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ASTR 200, reminder
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ASTR 200 – Frontiers of Astrophysics
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Instructor: Professor Gladman
Office: Hennings 300B
Lectures here (Henn 202)
12:00 on M,W,F
Units for astronomy and astrophysics
au
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Units for astronomy and astrophysics
au
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Angular Measurements
Full circle = 360º
1º = 60 (arcminutes)
1 = 60 (arcseconds)
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angular diameter
Diameter
Angular diameter(o)
Angular diameter
---------------------- = ---------------------- = ---------------2 Distance
360 o
2 radians
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For those with integral calculus:
Prove by integrating the surface
element (sinθ dθ dφ) on a unit
sphere that the area is 4π
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Units for astronomy and astrophysics
au
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Units for astronomy and astrophysics
au
+c
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Their values depend on the
system of units one is using!
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A light year
Julian year is exactly 365.25 days
so: 365.25 d * 24 h/d * 60 min/h * 60 s/min
= 31,557,600 seconds = 3.15576 x 107 s unit
c = 2.99792 x 108 m/s
physical constant
(what would it be in cm/s?)
ly = 2.99792 x 108 m/s * 3.15576 x 107 s
= 9.46072 x 1015 m
This is a 'derived unit' based on a constant
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Starting our steps out into the universe
The first human steps were to understand the
scale of :
Our planet
The Moon
The Sun
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Observations of the Moon
Aristotle realizes the Earth is a sphere
Erathostenes uses simple geometry to determine
the size of the Earth
Aristarchus realizes this gives the diameter of the
Moon via eclipse observations
Once one knows the diameter of the Moon, you
can calculate its distance!
Lunar Eclipse Sequence
Lunar
Phase
Cycle
Lunar Eclipse Sequence
On the summer
solstice, the sun
shone straight
down a well in
Syene
On the summer
solstice, the sun
shone straight
down a well in
Syene
On the same day,
an obelisk in
Alexandria cast
a 7.2 degree
shadow...
The Eratosthenes experiment
Relies that Sun is far away.
7.2/360 must be
distance from SyeneAlexandria divided
by circumference
(D) of the Earth
5000 stades
The distance from
Syene to Alexandria
was known, which
gives Earth's
diameter!
D
see also text
Fig on p. 33
The Eratosthenes experiment
Relies that Sun is far away.
7.2/360 must be
distance from SyeneAlexandria divided
by circumference
(D) of the Earth
7.2
5000
--- = -----360
πD
5000 stades
The distance from
Syene to Alexandria
was known, which
gives Earth's
diameter!
D
360*5000
see also text
D = ----------= 80,000
Fig on
p. 33 st
7.2*π
*0.185 km/st
D=14,800 km
So, we knew the Earth's diameter
How does that help get the MOON's diameter
or distance?
So, we knew the Earth's diameter
How does that help get the MOON's diameter
or distance?
Does the relation :
Diameter
Angular diameter(o)
Angular diameter
---------------------- = ---------------------- = ---------------2 Distance
360 o
2 radians
help???
Lunar Eclipse Sequence
Aristarchus
Eclipse observations implied ;
Diameter of Moon about 1/3 diameter of Earth
Thus, diameter of Moon about 5000 km
This gives distance to Moon!
Board : use angular diameter of Moon is 0.5 deg.
Conclude: D ~ 573,000 km.
Actually 385,000 km...
First step in the cosmic distance scale...
Distance to Sun
Trickier...
Aristarchus had an argument about the quarter
moon, but was off by a lot (see text)
Wasn't done correctly until transits of Venus
were done using telecope
This didn't prevent (next week) accurately
getting the RELATIVE scale of the planetary
orbits
What about distances to Stars?
The ancients had a REALLY tough time
with this question
IF stars are physical objects like planets,
they SHOULD exhibit parallax...
Geocentric parallax
(diurnal)
Heliocentric parallax
(annual, stellar)