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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 10 26 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:-

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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 19 th 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:-

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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.

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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 (100 1/5 = 2.512). The scale is logarithmic because each step corresponds to multiplying by a constant factor.

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