Stars

stars

Parallax and Magnitude

2p

1AU

1AU

61Cygni

To distant starp

p

• A Star with a parallax of 1 arc-second is

• 1 parsec from the Earth

• 1 par ( allax) sec ( ond )

• Distance ( pc ) = 1 .

• Parallax ( s )

61 Cygni is 0.3 seconds of arc

• Distance = 1

• 0.3

• = 3.33 pc from Earth.

Consider a star 1 parsec from Earth

1AU

CIRCUMFERENCE=60 X 60 X 360 AU

1 PARSEC

CIRCUMFERENCE = 2π parsec

• So 2π parsecs = 60 x 60 x 360 AU•

• 1 parsec = 5 x 10 AU

• = 3.26 LIGHT YEARS

• 61 Cygni is 3.33 x 3.26 Light Years

About 11 Light Years away

Looking At Brightness

• Using the inverse square law

• Observed Brightness 1 .

• Area

• 1 .

• distance²

•Magnitude

Ancient Greeks

• Brightest stars = Magnitude 1

• Dimmest stars = Magnitude 6

19th CENTURY

LIGHT from a magnitude 1 star was

100 times brighter than from a magnitude 6 star.

•A Difference of 5 magnitudes

•Corresponds to a ratio of 100

• Since

• 2.5 x 2.5 x2.5 x 2.5 x 2.5 = 100

• A Difference of 1 magnitude

• Corresponds to a ratio of 2.5 in the measured intensity of light

• The Sun has a magnitude of -26.7

• The dimmest star using a giant telescope + 25

• Naked eye +6

PROBLEMS

• How bright a star is ( apparent magnitude)

• Doesn’t tell us how bright a star really is.

• Why not ?

• It may be brighter, but distant

• It may be dimmer ,but closer.

• Stars are not all the same!

ABSOLUTE MAGNITUDE

• Defined as equal to the apparent magnitude the star would have at a distance of 10 parsecs from Earth.

• The absolute magnitude of stars ranges from – 10 to +15

• Absolute Magnitude = M

• Apparent magnitude = m

• Distance = d

• M = m – 5 log d

• 10

Sirius

• Apparent magnitude – 1.46

distance = 2.65 parsecs from Earth.

Absolute Magnitude M = - 1.46 -5 log(0.265)

= - 1.46 – 5( -0.58)

= - 1.46 + 2.9

= 1.44

• Period = 5.75 days

• Magnitude increases at twice the rate it falls.

• Magnitude changes by 0.7

• Hence intensity ratio =

• = 1.9