Chapter 6: The Family of Stars
6.1 Star Distances
• In surveying, two stakes are driven into the ground and the distance between them is
called the baseline
• They then choose a landmark, establishing a triangle marked by the two stakes and the
• They survey the two angles created in the triangle and thus can find the distance to the
landmark using simple trigonometry.
• Astronomy uses a similar method to calculate star distances
• They use an extremely long baseline, the size of Earth’s orbit.
• Stellar Parallax: The small apparent shift in position of a nearby star relative to distant
background objects due to Earth’s orbital motion. (The shift seen across a baseline of 1
AU rather than 2 AU)
• The measurements tell the size of the triangle and thus the distance to the object in
• Measuring parallax is difficult because of the small angle.
• The distances between stars is so large that using kilometres or Astronomical Units is
• Instead, Light-years and parsecs are used
• Light-year: The distance light travels in one year
• Parsec: The distance to a hypothetical star whose parallax is 1 second of arc.
• The word parsec was created by combining parallax and arc second
• A parsec is 206.265 AU (roughly 3.26 light-years)
• The blurring caused by Earth’s atmosphere makes star images appear to be about 1 arc
second in diameter, and that makes it difficult to measure parallax.
• You cannot measure parallax with an uncertainty smaller than about 0.002 arc seconds
6.2 Apparent Brightness, Intrinsic Brightness and Luminosity
• Intrinsic Brightness: A measure of the amount of light a star produces
• An intrinsically very bright star might appear faint if it is far away. Therefore, you must
take distance into account to know the intrinsic brightness of a star.
Brightness and Distance • Brightness is related to the flux of energy in joules (J) per second falling on 1 square
• Flux: A measure of the flow of energy out of a surface. Usually applied to light.
• A flux of one joule per second is also known as one watt
• Eg. The wattage of a light bulb tells you its intrinsic brightness. The apparent
brightness of a light bulb depends on its distance from you
• Another example: If you placed a screen 1 square metre near a light bulb, a certain
amount of flux would fall on the screen. Moving the screen twice as far from the bulb
would cause the light to cover an area four times larger and the screen would receive
one-fourth as much light. Tripling the distance would cause the screen to receive
only one-ninth as much light.
• Inverse square relation: the flux you receive from a light source in inversely
proportional to the square of distance to the source
• Absolute Visual Magnitude: Intrinsic brightness of a star. The apparent visual
magnitude the star would have of it were 33 light-years away.
• The Sun’s absolute visual magnitude is easy to calculate because its distance an
apparent magnitude are well known.
• The absolute visual magnitude of the Sun is 4.8. Therefore, if the Sun were 33ly from
Earth, it would have the apparent magnitude of 4.8 and look no brighter to your eye
than the faintest star in the handle of the Little Dipper.
• Luminosity: The total amount of energy a star radiates per second at all
• Stars emit over 100,000 time more visible light than the Sun
• Hot stars emit a great deal of ultraviolet radiation that you can’t see
• Cool stars emit infrared radiation
• The luminosity of the Sun is about 4 x 10^26 watts (joules per second)
• You can express a star’s luminosity in two ways: (1) you can say the star Capella is
100 times more luminous than the Sun. (2) Express it in real energy units by
multiplying by the luminosity of the Sun. The Luminosity of Capella is 4 x 10^28 watts
6.3 Star Temperatures
• Stars typically have a surface temperatures of a few thousand or tens of thousands of
• The centres of the stars are much hotter than their surfaces – many millions of degrees
hotter – but the spectra tell only about the outer layers from which the light you see
departed. • If the surface of a star is as cool as the Sun or cooler, there are few violent collisions
between atoms to excite the electrons.
• Most will have atoms in the ground state
• You should expect to find weak hydrogen Balmer absorption lines in the spectra of very
• In the surface layers of stars hotter than 20,000 K, there are many violent collisions.
Exciting electrons to high energy or knocking the electrons out of most atoms and they
• Few hydrogen atoms will have electrons
• Weak hydrogen Balmer lines in the spectra
• Stars at an intermediate temperature , about 10,000 K, the collisions have the correct
amount of energy to excite large numbers of electrons into the second energy level.
• Strong hydrogen Balmer lines
• Hot and cool – weak
• Medium – strong
• Astronomers can determine a star’s temperature by comparing the strengths of its
spectral lines with the predicted strengths
• Astronomers have found that the ho