Download Solar Eclipses

PHYS 3380 - Astronomy
I will be in Bulgaria at a science conference next
week. Dr Lindsay King will be teaching the classes
on Monday and Wednesday in my absence.
PHYS 3380 - Astronomy
The Small-Angle Formula
- a mathematical approximation
- relates the linear size
(D) of an object to its
angular size (α) and its
distance from the
observer (d)
- is a valid approximation
if α is small.
d
α
D
 
D  2d sin  
2 
  

sin   (when
is small)
2  2
2
so
D  d
 is given in arcseconds (206, 265 is the
number of arcseconds in a radian)
D  206,265"
 =  
d 
rad
For the moon :
 3478 km  206,265"
 = 
 1866"

rad
384,400 km 
For the Sun :
 1.39  10 6 km  206,265"
 = 
 1916"

8
rad
1.496  10 km
PHYS 3380 - Astronomy
Solar Eclipses
We are fortunate - the sun appears approximately as large in the
sky (same angular diameter ~ 0.50) as the moon.
 When the moon passes in front of the sun, the moon can cover
the sun completely, causing a total solar eclipse.
PHYS 3380 - Astronomy
Types of Solar Eclipses
Total
If the eclipse occurs when the Moon
is close to the Earth - umbra covers
small area of Earth’s surface (no more
than 270 km in diameter) - anyone in
this area sees a total eclipse.
Partial
Anybody in penumbral shadow (about
7000 km in diameter) will see a partial
eclipse.
Annular
If the eclipse occurs when the Moon
is far from the Earth - the umbra does
not reach the Earth, only the penumbra.
Anyone in this area directly behind the
umbra sees an annular eclipse
PHYS 3380 - Astronomy
Evolution of a Partial Solar Eclipse Animation
PHYS 3380 - Astronomy
Evolution of a Total Solar Eclipse Movie
PHYS 3380 - Astronomy
Earth and Moon’s Orbits Are Slightly Elliptical
Apogee =
position furthest
away from Earth
Perihelion = position
closest to the sun
Earth
Perigee = position
closest to Earth
Moon
Sun
(Eccentricities greatly exaggerated!)
Aphelion
= position
furthest
away
from the
sun
PHYS 3380 - Astronomy
Annular Solar Eclipses
When Earth is near perihelion, and
the moon is near apogee, we see
an annular solar eclipse.
Perigee
Apogee
Perihelion
Aphelion
The angular
sizes of the
moon and the
sun vary,
depending on
their distance
from Earth.
PHYS 3380 - Astronomy
Almost total, annular eclipse of May 30, 1984
PHYS 3380 - Astronomy
Eclipses Twice A Month? Animation
Why don’t we have eclipses every new and full Moon?
PHYS 3380 - Astronomy
Moon’s orbit tilted 5° to ecliptic plane
- Crosses ecliptic plane only at the two nodes
- Eclipse possible only when full/new occur near nodes
PHYS 3380 - Astronomy
Moon’s Orbital Tilt
PHYS 3380 - Astronomy
Conditions for Eclipses
The moon’s orbit is inclined against the ecliptic by ~ 50.
A solar eclipse can only occur
if the moon passes a node
near new moon.
A lunar eclipse can only occur if
the moon passes a node near
full moon.
PHYS 3380 - Astronomy
Eclipse Seasons
Eclipse season - a period in a given year during which the
Earth-Sun line falls near the line of nodes of the Moon’s
orbit, so that lunar and solar eclipses can take place happens twice a year
PHYS 3380 - Astronomy
Eclipse Seasons
If New Moon takes place within about
17° of a node, then a solar eclipse will be
visible from some location on Earth.
The Sun makes one complete circuit of
the ecliptic in 365.24 days
• average angular velocity is 0.99°
per day.
• takes 34.5 days for the Sun to cross
the 34° wide eclipse zone centered
on each node.
• Moon's orbit with respect to the Sun
has a mean duration of 29.53 days so
there will always be one and possibly
two solar eclipses during each 34.5day interval when the Sun passes
through the nodal eclipse zones.
These time periods are called eclipse
seasons
PHYS 3380 - Astronomy
So eclipses should be easy to predict - every six months at
nodes when Moon crosses the ecliptic. However, the
Moon’s orbit also precesses making prediction difficult.
Moon’s Orbital Precession Animation
Eclipse seasons recur every 173.31 days (~19 days earlier
each year) and last about 24 days for lunar eclipses and about
37 days for solar eclipses.
PHYS 3380 - Astronomy
Predicting Eclipses
Solar eclipse one of the most awe inspiring events
in human history - difficult for ancients to predict
because of orbital precession and narrow region of
occurrence. First historical solar eclipse date
precisely known - May 28, 585 BC. Opposing
armies in Turkey massing for battle - eclipse
frightened them so much, they put down their
weapons and signed a treaty.
Combination of changing dates of eclipse seasons
(Lunar orbital precession) and 29 1/2-day cycle of
lunar phases - solar eclipses occur in 18 year, 11
1/3 day cycle - saros cycle.
PHYS 3380 - Astronomy
Saros Cycle
Eclipses repeat
- after one saros cycle, moon and nodes of its orbit return to
same place wrt the sun
- one saros contains 223 lunar months
- changes location on Earth because of the extra 1/3 day moves 8 hours of longitude west of the previous eclipse
- repeats in same location after 3 saros cycles
PHYS 3380 - Astronomy
Paths of Total Solar Eclipses
Paths of same color represent successive saros cycles.
PHYS 3380 - Astronomy
PHYS 3380 - Astronomy
Solar Eclipses Through 2020
PHYS 3380 - Astronomy
Annular Eclipse of September 1, 2016
https://youtu.be/yqQ3bvVQuD8
PHYS 3380 - Astronomy
Tides
The gravitational attraction of the Moon varies as the square of the
distance (Newton’s Law of Gravitation) - gravity stronger on side facing the
Moon than on opposite side. The Moon pulls the ocean water towards it on
facing side - creates tide - and pulls the Earth away from the ocean water
on the other side - reason for tides twice a day. Time of tides varies by 50
min per day - Moon at its highest point every 24 hrs 50 min because Moon
orbits Earth while Earth rotates.
PHYS 3380 - Astronomy
The Sun also causes tides - why
are they weaker than the
Moons’?
Neap tides - when Moon’s and
Sun’s gravitational forces work at
right angles
Spring tides - when
Moon’s and Sun’s
gravitational forces
add up
PHYS 3380 - Astronomy
Tidal Bulge
Because the Earth rotates, friction drags the tidal bulges off of the EarthMoon line.
PHYS 3380 - Astronomy
Tides
PHYS 3380 - Astronomy
The Moon pulls on tidal bulge - slows Earth’s rotation
The excess mass in Earth’s tidal bulge exerts a gravitational attraction on the
Moon that pulls the Moon ahead in its orbit - Moon moves farther away Conservation of Angular Momentum
PHYS 3380 - Astronomy
The Tidally-Locked Orbit of the moon
The Earth also exerts
tidal forces on the moon’s
rocky interior.
 It is rotating with the
same period around its
axis as it is orbiting Earth
(tidally locked).
 We always see the
same side of the moon
facing Earth.
PHYS 3380 - Astronomy
Astronomical Time Periods
PHYS 3380 - Astronomy
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
PHYS 3380 - Astronomy
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.
PHYS 3380 - Astronomy
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.
PHYS 3380 - Astronomy
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.
PHYS 3380 - Astronomy
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. Discrepancy called Equation
of Time - leads to analemma - shape of Sun’s yearly path in the sky.
PHYS 3380 - Astronomy
The Analemma
Images of the Sun at same time
at 8 - 10-day intervals over the
course of a year:
– Altitude variation due to
annual north-south
oscillation of the Sun’s
declination angle - axial tilt
– East-west spread due to
variation in Sun’s motion wrt
to the stars - axial tilt and
ellipticity
–Distortion of figure 8 due to
ellipticity of Earth’s orbit.
In northern hemisphere - if Sun’s position east of where your watch
indicates it would be, Equation of Time is negative. If Sun to the west, the
Equation of Time is positive.
PHYS 3380 - Astronomy
The analemma shows where the sun is at any given time of day, on any
day of the year - it rises, crosses the sky, and sets. From northern
latitudes, the analemma slants upward and to the left at "sunrise" and
upward and to the right at "sunset". (The analemma is vertical at local
noon.)
Why do the earliest sunset, latest sunrise, and shortest day of the year
occur on different dates?
PHYS 3380 - Astronomy
Latest sunrise occurs when the last part of the analemma rises - this doesn’t
happen when the sun is "at the bottom" of the analemma (December 21st)
but a few days later (January 3th). Earliest sunset occurs when the first part
of the analemma sets below the western horizon. Again, occurs a few days
(December 8th) before the sun reaches "the bottom" of the analemma
(December 21st). Same reasoning for solstice.
PHYS 3380 - Astronomy
Often printed
on globes
and…
Turned vertical, the analemma
can be used to determine solar
declination and Equation of Time
sundials