Transcript NATS1311_091108_bw - The University of Texas at Dallas

NATS 1311 - From the Cosmos to Earth
Lunar Phase Terminology
Phases of the Moon’s 29.5 day cycle
new
crescent
first quarter
gibbous
waxing
full
gibbous
last quarter
crescent
waning
NATS 1311 - From the Cosmos to Earth
New Moon  First Quarter  Full Moon
NATS 1311 - From the Cosmos to Earth
Full Moon  Third Quarter  New Moon
NATS 1311 - From the Cosmos to Earth
Earthshine
The dark portion of the lunar face is not totally dark - you can see the
outline of the full face of the Moon even when the Moon is not full - in
particular the crescent phase.
Because the crescent phase is nearly a new moon as seen from Earth, the
Earth is nearly full as viewed from the moon.
The light of Earth illuminates the night moonscape - just as the full moon
illuminates the Earth landscape.
Because Earth is much larger than the Moon, the full earth is much bigger
and brighter in the lunar sky than the full moon is in Earth's sky. This faint
light illuminating the “dark” portion of the Moon's face is often called the
ashen light or earthshine.
NATS 1311 - From the Cosmos to Earth
The “Dark” Side of the Moon
Near Side
Far Side
The Moon is tidal locked with the Earth - one side faces the Earth at all
times - term dark side would better be called the far side - the hemisphere
that never can be seen from Earth. Was not seen until first spacecraft
orbited the moon and sent back pictures of the far side.
NATS 1311 - From the Cosmos to Earth
Names of the Full Moons
January
February
March
April
May
June
July
August
September
October
November
December
Wolf Moon
Snow Moon
Worm Moon
Pink Moon
Flower Moon
Strawberry Moon
Buck Moon
Sturgeon Moon
Harvest Moon
Hunter's Moon
Beaver Moon
Cold Moon
NATS 1311 - From the Cosmos to Earth
Blue Moon
Modern folklore - a Blue Moon is the second full Moon in a calendar month can occur in any month but February, which is always shorter than the time
between successive full Moons (29 1/2 days).
Ecclesiastical version - occurs when a season has four full Moons, rather
than the usual three - the third is the Blue Moon - found only in February,
May, August, and November, one month before the next equinox or solstice.
The result of following rules laid down as part of the Gregorian calendar
reform in 1582. The ecclesiastical vernal (spring) equinox always falls on
March 21st, regardless of the position of the Sun. Lent begins on Ash
Wednesday, 46 days before Easter, and must contain the Lenten Moon,
considered to be the last full Moon of winter. The first full Moon of spring is
called the Egg Moon (or Easter Moon, or Paschal Moon) and must fall within
the week before Easter. Only by naming the third moon the Blue Moon will
the names of the other full Moons, such as the Moon Before Yule and the
Moon After Yule, fall at the proper times relative to the solstices and
equinoxes.
NATS 1311 - From the Cosmos to Earth
Astronomical Time Periods
NATS 1311 - From the Cosmos to Earth
Definitions of a Day
•
Sidereal Day
– Time from one transit of a star across the meridian to the next.
– Related to the Stars
•
Apparent Solar Day – Time from one transit of sun across the meridian to the next.
– From one high noon to the next
– Related to the sun
•
Mean Solar Day
– Time between successive transits of mean sun.
– Average of apparent solar days over one year.
– Defined to be 24 Hours
NATS 1311 - From the Cosmos to Earth
Sidereal Day
Sidereal - “related to the stars” - the time it takes for any star to make a
circuit of the sky - about 23 hours 56 minutes. Measure of the Earth’s
rotation - varies about 1 second in 45,000 years. Today defined relative to
an ensemble of extra-galactic radio sources.
NATS 1311 - From the Cosmos to Earth
Solar Day
The time it takes for the Sun to make one circuit around the local sky length varies over course of year (up to 25 seconds longer or shorter)
but averages 24 hours.
NATS 1311 - From the Cosmos to Earth
Why is a Sidereal Day Shorter than a Solar Day?
One full rotation represents a sidereal day - but while orbiting the
Sun, Earth travels in its orbit (about 1 degree per day). So the Earth
must rotate slightly farther to point back at the Sun - solar day.
NATS 1311 - From the Cosmos to Earth
Mean Solar Day
Length of solar day varies over course of year - averages about 24 hours mean solar day.
Two reasons for variance.:
1. Earth's orbit is not a perfect circle - it’s an ellipse - Earth
moves faster when it is nearest the Sun and slower when it is
farthest from the Sun.
2. Earth's axial tilt - the Sun appears to move at an angle to
equator during the year - apparently moves fast or slow depending
on whether it is apparently far from or close to the equator.
Apparent solar days are shorter in March and September than
they are in June or December.
Solar day may differ from a mean solar day by as much as nearly 22 s
shorter to nearly 29 s longer. Because many of these long or short days
occur in succession, the difference builds up to as much as nearly 17
minutes early or a little over 14 minutes late.
NATS 1311 - From the Cosmos to Earth
Synodic Month vs Sidereal Month
Synodic month
- the time it takes for the moon to complete its cycle of
phases - or to come back to the same position with respect
to the Earth-Sun line - about 29 1/2 days
Sidereal month
- the time it takes for for the moon to complete one orbit
relative to the position of the stars - about 27 1/3 days
NATS 1311 - From the Cosmos to Earth
Synodic vs Sidereal Month Animation
NATS 1311 - From the Cosmos to Earth
Tropical vs Sidereal Year
Sidereal year
- time it takes for Earth to complete one orbit relative to the stars
or the time for the Sun to return to the same position in respect to
the stars - the orbital period of the Earth
Tropical year
- calendar year - time from spring equinox to spring equinox about 20 minutes shorter than a sidereal year - because of
precession. Changes not only the orientation of Earth’s axis but
the location in Earth’s orbit of the seasons. 26,000 year
precession period means that location of solstices and equinoxes
among the stars shifts by 1/26,0000 around the orbit.
1/26,000th of a year is about 20 minutes.
NATS 1311 - From the Cosmos to Earth
A tropical year is about 365.242191 days long - requires leap year every 4
years to keep solstices and equinoxes on same calendar date.
After 100 years, in error by more than 3/4 day:
100 tropical years - (75 years + 25 leap years) = 36524.2191-36525 =
0.7809 days
Skip leap year every 100 years
After 400 years error of nearly a day:
400 tropical years - (304 regular years + 96 leap years)=146,096.876 146,096 = 0.876
So add a leap year every 400 years.
Earth’s rotation slowing - tidal drag - add about 29 leap seconds every 100
years.
NATS 1311 - From the Cosmos to Earth
Leap Seconds
Ephemeris Time - the average mean solar time between 1750 and
1890 (centered on 1820) - the period during which the observations on
which Simon Newcomb's Tables of the Sun, which formed the basis of
all astronomical ephemerides from 1900 through 1983, were
performed.
Universal Time (UT) - timescale based on the rotation of the Earth. - a
modern continuation of the Greenwich Mean Time (GMT), i.e., the
mean solar time on the meridian of Greenwich, England.
Ephemeris Time and Universal Time are different because the
Earth’s rotation is slowing down due primarily due to tidal friction
ΔT - the time difference obtained by subtracting Universal Time from
Ephemeris Time.
NATS 1311 - From the Cosmos to Earth
Initially, second defined as 1/86,400th of a mean solar day in the year
1820. Now use stable atomic clocks
one second =time for a cesium atom to make 9,192,631,770
vibrations
Rotation of Earth slowing down
- tidal friction, atmospheric circulation, internal effects, transfer of
angular momentum to the Moon orbital motion, etc…
To a first approximation
- tidal forces slow Earth's rate of rotation by 2.3 ms/day/cy.
- melting of continental ice sheets at the end of the last ice age
removed their tremendous weight
- allowed land under them to begin to isostatically rebound
upward in the polar regions - continues to this day
- causes Earth's rate of rotation to speed up by 0.6 ms/day/cy.
The net tidal acceleration or the change in the length of the mean solar
day is +1.7 ms/day/cy.
NATS 1311 - From the Cosmos to Earth
dT
 (1.7ms/day /cy)t
dt
t in centuries
dT  (1.7ms/day /cy)tdt
 dT  1.7ms/day /cy  tdt
1 2
T  (1.7ms/day /cy) t
2
1.7ms/day /cy  62s /cy 2
T  31s /cy 2 t 2
year 1820
100
2


year
1820
T  31s /cy 2 

 100

Let t 
NATS 1311 - From the Cosmos to Earth
Actual T varies significantly because of aforementioned effects.
- all values of ΔT before 1955 depend on observations of the
Moon, either via eclipses or occultations
- now, orientation of the Earth relative to an inertial reference
frame formed by extra-galactic radio sources is used
NATS 1311 - From the Cosmos to Earth
Modern Time Scales
Temps Atomique International (TAI) or International Atomic Time weighted average of the time kept by about 200 cesium atomic clocks
in over 50 national laboratories worldwide - available since 1955
UT1 - timescale defined by the Earth's rotation
- computed by the International Earth Rotation and Reference
Systems Service (IERS).
- TAI was defined such that TAI = UT1 on January 1, 1958.
Coordinated Universal Time (UTC) - basis for legal time worldwide,
- TAI became the international standard on which UTC is
based on January 1, 1972.
- UTC always differs from TAI by an integral number of
seconds.
- in mid 2005, behind TAI by 32 seconds
- difference due to leap seconds periodically inserted into
UTC to keep it from drifting more than 0.9 seconds from UT1
23 leap seconds since first leap second added in 1972 - last was
added on December 31, 2005 - first in 7 years