Post on 27-Jun-2015
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stars
Parallax and Magnitude
2p
1AU
1AU
61Cygni
To distant starp
p
• A Star with a parallax of 1 arc-second is
• 1 parsec from the Earth
• 1 par ( allax) sec ( ond )
• Distance ( pc ) = 1 .
• Parallax ( s )
61 Cygni is 0.3 seconds of arc
• Distance = 1
• 0.3
• = 3.33 pc from Earth.
Consider a star 1 parsec from Earth
1AU
CIRCUMFERENCE=60 X 60 X 360 AU
1 PARSEC
CIRCUMFERENCE = 2π parsec
• So 2π parsecs = 60 x 60 x 360 AU•
• 1 parsec = 5 x 10 AU
• = 3.26 LIGHT YEARS
• 61 Cygni is 3.33 x 3.26 Light Years
About 11 Light Years away
Looking At Brightness
• Using the inverse square law
• Observed Brightness 1 .
• Area
• 1 .
• distance²
•Magnitude
Ancient Greeks
• Brightest stars = Magnitude 1
• Dimmest stars = Magnitude 6
19th CENTURY
LIGHT from a magnitude 1 star was
100 times brighter than from a magnitude 6 star.
•A Difference of 5 magnitudes
•Corresponds to a ratio of 100
• Since
• 2.5 x 2.5 x2.5 x 2.5 x 2.5 = 100
• A Difference of 1 magnitude
• Corresponds to a ratio of 2.5 in the measured intensity of light
• The Sun has a magnitude of -26.7
• The dimmest star using a giant telescope + 25
• Naked eye +6
PROBLEMS
• How bright a star is ( apparent magnitude)
• Doesn’t tell us how bright a star really is.
• Why not ?
• It may be brighter, but distant
• It may be dimmer ,but closer.
• Stars are not all the same!
ABSOLUTE MAGNITUDE
• Defined as equal to the apparent magnitude the star would have at a distance of 10 parsecs from Earth.
• The absolute magnitude of stars ranges from – 10 to +15
• Absolute Magnitude = M
• Apparent magnitude = m
• Distance = d
• M = m – 5 log d
• 10
Sirius
• Apparent magnitude – 1.46
distance = 2.65 parsecs from Earth.
Absolute Magnitude M = - 1.46 -5 log(0.265)
= - 1.46 – 5( -0.58)
= - 1.46 + 2.9
= 1.44
• Period = 5.75 days
• Magnitude increases at twice the rate it falls.
• Magnitude changes by 0.7
• Hence intensity ratio =
• = 1.9