Transcript Apparent Magnitude - RanelaghALevelPhysics

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
4R
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.