Astronomy 1 - Lecture for September 21, 1998
Date: Monday September 21, 1998
Text Chapters (Chaisson) = #1
HOMEWORK
(Homework Assignment assigned last Wednesday due on Wednesday Sept 23)
EQUIPMENT AND VISUAL AIDES
TRANSPARENCIES
- Siderial Time and Hour Angles
- Precession of the Equinox
- Sundial Time
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Astronomical Events:
New Moon - Sept 20 (Sunday) Moon at Apogee on 23rd = High Tides
Vernal Equinox - Sept 23 (Wednesday)
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LECTURE
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I. Siderial Time (See Previous Notes (Sept 16) also)
Hour Angle of Vernal Equinox
(moves westward wrt Sun by 0.986 deg/day)
(rises earlier each day - siderial day shorter)
Motion of Earth in orbit and Rotation of Earth -
Siderial Day = Solar Day - 4 minutes
-- relation of ST and Hour Angle of a Star (or Sun) DIAGRAM
==> ST = HA + RA <== Useful formula
EXAMPLE 1: Find ST at 8pm ADT tonight (approx)
HA(sun) = 8 - 1 (daylight) = ~7 h
RA of Sun (near Autumnal Equinox = ~12 h )
ST = 7 h + 12 h = 19 h Siderial Time
EXAMPLE 2: Find Hour angle of Arcturus at 8 pm ADT tonight
RA (arcturus) = 14.25 h
HA = ST - RA
= 19 h - 14.25 h = 4.75 h ( = 71 degrees)
Also SEE MY Java Script Page
"Calculations of Julian Day, Siderial Time, Equation of Time and Longitude Offset"
This page will do the calculation for you. Formulas are embedded in the web page
(DO NOT USE THE SIDERIAL TIME CALCULATION - I HAVE TO CORRECT AN ERROR -)
I. Time Zones (All discussed previous lecture)
- Local Apparent Solar Time (Sundial time)
hour angle of the true Sun
- Local Mean Solar Time
hour angle of the mean Sun
Equation of Time
> Changing declination
fastest at solstices (Jun, Dec)
= Sun ahead in summer, winter
slowest near equinoxes (Mar, Sep)
= Sun slow in spring, fall
> Elliptical Orbit of Earth
fastest at perihelion (Jan)
= Sun ahead in winter
slowest at aphelion (Jul)
= Sun late in summer
==> (DIAGRAM of EQUATION OF TIME)
==> SUNDIAL EXAMPLE
Sundial Time = 3:30 pm on Sept 22 in Wolfville
Wolfville late by 17 min
Sundial slow by 17 min
3:30 +:17 = 3:47
Transit Time = 11:55 (Sun Fast by 7 min)
Sundial fast by 7 min
3:47 -:07 = 3:40 pm AST
Daylight time = Standard time + 1 hour
3:40 + 1:00 = 4:40 pm
IV. Standard Time
Effect of Longitude relative to Time Zone meridian
Wolfville: W64 22' 10" 1deg = 4 min time
Sunset/rise later by (4+22/60) * 4 = 17.5 min
than Louisburg, NS at W60
Quebec City: W 71
When does the sun rise if predicted 7 am EST
(Std meridian = 5*15 = 75)
diff = 75 - 71 = 4 degree East
Sunrise earlier at Quebec by 4*4 = 16 min
7:00 - :16 = 6:44 am EST
-- Precession of the Axis of Rotation of the Earth (26,000 years)
Gyroscope Demo
Variation of North Star position (
Show Transparency indicating where NCP was)
Change in RA, dec of celestial objects (Epochs)
50"/year = 360deg*60*60/26,000
[declination changes by a smaller amount depending on it value]
Tropical (365.2422 days) [equinox to equinox]
Siderial Year (365.2564 days) [star back to star]
365.2565 - 365.2422 = 0.0143 days
From 365 days/26,000 = 0.014 days difference
- Motion of the Moon and Phases
==>Lunar Phases JAVA PAGE Help
Diagram (transparency)
example: What approx time does the 1st quarter Moon set? ....
90 deg behind Sun so set 6 hrs after the Sun
Where is the Full Moon at Sunset? .... Rising in the East
- Siderial and Synodic Periods of the Moon
- Advance of Moon Set
- Harvest Moon
Siderial Period = 27.3 days (From absolute position back to that position)
Synod Period = 29.5 days (New Moon to New Moon)
When things move in the same direction:
1/P(synodic) = 1/P(siderial) - 1/P(year)
[synodic - siderial relation]
= 1/27.3 - 1/365.24 = 0.03389 = 1/29.5
Moon Motion among the Stars = 360deg/27.3 days
= 13.19 deg/day = 0.55 deg/hour
(~1 diameter/ hour)
The Moon Moves 13.2 deg/day eastward while the Sun move 1 deg/day eastward.
The Earth has to rotate 13.2 degrees farther to have Moon rise.
Delay in Moon rise /day = 13.2/15 hours = 0.88 = 52.8 minutes
Harvest Moon Geometry (exercise next week)
Moons Orbit
- Phase of Moon and Rotation of the Earth
- Shadow ot the Moon --> Solar Eclipse
- Shadow of the Earth --> Lunar Eclipse
Inclination of Orbit (5 deg) to ecliptic
Eccentricity of Orbit = 0.055 (Perigee 363,000 km, Apogee 405,000 km)
Moon 28.3 'arc Apogee, 33.5' arc Perigee
DIAGRAM of Moon's Angular Size
Line of Nodes (2 - 6 months apart)
AT PRESENT Eclipse region is Feb,Mar and Aug,Sep (1998)
(Solar Eclipse region is slightly bigger)
due to motion of the line of nodes during the year.
-- Lunar Eclipse (Example Nov 18, 1994 [overhead]) Moon moves 1/2 degree/hour
- requires 1 hour to move across the Penumbra and 2 hours to move through
the Umbra (2 hours total max)[transparency of Hanbook diagram]
Solar Eclipse (Example Feb 26, 1998 through the Carribean)
Speed of Paths - Earth is rotation West ot East (0.46 km/s at equator)
- Moon is moving relative to the Earth West to East (0.95 km/s)
So the Shadow sweeps West to East at about 0.95 - 0.46 ~ 0.5 km/s
-- How big is the shadow?
The Feb 26, 1998 Eclipse is 3.5 minutes long - Size = 0.5km/s*210 s =
105 km shadow (Umbral)
ECLIPSE PAGE of Fred Espenak
Map of August 11, 1999 Total Solar Eclipse off Nova Scotia
-Use ECU to show the Aug 11, 1999 Eclipse
Solar Eclipse PHOTOGALLERY - Fred Espenak
-- Saros Cycle
Regression (Precession) of the Nodes of the Moon's Orbit
[Think of the orbiting Moon as a top that has the pull of the Sun on it.]
- Eclipse season moves 20 days earlier every year
Period = 18.61 years = 6797 days = 230.2 Lunar Periods (29.5 days)
Draconic Month (period from node to node = 27.21222 days
Synodic Month (New Moon to New Moon) = 29.53059 days
NOTE: 223 Synodic Months = 242 Draconic Months = 6585.32 days
~ 18years 11 days
(note the 1/3 day left over)
Every 18 years there is a repeat of the geometry of the previous Solar Eclipse.
(also Lunar)
except that it occurs 1/3 of the way further around the Earth.
Also they gradually move north and are lost. - so they do not go on forever.
Examples: June 20, 1955
June 30, 1973
July 11, 1991
July 22, 2009
Aug 2, 2027
Aug 12, 2045
There are of course other Saros Series going on at the same time.
L.Bogan - Sept 20, 1998