Astronomy Toolkit

Magnitudes Apparent magnitude Absolute magnitude The distance equation Luminosity and

intensity Units and other basic

dataLogarithms

Magnitudes

• Hipparcos classified the stars visible to the naked eye into six different brightness classes called magnitudes

• Hipparcos chose to categorize the brightest stars as magnitude 1, and the faintest as magnitude 6 (smaller numbers are brighter stars)

• The magnitude system of Hipparcos is still in use today in a slightly revised form

Hipparcos of Nicaea (c.190 – c.120 BC) at workHipparcos, a Greek astronomer, invented the first scale to rate the brightness of the stars.

Modern Magnitudes• The magnitude scale is

logarithmic• The difference in

magnitude between two stars can be expressed as a function of the ratio of their brightness

)/log(5.21221 starstarstarstar IImm

)(4.05.2 21

21

1

2 1010 starstar

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star

star mmmm

I

I

Apparent Magnitude• Some stars appear bright and

others very faint in the sky• The apparent magnitude “m” of a

star is a measure of how bright it appears in the sky– Some faint stars are intrinsically bright,

but are very distant– Some bright stars are very faint but

happen to lie close to us

• A star’s apparent magnitude tells us little about the star

• We need to know stars’ distances from Earth

The apparent magnitude of the Sun is -26!

Absolute Magnitude

• The absolute magnitude “M” of a star is defined as the apparent magnitude a star would have if it were placed at a distance of 10 parsecs

• The absolute and apparent magnitudes are related by the distance equation, where D is the distance in parsecs

5)(log5)(log5 101010 DpcMm D

Playing with Magnitudes

• The star α Orionis (Betelgeuse) has an apparent magnitude of m = 0.45 and an absolute magnitude of M = –5.14

• What is the distance to Betelgeuse?

0.45 – (-5.14)=5log10(D)-5

5.59/5 + 1 = log10(D)D=102.12 =131 parsecs

5)(log5 10 DMm

Luminosity• The total energy emitted by the star each second is called its luminosity, L

• Luminosity is measured in watts (power = energy per second)

• Knowing the apparent magnitude and the distance of a star, we can determine its luminosity

• The star radiates light in all directions so that its emission is spread over a sphere

• To find the intensity, I, of light from a star at the Earth (the intensity is the emission per unit area), divide the star’s luminosity by the area of a sphere, with the star at the centre and radius equal to the distance of the star from Earth, D.

I = L/(4πD2)

Units and Other Basic Data• Angle

– 1 arcminute = 1/60 of a degree = 2.9089 × 10-4 radians– 1 arcsecond = 1/3600 of a degree = 4.8481 × 10–6 radians– 1 milliarcsecond (mas) = 1/1000 arcsecond

• Speed of light (c) = 2.997 × 108 m/s

• Distance– Astronomical Unit – 1.5 x 108 km– Light Year ~ 1013 km– Parsecs

• 1 parsec (pc) = 3.086 × 1013 km = 3.26 light-years• 1 kiloparsec (kpc) = 1000 parsec = 3,260 light-years• 1 Megaparsec (Mpc) = 106 parsec = 3,260,000 light-years

– 1 nanometer (nm) = 10–9 m

More Units• Velocity – kilometers per second

• Mass – in units of the mass of the Sun

2 x 1030 kg

• Luminosity – in units of the solar luminosity

4 x 1026 watts = 4 x 1026 joules sec-1