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Apparent Magnitude Astrophysics Lesson 7 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 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! Stars have a range of L Relative Sizes 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:- L I 2 4R 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. 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! 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:- I2 ( m1 m2 ) / 5 100 I1 Apparent Magnitude • By logging both sides by 10, this can be rewritten:- I2 m2 m1 2.5 log I1 • Where m is the apparent magnitude • And I is the intensity. Apparent Magnitude Scale • Have a go! Apparent Magnitude Scale • 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.