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:- 24 R

LI

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:-5/)(

1

2 21100 mm

I

I

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

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.