Download How Do We Know the Earth is Spherical?

Lec 3: 31 August 2011
Chapter 2: The Celestial Sphere
LAST TIME - The Layout of the Sky
• 
The Appearance of the Sky (from Earth)
• 
Describing “Location” on the Sky
You should
practice until
you clearly
understand...
HORIZON ZENITH
MERIDIAN ALTITUDE
AZIMUTH
-- altitude-azimuth
-- constellations
TODAY - The Celestial Sphere
•  Chapter 2 Pre-Quiz
•  Spherical Earth and Celestial Coordinates
•  The Celestial Sphere
MONDAY - The Daily Motion of the Sky
How Do We Know the Earth is Spherical? • 
• 
• 
• 
Columbus? Views from space? Shadows of Earth on Moon? Sun, Moon, and Planets are; maybe we are too?
Can we demonstrate it?
–  If Earth were flat (but stars still a long ways away),
everyone would see same sky. Star at zenith would
always be at zenith. –  Azimuth and Elevation would be same for everyone.
•  But it’s NOT the same for everyone! This has
been known for thousands of years!
How Do We Know the Earth is Spherical? •  Columbus? •  Shadows of Earth on Moon? Ancient astronomers determined that the Earth is Spherical
(and they could measure its size)
• 
In the town of Syene, the Sun
shone directly down a vertical
shafts on the summer solstice
• 
In Alexandria, the position of the
sun was 7° away from vertical
(~1/50th of a circle)
• 
Around 200 B.C., the Greek
astronomer Eratosthenes used 50x
the distance between Alexandria
and Syene to get a circumference
of the earth of about 42000 km
(the actual is about 40000
kilometers)
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Location in the Sky. III. “Global”
1.  On Earth....
•  latitude: angle from equator (+ = north) •  longitude: angle from prime meridian (east or
west) Analog: azimuth and elevation viewed from center of Earth
Charleston: 32o 46’ 35” North & 79o 55’ 53” West
• 
• 
How do we put a similar grid on the sky?
We first need a POLE and EQUATOR ...
The “Celestial Sphere”
“Landmarks” on the
celestial sphere are
projections of those on
the Earth:
•  Celestial poles are
where the Earth’s axis of
rotation would intersect
the celestial sphere
  Polaris is less than 1°
away from the north
celestial pole, which is
why it is called the North
Star or the Pole Star.
•  Celestial equator
divides the sky into
northern and southern
hemispheres
The View From a Spherical Earth
Altitude of celestial poles
and equator depends on your
latitude:
•  North Pole (lat=90o)
Location in the Sky. III. “Global”
1.  On Earth....
•  latitude is angle from equator (+ = north) •  longitude is angle from prime meridian (E or W)
•  alt(NCP) = 90o
•  alt(CE) = 0o
•  Equator (lat=0o)
• 
To make a similar grid on the sky, we use the North
and South Celestial Poles and the Celestial Equator
•  alt(NCP) = 0o
•  alt(CE) = 90o (E->W)
•  Charleston, SC (lat=33o)
•  alt(NCP) = 33o
•  alt(CE) = 57o (at the
meridian; E->W)
2.  On the Sky...
• 
• 
The Celestial Sphere
Celestial Equator divides sky into
northern and southern hemispheres
DECLINATION. Celestial latitude. Lines of
constant DEC parallel to equator. Measured north
(+) or south (-) of celestial equator, like latitude on
Earth. •  From north pole, see only northern
hemisphere
•  From south pole, see only southern
hemisphere
•  From equator, see both hemispheres!
RIGHT ASCENSION. Celestial longitude. Lines
of constant RA perpendicular to celestial equator,
and all pass through celestial poles. Measured in
HOURS (0-24; 24 hours=360 degrees; so 1 hour =
15 degrees)
•  From Charleston, see from -57o to
+90o declination
WARNING:
This figure is misleading!
Celestial Equator runs from East to
West. Apparent motion on sky
depends on whether object is north
or south of celestial equator
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Rotation of the Earth
•  Spherical Earth “rotates” once in 24 hours
(we will see next time that it’s actually 23h 56m)
•  Earth’s rotation is from west to east (counterclockwise
viewed from above north pole)
•  Sky appears to rotate east to west once in 24 hours
(opposite sense of Earth’s rotation)
•  “Axis” of rotation through north and south poles
–  projects to north celestial pole (NCP) and south celestial pole (SCP)
•  Equatorial plane perpendicular to axis
–  cuts through our equator
–  projects to circle on the sky called the celestial equator (CE)
Apparent Daily Motion of the Sky
•  Sun, Moon, planets, stars, etc. rise in East and
set in West?
–  well, sort of, but not really
–  what do they do in between?
•  Not everything is up for 12 hours! Some things
never rise or set. Some are up for 24 hours.
•  Path across the sky, and how long things are
“up” depends on:
–  your latitude on Earth
–  object’s declination in the sky
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