Transcript Our Place in the Cosmos Elective Course Autumn 2006

Our Place in the
Cosmos and
Introduction to
Astrophysics
Lecture 4
Patterns in the Sky Earth’s Motion about the Sun
Summary of Previous Lecture
• Night and day, and the apparent motion of the
Sun and stars are due to the Earth’s rotation
• Latitude may be determined from the altitude of
the celestial poles
• Changing altitude of pole with latitude provides
estimate of Earth’s radius
• Earth’s rotation demonstrated directly by two
observable effects: Foucault pendulum and
Coriolis effect
Earth’s Orbit around Sun
• Earth orbits the Sun in same direction as its spin
(counterclockwise as viewed from above North
Pole) taking 1 year for a complete orbit
• Responsible for seasons and changing patterns
of stars through the year
• Overhead at midnight, one is looking away from
the Sun
• This direction changes throughout the year and
so we see different stars - six months from now
we will be looking in the opposite direction at
midnight
Spring
40 deg
north
Summer
Autumn
Winter
The Ecliptic
• The Sun traces out a great circle against the
background stars along a path known as the
ecliptic
• The constellations along the ecliptic are the
signs of the zodiac
• Nothing significant about these constellations just random patterns of distant stars that happen
to lie near the plane of the Earth’s orbit about the
Sun
September 1
Sun in Leo
apparent path of Sun
Measuring Earth’s Motion
• Rain falling vertically will appear to be falling at
angle from a moving car
• By the time the raindrop has fallen from the top
of the window to the bottom, the car has moved
forward, and so raindrop appears to be moving
backwards
• In the same way, light from a distant star
appears to be coming from a slightly different
direction due to Earth’s motion through space
• Over the course of a year stars appear to trace
out a loop - aberration of starlight
Aberration of Starlight
• Cannot be detected by human eye but easily
detectable with a telescope
• Aberration of starlight first detected in 1720s by
Samuel Molyneux and James Bradley
• They showed that Earth moves on roughly (but
not exactly) circular orbit about the Sun with
average speed 29.8 km/s
• Since distance = speed  time, one may multiply
this speed times the time for one orbit to find the
circumference of the Earth’s orbit: 942 million km
Distance to the Sun
• For a nearly-circular orbit, radius is
circumference divided by 2: 150 million km
• This distance, the average distance between the
Earth and Sun is known as one astronomical
unit (AU)
• Modern measurements use radar signals
bounced off Venus
• The AU provides the basis for the astronomical
distance scale
The Seasons
• The seasons are not a result of the
ellipticity of Earth’s orbit (it is too small)
• They result from the combined effects of
• Earth’s spin on its axis
• Earth’s orbit about the Sun
• Misalignment of the axes of these two
motions
The Seasons
• If Earth’s rotation axis were perpendicular
to the ecliptic plane, the Sun would always
lie in the celestial equator, and above the
horizon for exactly 12 hours per day, every
day
• There would be no seasons
• In fact, rotation axis is tilted by 23.5 from
perpendicular, pointing in a fixed direction
as Earth orbits the Sun
Animation
The Seasons
• Thus for parts of the year the North Pole is tilted
towards the Sun and hence the northern
hemisphere has more than 12 hours of sunshine
per day (northern summer), while it is winter in
the south
• Six months later, the North Pole is tilted away
from the Sun and northern days are shorter than
12 hours (northern winter, southern summer)
• As well as longer days in summer, Sun is more
directly overhead and hence sunlight more
intense
Equinoxes
• Equinoxes are the times when the Sun’s
apparent orbit crosses the celestial equator and
the Earth’s rotation axis is perpendicular to the
direction to the Sun
• Twice each year:
• Spring (or vernal) equinox around 21 March
• Autumn equinox around 23 September
• Equinox = “equal night” - day and night both last
for 12 hours everywhere
Solstices
• At the (northern) summer solstice (“Sun standing
still”), around 21 June, the Sun reaches it’s most
northerly point, when North Pole points most
directly towards Sun - midsummer’s day
• At winter solstice, around 22 December, North
Pole tipped most directly away from Sun midwinter, the shortest day of the year
• Northern summer solstice is southern winter,
and vice versa
Anim
Land of the Midnight Sun
• Above the Arctic Circle (66.5 deg north) Sun is
circumpolar around midsummer - 24 hour
daylight (“land of the midnight sun”)
• Same true below Antarctic Circle
• Temperatures remain cool as Sun is never very
high in the sky
• There are equally long periods in winter when
the Sun never rises
The Equator
• On the equator all stars, the Sun included, are
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above the horizon 12 hours per day
Days and nights are each 12 hours long
throughout the year
Sun passes directly overhead on the equinoxes
Sun is furthest from overhead at the summer
and winter solstices
The equator thus experiences eight seasons a
year: two summers, two winters, two springs and
two autumns, although no season is very
different from another
The Tropics
• Between latitudes 23.5 deg south and north,
twice during the year, the Sun will be directly
overhead at noon
• This band is known as the tropics and is
bounded by the tropic of Cancer to the north and
the tropic of Capricorn to the south
• Where do these names come from? Summer
solstice is located in Taurus, winter in Sagittarius
Summer Sun
in Taurus
apparent path of Sun
Winter Sun
in Sagittarius
Precession of the Equinoxes
• Earth’s axis wobbles slightly (like a spinning top)
taking 26,000 years to complete one orbit of
precession
• North celestial pole tracks out a large circle
amongst the stars
• Polaris is currently close to NCP, but it has not
always been!
• Celestial equator remains perpendicular to
rotation axis, so the locations where it crosses
the ecliptic - the equinoxes - also change
Precession of the Equinoxes
• This is known as precession of the equinoxes
• Tropics so-named due to Sun’s location at
equinoxes in Ptolemey’s time, not today
• This shift of the seasons through the year from
century to century played havoc with
construction of reliable calendars
• In 1752 England and colonies dropped 11 days
from calendar year to fall into line with rest of
Europe. Mass rioting ensued from these 11
days being “stolen” from people’s lives
Leap years
• Modern calendar based on a tropical year of 365.242199
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days, the time from one spring equinox to the next
Leap years prevent extra fraction of a day causing the
seasons to “drift” through the year
Leap years have 366 days (extra day is 29 Feb) instead
of 365
Leap year every four years gives an average of 365.25
days/year, so not every 4th year is a leap year
Century years apart from those divisible by 400 (eg.
2000) remain as 365 day years
Summary
• Our view of the stars changes during the year
• The ecliptic is the apparent yearly path of the
Sun against the stars
• From simple observations of the aberration of
starlight one may infer the orbit of the Earth
about the Sun and the distance to the Sun
• The seasons are explained by the rotation of the
Earth, the orbit of the Earth about the Sun and
the fact that the Earth’s rotation axis is at an
angle relative to the orbital axis
Seminar Quiz Q1
• Draw a picture of the Earth showing the
location of an observer at our latitude and
his or her horizon.
• Mark the direction of the north and south
celestial poles and the celestial equator.
• For how many hours per day is a star on
the celestial equator visible?
Seminar Quiz Q2
• A soldier fires a cannon directly at a
distant target toward the east and makes a
perfect hit. She then fires a shot directly at
another target to the north, but the shot
lands west of this target.
• Was the soldier in Australia or Canada?
• Would she have fared better on the
equator?
Seminar Quiz Q3
• You are half way between the Carolinas
and Bermuda heading due east, and you
know there is a hurricane nearby. A strong
wing is blowing straight out of the south.
Would you continue on to Bermuda or
head back?
Seminar Quiz Q4
• In which direction does the Sun rise on the
morning of the spring equinox?
• In the summer, does the Sun rise further
north or further south?
• And in the winter?
Seminar Quiz Q5
• Suppose the Earth’s axis were tilted at an
angle of 35 instead of 23.5 degrees to its
orbit.
• At what latitudes would the Arctic and
Antarctic circles and the Tropics be
located?
• What effect would this have on our
seasons?