Download MOVEMENT OF THE SUN ON THE SKY

MOVEMENT OF THE SUN ON THE SKY
ASTRONOMICAL VIEW OF THE WORLD – LECTURE 3
JONI TAMMI
BASIC CELESTIAL MECHANICAL PHENOMENA
Outline of the day
• Previous assignments
• Very basics of planetary motion
• How does the Sun behave from a terrestrial
point of view?
• Why is this important to be aware of?
LAST WEEK’S ASSIGNMENTS
1. Astronomical distances
2. Moon phases MCQ
3. Kepler’s laws
Speed of light:
300 million metres each second
Year:
31.6 million seconds
Light-year:
9.5 × 1015 m
Sidenote: astronomer’s don’t really use
light-years with large distances, but parsecs
(1 pc = 3.26 ly), and kpc, Mpc, Gpc.
LAST WEEK’S ASSIGNMENTS
1. Astronomical distances
2. Moon phases MCQ
3. Kepler’s laws
Grading:
0p No answer, completely misunderstood,
or clearly no effort.
1p Some roughly correct distance found for
1-3 of the sources, and equivalent time
mentioned in the answer. If only distances
mentioned for sources without any time
consideration, then 1 point.
2p For all four sources distance/time, with
also discussion/mentioning of what
happened when the photons left (no
matter how short).
a) the North Star (Polaris, Pohjantähti)
~1580 CE – Johannes Kepler gets
interested in astronomy
b) the centre of the Milky Way
24 000 BCE – Homo sapiens vs
Neanderthals
c) Andromeda galaxy
2.5 mya (million years ago) – first hominids
d) the radio galaxy Cygnus
600 mya – the first animals
ASSIGNMENT QUIZ: MOON PHASES AROUND THE WORLD
Which of the
following claims
are true?
a) Everyone on Earth sees the same Moon phase during a given night.
Select one or
more:
c) Each lunar (Moon) eclipse is visible only from a small region on Earth.
b) When we in Finland see a growing crescent, people in Australia see
decreasing crescent.
d) If you have a mnemonic for the direction of moon phases, you need to
reverse it in the southern hemisphere.
e) Lunar (Moon) eclipse can only happen during new moon.
f) The far side of the Moon (the one not visible to us) is called the "dark
side" because it only sees the Sun during a solar eclipse.
g) Solar eclipse can only happen during new moon.
ASSIGNMENT QUIZ: MOON PHASES AROUND THE WORLD
Which of the
following claims
are true?
a) Everyone on Earth sees the same Moon phase during a given night.
Select one or
more:
c) Each lunar (Moon) eclipse is visible only from a small region on Earth.
b) When we in Finland see a growing crescent, people in Australia see
decreasing crescent.
d) If you have a mnemonic for the direction of moon phases, you need to
reverse it in the southern hemisphere.
e) Lunar (Moon) eclipse can only happen during new moon.
True
f) The far side of the Moon (the one not visible to us) is called the "dark
side" because it only sees the Sun during a solar eclipse.
False
g) Solar eclipse can only happen during new moon.
ASSIGNMENT QUIZ: THE NEXT MOON PHASE
The Moon looks like in the image below
(about 50% lit, from the left). What does
the Moon look like after one week?
Phases (each after ~one week):
1. New moon
2. Growing half
3. Full moon
4. Decreasing half
Image shows decreasing half,
so after a week, we have new moon.
ASSIGNMENT QUIZ: MOON IN A FEW NIGHTS
Assuming you're in Finland and the Moon
looks like in the attached picture (about
60% lit, from the right), what will it look
like in a few nights?
We’re a couple of days past growing
half moon, heading towards a full
moon within a week.
So in a few nights it will look like
full moon.
ASSIGNMENT QUIZ: EARTHRISE
If you are standing on the Moon, would
you see the Earth rise and set in a similar
way the Moon does as seen on Earth?
a) Yes, because of symmetry: if the Moon
rises and sets as seen from Earth, then the
Moon rises and sets as seen from the
Moon.
b) Yes, because the Moon rotates around its
axis, so everything rises and sets in the
same way than on Earth.
c) No, because the direction of the Earth on
the Moon sky only depends on where you
are located on the Moon, so the Earth
doesn't rise or set.
d) No, because there is no atmosphere on the
Moon, so objects don't rise and set there.
ASSIGNMENT QUIZ: EARTHRISE
If you are standing on the Moon, would
you see the Earth rise and set in a similar
way the Moon does as seen on Earth?
a) Yes, because of symmetry: if the Moon
rises and sets as seen from Earth, then the
Moon rises and sets as seen from the
Moon.
b) Yes, because the Moon rotates around its
axis, so everything rises and sets in the
same way than on Earth.
c) No, because the direction of the Earth on
the Moon sky only depends on where you
are located on the Moon, so the Earth
doesn't rise or set.
d) No, because there is no atmosphere on the
Moon, so objects don't rise and set there.
ASSIGNMENT QUIZ: EARTHRISE
If you are standing on the Moon, would
you see the Earth rise and set in a similar
way the Moon does as seen on Earth?
a) Yes, because of symmetry: if the Moon
rises and sets as seen from Earth, then the
Moon rises and sets as seen from the
Moon. (Not a symmetric situation)
b) Yes, because the Moon rotates around its
axis, so everything rises and sets in the
same way than on Earth. (Except Earth)
c) No, because the direction of the Earth on
the Moon sky only depends on where you
are located on the Moon, so the Earth
doesn't rise or set.
d) No, because there is no atmosphere on the
Moon, so objects don't rise and set there.
(Atmosphere is irrelevant)
LAST WEEK’S ASSIGNMENTS
1. Astronomical distances
2. Moon phases MCQ
3. Kepler’s laws (next)
PART 1:
HOW DOES THE EARTH MOVE IN SPACE
TWO MAIN COMPONENTS
1. Around the Sun
2. Around the axis
ASSIGNMENT: KEPLER’S LAWS
Explain the essence of the laws to your 7-year
old niece who is smart and knows that planets
go around the Sun, but who doesn't know
what focus or period or ellipse mean
Grading:
0p No answer, completely misunderstood,
or clearly no effort.
1p The answer contains 1-2 of the following
ideas (see below) in any form.
2p The answer contains the following ideas
(see below) in any form.
The essential ideas:
•
Planets go around the sun
•
The closer the planet is to the sun,
the faster it moves
•
The year of the planet is longer
the farther it is from the Sun
• Planets go around the sun, and it looks like
a squished circle. The bigger the circle, the
longer it takes to go around the
sun. Sometimes the planet are closer to the
sun, then they move faster. Sometimes the
planet is far away from the sun, then they
slow down.
• 1st law says that planets' paths around the
Sun are circles or ovals.
2nd law says that planets move faster when
nearer to the Sun.
3rd law says that length of a year on
different planets are linked, depending on
the distance from the Sun.
1. Around the Sun
FIRST LAW OF PLANETARY MOTION
Ellipse,
with the Sun
in focus
• Focus (foci), one empty
• Eccentricity
• Perihelion, aphelion
1. Around the Sun
KEPLER’S SECOND LAW
Equal area
in equal time
•  Far away, goes slower
1. Around the Sun
KEPLER’S THIRD LAW
The bigger the orbit,
the longer the period
(longer way to go
+ going slower)
1. Around the Sun
TWO MAIN COMPONENTS
1. Around the Sun
• With respect to stars in 1 year
• Perihelion
• Closest to the Sun (0.89 AU)
• Moving faster (30.3 km/s)
• 4.1.2017
• Aphelion
• Farthest from the Sun (1.02 AU)
• Moving slower (29.3 km/s)
• 3.7.2017
1. Around the Sun
TWO MAIN COMPONENTS
1. Around the Sun
• Orbital plane  Ecliptic
• Projection of the plane
of the solar system
• Sun & planets always
on/near ecliptic
THE ZODIAC
• Sun (and the Ecliptic)
always passes
through the same
constellations.
• Zodiac
”Circle of animals”
• Origin from astrology:
• 12 ”Sun signs”
in the West
• 24 ”Solar terms”
in the East
2. Around the axis
TWO MAIN COMPONENTS
1. Around the Sun
2. Around the axis
• With respect to stars in 1 year
• With respect to the Sun in 1 day
• Perihelion
• Closest to the Sun (0.89 AU)
• Moving faster (30.3 km/s)
• 3.1.2016
• Aphelion
• Farthest from the Sun (1.02 AU)
• Moving slower (29.3 km/s)
• 4.7.2016
2. Around the axis
ROTATION OF THE PLANET
One rotation in one day
= 360° in 24 h
| : 24
= 15° in 1 h
| : 15
=
1° in 4 min
 Sky rotates at the same
speed 15°/ h
Celestial
North pole
2. Around the axis
• Altitude of the pole = Latitude
ROTATION OF THE PLANET
”Solar
system
north”
2. Around the axis
”Earth north”
23.5°
Axial tilt: 23.5°
Ecliptic
Plane of the Solar System
Wikiscient
@ Wikimedia
TILT OF EARTH’S AXIS  SEASONS
SPECIAL CASE: WINTER SOLSTICE (SOUTH SOLSTICE)
Sun below the
horizon whole day.
Last Sunday (17.1.)was
the first day for two
months when sun was
visible in Utsjoki.
Wikimedia
SPECIAL CASE: SUMMER SOLSTICE (NORTH SOLSTICE)
Wikimedia
PRECESSION: TILT OF THE AXIS CHANGES SLOWLY
26 000 years
1° per 72 years
Two effects
Image and Animation by Robert Simmon, NASA GSFC
Direction of
the axial tilt
Animation: http://earthobservatory.nasa.gov/IOTD/view.php?id=541
TWO EFFECTS OF THE PRECESSION
1. Pole star changes
Equinoxes shift
TWO EFFECTS OF THE PRECESSION
2. Equinoxes shift
SUN IN DIFFERENT CONSTELLATIONS
Aries April 18—May 13
Taurus May 13—June 21
Gemini June 21—July 20
Cancer July 20—August 10
Leo August 10—September 16
Virgo September 16—October 30
Libra October 30—November 23
Scorpius November 23—November 29
Ophiuchus November 29—December 17
Sagittarius December 17—January 20
Capricorn January 20—February 16
Aquarius February 16—March 11
Pisces March 11—April 18
MOVEMENT ON THE SKY – SUMMARY
Ecliptic (Solar system plane)
Celestial Equator
• Cycle: 1 year
• Cycle: 1 day
• Sun’s movement: ~ 1° / 1 day
• Sun’s movement: ~ 1° / 4 min
• Motion parallel to ecliptic
• Motion parallel to equator
• Direction changes,
depends on the time of the year
• Direction always East – South – West,
but depends on latitude of the observer
• Ecliptic coordinates
• Equatorial coordinates
• Sun and planets always on Ecliptic
• Rises from the east, highest in the south, sets in west
PART 2:
SUN’S MOTION ON THE SKY
THIS WEEK’S PRELIMINARY WORK
1. Sunrise and sunset directions
Espoo
DIRECTION OF SUNRISE/SET
Summer
solstice
Spring &
Autumn
equinoxes
Winter
solstice
http://www.gaisma.com/
http://www.sunearthtools.com/dp/tools/pos_sun.php
Utsjoki
DIRECTION OF SUNRISE/SET
http://www.gaisma.com/
http://www.sunearthtools.com/dp/tools/pos_sun.php
Tarja Trygg @ Aalto ARTS
www.solargraphy.com
Midsummer
Spring / Fall
Midwinter
Tunç Tezel http://apod.nasa.gov/apod/ap080922.html
DIRECTION OF SUNRISE/SET
-- MORE COMPLICATIONS
1. Daylight savings time
+1 hour in summer
2. Local sun time vs. timezone’s
mean sun time
Up to ~1 hour difference
3. Equation of time (orbital speed)
Up to ~15 minutes difference
DIRECTION OF SUNRISE/SET
-- MORE COMPLICATIONS
1. Daylight savings time
+1 hour in summer
2. Local sun time vs. timezone’s
mean sun time
Up to ~1 hour difference
3. Equation of time (orbital speed)
Up to ~15 minutes difference
DIRECTION OF SUNRISE/SET
-- MORE COMPLICATIONS
1. Daylight savings time
+1 hour in summer
2. Local sun time vs. timezone’s
mean sun time
Up to ~1 hour difference
3. Equation of time (orbital speed)
http://www.xkcd.com/1335/
Up to ~15 minutes difference
DIRECTION OF SUNRISE/SET
Local sun time is 12:00
-- MORE COMPLICATIONS
when the sun is exactly in
the south.
1. Daylight savings time
+1 hour in summer
2. Local sun time vs. timezone’s
mean sun time
”Solar midday” in
Otaniemi 2 minutes
earlier than in Metsähovi.
Up to ~1 hour difference
3. Equation of time (orbital speed) Our timezone’s mean
time is based on the 30°
Up to ~15 minutes difference
meridian
 Helsinki 20 minutes
behind.
20°
25°
30°
DIRECTION OF SUNRISE/SET
-- MORE COMPLICATIONS
1. Daylight savings time
+1 hour in summer
2. Local sun time vs. timezone’s
mean sun time
Up to ~1 hour difference
3. Equation of time (orbital speed)
Up to ~15 minutes difference
ANALEMMA
Caused by the varying
orbital speed of Earth
Summer
(North)
solstice
Caused by the
angle between
the horizon and
the Ecliptic
Winter
(South)
solstice
Tunç Tezel http://apod.nasa.gov/apod/ap131014.html
Length of the Day
ROTATION OF THE EARTH
With respect to the stars
With respect to the Sun
• From star-rise to star-rise
(actual rotation of the Earth)
• From sun-rise to sun-rise
(easy to see, but changes every day)
• Sidereal day: 23h 56m 4s
• Synodic day: 24h sharp (by definition)
SYNODIC DAY > SIDEREAL DAY
1 sidereal
day
SYNODIC DAY > SIDEREAL DAY
• 4-minute difference between the
sun and the stars
• I.e., any particular
star/constellation rises 4 minutes
earlier every day
-> Different consellations are
visible at different times of
the year
Same thing with the Moon
27.3 d to go around WRT
the Earth
29.5 d to go around WRT
the Sun (same phase)
1 sidereal
day
1 synodic
day
Length of the year
ORBIT OF THE EARTH
With respect to the stars
With respect to Sun
• Sidereal year:
365d 6h 9m 10s
365.2564 days
• Solar / tropical year:
365d 5h 48m 45s
365.2422 days
• Back to same place
WRT stars (universe)
• E.g. between two midsummers
• About 20 minutes shorter than WRT stars
Definition:
(Astronomical year or)
Julian year = 365.25 days
(exact)
LENGTH OF THE YEAR
Earth’s rotation and orbit are not linked.
 Year and day are not linked.
Astronomical year:
365.25 days
Calendar year:
365.00 days
Difference:
.25 days
In other words,
when we are counting days,
our year ends 0.25 days
too early every year.
• After 4 years, the calendar
is one full day off.
• After 8 years, 2 days off.
• After 500 years, midwinter
is in May.
LEAP YEARS
Calendar ends 6 hours (0.25 days) early.
 1 full day after 4 years.
 Add 1 day every 4th year to reset the offset.
Actually 0.2425 = + 1/4 − 1/100 + 1/400.
(Gregorian calendar still gets 1-day error in 8000 years.)
HELIACAL RISING
• 4-minute difference between the sun
and the stars
• A star rises right before the sunrise after a
long time
• I.e., any particular star/constellation
rises 4 minutes earlier every day
• Sun too close to the star  overshines
• Only when the Sun gets farther away, the
star becomes visible
• Happens at the same time every year
HERE’S THE PAST HOUR CONDENSED
Part 1: How does the Earth move in space?
•
Component 1: Around the Sun
•
Kepler's laws
•
Orbit
•
Year
•
Sidereal year
• The time it takes to make one full round around the Sun
• 365.2564 days
•
Solar/tropical year
• The time between two seasons (e.g. two midsummers)
• 365.2422 days
•
Calendar year
• 365 days or 366 days
•
Astronomical/Julian year
• Defined to be exactly 365.25 days
•
Leap years needed to match the 1/4-day difference between
calendar and real year
•
Component 2: Around its axis
•
Day, hours, time zones
•
4-minute difference between synodic and sidereal day
• Heliacal rising (homework?)
•
Polar star
•
Tilt of axis
•
"Around the Sun" + "Tilt of axis" --> Seasons
•
"Around its axis" + "Precession" --> Two effects
•
Change of the polar star
•
Shift of the equinoxes / shift of "horoscope signs"
Part 2: Sun’s motion on the sky (Two coordinate systems)
•
Because of "Component 1":
•
Orbital plane
•
Sun seems to move in a plane -> Ecliptic plane
•
Sun and planets are always near the ecliptic
•
Sun always passes through the same constellations -> Zodiac (13
constellations)
•
Also planets pass through the same constellations
•
Because of "Component 2":
•
Rotation of the sky in 24 hours
•
Sun moves across the sky
•
Stars move across the sky
•
Because of "Component 1" + "Component 2":
•
Winter solstice: when the hemisphere points away from the Sun
•
Summer solstice: when the hemisphere points towards the Sun
•
Spring/Fall equinox: when both hemisphere point perpendicularly (neither points
toward the Sun)
PART 3:
WHY SHOULD WE CARE?
EXAMPLE: ”MANHATTANHENGE”
https://www.nytimes.com/2016/05/27/science/
when-is-manhattanhenge-2016.html
Preliminary work:
Sunlight “wins and fails”
”BIG BANG ECHO”
”Big bang echo”
(Marcus Copper, 2000)
University of Turku
SOLAR PANELS,
SATELLITE ANTENNAS, ETC.
SUNDIALS
http://www.mojoptix.com/2015/10/25/mojoptix-001-digitalsundial/
DIY-SUNDIALS
SUNDIALS: ALSO DIGITAL (THANKS TO 3D PRINTING)
Digital sundial engineering and details:
http://www.mojoptix.com/2015/10/25/
mojoptix-001-digital-sundial/
EXAMPLE: US MEMORIAL DAY MONUMENT
http://nerdist.com/the-sun-perfectly-illuminatesa-veterans-day-memorial-each-year/
ANCIENT MEGALITHS
NEXT
This week
Next week
• “Heliacal rising [3p]
• L4: “One planet, one sky, one people”
• “Daylight saving time in the 21st century [3p]”
• First learning diary deadline next Monday,
23.1. at 08:00.
• https://mycourses.aalto.fi/course/view.php?id
=13379&section=16
• At 08:01the submitted learning diaries are
automatically sent for assessment, and it is not
possible to add late learning diaries to the
workflow. Thus: set your own deadline at least
a day or two earlier.