Transcript Light Collection Magnitude limit of 14” scope

Astronomy Basics
• Where is it?
– Angular positions in the sky
– How far is it?
• How to see it?
– Telescopes
Positions on the Celestial Sphere
• How to locate
(and track)
objects from a
spinning, orbiting
platform in
space….
Positions on the Celestial Sphere
The Altitude-Azimuth Coordinate System
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Coordinate system based on observers local
horizon
Zenith - point directly above the observer
North - direction to north celestial pole NCP
projected onto the plane tangent to the earth
at the observer’s location
h: altitude - angle measured from the horizon
to the object along a great circle that passes
the object and the zenith
z: zenith distance - is the angle measured
from the zenith to the object z+h=90
A: azimuth - is the angle measured along the
horizon eastward from north to the great
circle used for the measure of the altitude
Changes in the Sky
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Coordinates continuously changing in
alt-az system for all celestial objects
(except geo-stationary satellites)
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Earth’s rotation
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Earth’s orbit about Sun
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Proper motion of objects
– The moon
– Planets
– Asteroids
– Comets
– Satellites….
Milky Way From Frisco
Peak. Paul Ricketts 
Motion of Stars about NCP
Earth’s Rotation
• Earth’s rotation is responsible for the
“rapid” motion of objects through the
sky
Mud springs point 2 hour exposure
of NCP. Paul Ricketts
Tilt of Earth’s Axis
• Position of sun, moon and
planets on celestial sphere
significantly influenced by
the tilt of Earth’s axis.
• Stars far enough away that
seasonal variation of position
on celestial sphere not
significantly influenced by
the tilt of Earth’s axis…
• On timescale of thousands
of years, however, position
of even stars move on
celestial sphere due to
precession!!!!
Earth’s Orbit about the Sun
Due to the Earth’s motion about the Sun :
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Line of sight to the sun sweeps through
the constellations. The sun apparently
moves through the constellations of the
zodiac along a path known as the Ecliptic
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The constellations that are visible each
night at the same time changes with the
season
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A given star will rise approximately 4
minutes earlier each day
The Ecliptic.The path of the sun through
the year in equatorial coordinates.
Equatorial Coordinate System
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Coordinate system that results in
nearly constant values for the
positions of distant celestial objects.
Based on latitude-longitude
coordinate system for the Earth.
Declination - coordinate on celestial
sphere analogous to latitude and is
measured in degrees north or south
of the celestial equator
Right Ascension - coordinate on
celestial sphere analogous to
longitude and is measured eastward
along the celestial equator from the
vernal equinox  to its intersection
with the objects hour circle
Hour circle
Positions on the Celestial Sphere
The Equatorial Coordinate System
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Hour Angle - The angle between a
celestial object’s hour circle and the
observer’s meridian, measured in the
direction of the object’s motion around
the celestial sphere.
Local Sidereal Time(LST) - the
amount of time that has elapsed since
the vernal equinox has last traversed
the meridian.
Right Ascension is typically measured
in units of hours, minutes and
seconds. 24 hours of RA would be
equivalent to 360.
Can tell your LST by using the known
RA of an object on observer’s
meridian
Hour circle
What is a day?
The period (sidereal) of earth’s revolution
about the sun is 365.26 solar days. The
earth moves about 1 around its orbit in
24 hours.
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Solar day
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Is defined as an average interval
of 24 hours between meridian
crossings of the Sun.
The earth actually rotates about its
axis by nearly 361 in one solar
day.
Sidereal day
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Time between consecutive
meridian crossings of a given star.
The earth rotates exactly 360
w.r.t the background stars in one
sidereal day = 23h 56m 4s
Annalemma
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Position of sun at “noon”
Mean (average) solar day is 24
hours
Equation of time
Local Sidereal Time
LST = 100.46 + 0.985647 * d + long + 15*UT
d
is the days from J2000, including the fraction of
a day
UT is the universal time in decimal hours
long is your longitude in decimal degrees, East positive.
Add or subtract multiples of 360 to bring LST in range 0 to 360
degrees.
Precession of the Equinoxes
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Precession is a slow wobble of
the Earth’s rotation axis due to
our planet’s nonspherical shape
and its gravitational interaction
with the Sun, Moon, etc…
Precession period is 25,770
years, currently NCP is within 1
of Polaris. In 13,000 years it will
be about 47 away from Polaris
near Vega!!!
A westward motion of the
Vernal equinox of about 50” per
year.
Celestial Coordinates Links…
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http://spiff.rit.edu/classes/phys445/lectures/radec/radec.html
http://home.att.net/~srschmitt/script_celestial2horizon.html
http://www.coyotegulch.com/articles/StellarCartography/na0002.html
http://tycho.usno.navy.mil/sidereal.html
http://www.jgiesen.de/elevaz/basics/astro/stposengl.htm
http://idlastro.gsfc.nasa.gov/
http://idlastro.gsfc.nasa.gov/ftp/pro/astro/hor2eq.pro
http://idlastro.gsfc.nasa.gov/ftp/pro/astro/eq2hor.pro
Distance and Brightness
•Stellar Parallax
•The Magnitude Scale
Stellar Parallax
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Trigonometric Parallax:
Determine distance from
“triangulation”
tan   B /d
d  B /tan 
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Parallax Angle: One-half the
maximum angular displacement
due to the motion of Earth about
 Sun (excluding proper
the
motion)
d
1AU 1
 AU
tan p p
With p measured in radians
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PARSEC/Light Year
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1 radian = 57.2957795 = 206264.806”
Using p” in units of arcsec we have:
206,265
d
AU
p"
Astronomical Unit of distance:
PARSEC = Parallax Second = pc
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1pc = 2.06264806 x 105 AU
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The distance to a star whose parallax
angle p=1” is 1pc. 1pc is the distance at
which 1 AU subtends an angle of 1”
d
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1
pc
p"
Light year : 1 ly = 9.460730472 x 1015 m
1 pc = 3.2615638 ly
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•Nearest star proxima centauri has a
parallax angle of 0.77”
•Not measured until 1838 by Friedrich
Wilhelm Bessel
•Hipparcos satellite measurement
accuracy approaches 0.001” for over
118,000 stars. This corresponds to a a
distance of only 1000 pc (only 1/8 of
way to center of our galaxy)
•The planned Space Interferometry
Mission will be able to determine
parallax angles as small as 4
microarcsec = 0.000004”) leading to
distance measurements of objects up
to 250 kpc.
The Magnitude Scale
• Apparent Magnitude: How bright an object appears.
Hipparchus invented a scale to describe how bright
a star appeared in the sky. He gave the dimmest
stars a magnitude 6 and the brightest magnitude 1.
Wonderful … smaller number means “bigger”
brightness!!!
• The human eye responds to brightness
logarithmically. Turns out that a difference of 5
magnitudes on Hipparchus’ scale corresponds to a
factor of 100 in brightness. Therefore a 1
magnitude difference corresponds to a brightness
ratio of 1001/5=2.512.
• Nowadays can measure apparent brightness to an
accuracy of 0.01 magnitudes and differences to
0.002 magnitudes
• Hipparchus’ scale extended to m=-26.83 for the
Sun to approximately m=30 for the faintest object
detectable
Flux, Luminosity and the Inverse Square Law
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Radiant flux F is the total amount of
light energy of all wavelengths that
crosses a unit area oriented
perpendicular to the direction of the
light’s travel per unit
time…Joules/s=Watt
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Depends on the Intrinsic Luminosity
(energy emitted per second) as well
as the distance to the object
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Inverse Square Law:
F
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L
4r 2
Absolute Magnitude and Distance Modulus
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Absolute Magnitude, M: Defined to
be the apparent magnitude a star
would have if it were located at a
distance of 10pc.
Ratio of fluxes for objects of
apparent magnitudes m1 and m2 .
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•Distance Modulus: The connection
between a star’s apparent magnitude, m ,
and absolute magnitude, M, and its
distance, d, may be found by using the
inverse square law and the equation that
relates two magnitudes.
2


F
d
100(mM )/ 5  10  
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F 10 pc 
F2
 100(m1 m2 )/ 5
F1
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Taking logarithm of each side
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F1 
m1  m2  2.5log 10 
F2 
Where F10 is the flux that would be received
if the star were at a distance of 10 pc and d
 is the star’s distance measured in pc.
Solving for d gives:
d  10(mM 5)/ 5 pc
The quantity m-M is a measure of the
distance to a star and is called the star’s
distance modulus
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 d 
m  M  5log 10 (d)  5  5log 10
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10 pc 
A Brief talk about Telescopes
Types of Telescopes
Refractor
Reflector
Newtonian
Schmidt-Cassegrain
….
What Does a Telescope Do?
Light Collection
Image Formation
Pointing
Go-To Telescopes
Types
Refractor
Reflector
Catadioptric
Light Collection
The aperture of the optical instrument allows light coming from a source to be
collected for image formation. The larger the aperture the more light is collected,
therby allowing dimmer objects to be seen.
Meade LX200
14” diameter
Human Eye
1/4” diameter
99,314 mm^2
126 mm^2
Our 14” Meade has 788 times larger area than your eye
Light Collection
Magnitude limit of 14” scope
•Assume that the unaided eye can see down to 6th magnitude.
•The amount of light collected increases with light collection area
•14” scope hase 788 times the area of your eye
•Magnitude Definition
•Each 5 magnitudes  100 times the light
•Each magnitude  5 100 =2.51 times the light
2.51( M 2  M1 )  A2 / A1
log 10 (2.51( M 2  M1 ) )  log 10 ( A2 / A1 )
( M 2  M 1 )  log 10 ( A2 / A1 ) / log 10 (2.51)  2.896 / 0.399  7.24
With 14” scope should be able to see
down to magnitude 13.24
Image Formation
Lenses or Mirrors Focus light in such a way that the light rays emanating
from one point on the object is focused to one point in the focal plane
thereby forming an image of the object
Eyepieces and Magnification
• Need eyepiece to examine image
• Magnification =
Primary Focal Length
----------------------------Eyepiece Focal Length
Resolution
• The ability to make out detail of an object
– Separate binary stars
– See features on extended objects
• Diffraction limit
• Maximum useful magnification
Focal Ratio
• Focal Length/Aperture
• “Speed/Brightness” of optics
– f/8 requires 4x exposure time of f/4
• Field of View
• Smaller is faster and wider
Telescope Pointing
Mount types
Altitude-Azimuth
Equatorial Fork
German Equatorial
Dobsonian
Altitude-Azimuth Mount
Equatorial Fork Mount
German Equatorial
Dobsonian Mount
Go-To Telescopes
 Alignment of Equatorial Mount Scopes
 Basic Setup
 Computer
 Location and Time
 Use of Catalogs
 Use of Coordintes
 Telescope
 Finderscope alignment
 Basic Usage
 Finding and Centering Objects
 Focusing
Warnings !!!!!
Know the basic operation before turning on scope
Be prepared to switch off/ stop scope from slewing
Watch cables…..