The Sun and Moon

1
Time and Calendars
2
A.M vs. P.M.
Noon is defined as the time for a local observer
when the Sun crosses the meridian, which is the
line in the sky passing overhead from north to
south. A.M. Ante Meridian (before the Sun
crosses the meridian) P.M. Post Meridian (after
the Sun crosses the meridian)
3
The Length of a Day
The length of time for the Earth to complete one
full rotation is a sidereal day, which is 23
hours, 56 minutes, and 4 seconds. The length of
time from one noon until the next noon is a solar
day, which is 24 hours, on average. The solar
day is a little longer than the sidereal day
because the earth is revolving around the Sun
while it rotates.
4
Time Zones
Due to the curvature of the Earth, local noon
differs with longitude. Time zones account for
this difference. Each of 24 time zones is an
average of 15 degrees wide in longitude.
5
Time Zones
Everyone in a time zone records noon at the same
time, even though the Sun crosses the meridian at
this time only at the center of the zone. The Sun
crosses 30 min earlier or later than official
noon near the edges of the zone.
6
Length of a Month
The month is related to the Moons orbit around
the Earth, and can be measured two ways, just
like the day. The time for the Moon to complete
one full orbit around the Earth is a sidereal
month, which is 27.32 days. The length of time
for the Moon to complete one full cycle of phases
(e.g., from one new moon to the next one) is a
synodic month, which is 29.53 days.
As with the sidereal day and solar day, the
synodic month is a little longer than the
sidereal month because the Earth is revolving
around the Sun as the Moon orbits the Earth.
animation of sidearal and synodic month
7
Length of a Year
And once again, there are two ways to measure the
length of a year. The length of time for the
Earth to complete one full orbit around the Sun
is a sidereal year, which is 365.25637 days. The
length of time to complete a full cycle of
seasons (e.g., from one vernal equinox to the
next one) is a tropical year, which is 365.24219
days. The tropical year is different from the
sidereal year because of the precession of the
Earths spin axis, which causes the first day of
a given season to slowly move around the Sun over
thousands of years. Our calendar is based on
the tropical year. In other words, June 21 is
defined as the time of the summer solstice, when
the north pole is pointed in the direction of the
Sun.
8
Ancient Calendars

• Ancient people used calendars to
• Determine when to plant and harvest crops
• Determine when animals would migrate
• Set religious and secular holidays
• Since they had no mechanical means to mark time,
  they used the sky.
• Our modern calendar and clocks are based on these
  systems.

9
Lunar Calendars
Since the phases of the Moon are a natural way of
judging the passing of time, they were the basis
of the first calendars used by the Greeks,
Sumarians, Chinese, and other civilizations. 1
synodic month 29.53 days, so the Greeks
alternated between 29 and 30 days for their
months. 12 synodic months 354 days, so one
lunar year was 11 days short of one solar year.
Various civilizations have adopted complex
schemes of adding extra days and months to align
the lunar and solar calendars.
10
Solar Calendars
Egypt developed the first solar calendar (4000
BC), which consisted of 12 months, each with 30
days, plus 5 extra days to add up to 365 days.
They measured the solar year to be 365.25 days,
so Egyptians eventually added 1 extra day each 4
years (238 BC), which is the leap year. Julius
Caeser adopted the Egyptian leap year in 48 BC
for the Roman calendar. He also moved the first
day of the year from March to January. However,
a calendar with 365.25 days in a year still isnt
exactly right. Over a period of 128 years, this
calendar slips by 1 day relative to the true
solar year. By 1582, the vernal equinox had
slipped from March 21 to March 11. So Pope
Gregory III dropped 10 days from the calendar of
1582 the day after October 4 was October 15. To
correct this slippage in the future, only century
years divisible by 400 were leap years.
11
Modern Calendars and Clocks
But the Gregorian calendar still isnt perfect.
Its year differs by the true solar year by 25.96
seconds. We now use atomic clocks to record time
exactly, and leap seconds are added periodically
to keep the calendar properly aligned.

• The basic unit for time measurement is now the
  second
• The second used to be defined as (1/60) of (1/60)
  of (1/24) of the mean solar day
• Today, the second is defined using atomic clocks
• 1 second 9,192,631,770 cycles of a specific
  atomic transition in the cesium 133 atom
• 1 sidereal year 3.1558 x 107 s