apparent magnitude astrophysics lesson 7. learning objectives define luminosity & intensity. ...
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Apparent Magnitude
Astrophysics Lesson 7
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Learning Objectives
Define luminosity & intensity. Place astronomical objects with a range
of intensities on a magnitude scale.Recall and use the equation m = -2.5 lg
I + constant, where m is the apparent magnitude and I is the intensity.
Calculate the ratio in intensities given a difference in magnitude.
Define apparent magnitude
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Luminosity
• The luminosity of a star id the total energy emitted per second (units of Watts).
• The Sun’s luminosity is about 4 x 1026 W.
• The most luminous stars have a luminosity of about million times that of the Sun!
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Stars have a range of L
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Relative Sizes
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Brightness
• The intensity, I of an object is the power received from it per unit area at Earth.
• This is the effective brightness of an object.
• It can be calculated using the equation:- 24 R
LI
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Apparent Magnitude
• The Greek astronomer Hipparchus classified stars according to their apparent brightness to the naked eye, about 2000 years ago.
• Its scale was 1 for the brightest star to 6 for the dimmest star.
• It is still used today and is called the apparent magnitude scale.
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Apparent Magnitude
• Apparent magnitude, m is based on how bright things appear from Earth.
• It is related to intensity using the following equation:-
• m = -2.5 log I + constant
• Back to front and logarithmic (base 10!). Enjoy!
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Pogson’s Law
• In the 19th Century the scale was redefined using a strict logarithmic scale:
• A magnitude 1 star has an intensity 100 times greater than a magnitude 6 star.
Expressed mathematically this is:-5/)(
1
2 21100 mm
I
I
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Apparent Magnitude
• By logging both sides by 10, this can be re-written:-
• Where m is the apparent magnitude• And I is the intensity.
1
212 log5.2
I
Imm
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Apparent Magnitude Scale
• Have a go!
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Apparent Magnitude Scale
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• The apparent magnitude is given the code m. Magnitude 1 stars are about 100 times brighter than magnitude 6 stars. A change in 1 magnitude is a change of 2.512 (1001/5 = 2.512). The scale is logarithmic because each step corresponds to multiplying by a constant factor.