that ST runs faster than UT until exactly half a year later, when it is 12 hours. Another half-year later, the times again agree.

Local Sidereal Time - the hour angle of the first point of Aries

Greenwich Sidereal Time
local sidereal time on the Greenwich meridian

Julian Date (JD)
Jan 1, 4713 BC is the fundamental epoch from which this is decided. The Julian date is the number of days since this day.
There is no year 0 in astronomy. The year before 1 AD is defined as year 0. So, 10 BC is the year -9 in astronomy. That trick again: to go from BC year to astro year, subtract one and change sign.

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Coordinate systems:

On Earth:

Longitude
half-circle lines from North to South pole
Zero longitude runs through the site of the Royal Greenwich Observatory in England - the Prime Meridian (0 degrees long.)
Number of degrees east or west of the PM

Latitude
Full circle lines parallel to the equator (0 degrees latitude)
+ or - 90 degrees corresponds to the poles

International Date Line (IDL)
Near or along 180 degrees longitude line, through the Pacific Ocean
As we travel eastward around the globe, the hours get later roughly each 15 degrees (a time zone). When we cross the IDL, we go BACK one day. This keeps only 24 hours on the Earth at a time.

In the Sky:

Celestial Equator - imaginary line above the Earth's equator

Right Ascension (RA)
Celestial analog of longitude (both measure east-west)
Measured in hours (each hour of RA equals 15 degrees) along the celestial equator

Declination (dec)
Celestial analog of latitude (both measure north-south)
Measured perpendicularly above (+) or below (-) the celestial equator

RA and dec form a coordinate system fixed to the stars. To observers on Earth, the stars appear to revolve every 23 h 56 min. So, the coordinate system appears to revolve at the same rate. Of course, it is the Earth which is really moving (most noticeably).

Ecliptic
Although the stars are fixed in their positions in the sky, the Sun's position varies through the whole range of RA throughout the year. This path (the "apparent" path of the Sun) is called the ecliptic and is inclined 23.5 degrees with respect to the celestial equator (CE), since the Earth's axis is tipped by that amount. (The "ecliptic plane" is the plane that the Earth and Sun make.)

The ecliptic and CE cross at two points:

Vernal equinox
March 21 (approx)
the first day of Northern Hemisphere spring
the zero-point of RA
Sun's declination is 0 degrees
Nearly equal amounts of day and night

Autumnal equinox
Sep 23 (approx)
the first day of autumn
Sun's declination at 0 degrees
Nearly equal amounts of day and night

Two other noteworthy days:
Winter solstice
Dec 22 (approx)
Shortest day of the year in Northern hemisphere
9.5 h of daylight (in the DC area)
As you travel farther north, the days are even shorter
- in Anchorage, Alaska, the day will be 5 h long
- in Barrow, Alaska, the sun will not "come out" at all; noontime is like deep twilight
the North pole is angled most steeply away from the Sun

Summer solstice
June 21 (approx)
longest day of the year in the Northern hemisphere
amount of tipping toward Sun is greatest for N. hemisphere
Sun highest in sky (dec is 23.5 degrees)

Length of daylight depends on latitude, calendar date, but not longitude
Each point on the globe receives an average of 12 hours of light each day. So, students in Barrow, Alaska have several days of endless sunshine as well.

Since the Moon goes around the Earth, its RA changes through the entire range of values each month. Since its orbit is inclined to the CE, its dec also changes.