Stars

How do we measure distances in space?
○ Can look at apparent motion of an object against distant
background from two vantage points

Stars
★ Can replicate this on large scales with our changing
position of Earth over the course of the year
○ Increased baseline (distance between observation points) makes
for more noticeable observations

Stars
★ The parallax angle by which something appears to move is
inversely proportional to its distance:

Stars
★ Arcsecond: 1/3600 of a degree, roughly the smallest detail
we can make out with a telescope on the ground
★ We define the distance at which parallax (for a 1 AU
baseline) is 1 arcsecond to be a “parsec”
○ 1 pc = 3.26 light-years

Stars
★ The nearest star to
the Sun is Proxima
Centauri, part of
the three-star Alpha
Centauri system,
about 4 ly away
(around 1 pc)

Stars
★ Scale of distances
○ If the Sun is a marble, Earth is a grain of sand orbiting 1 m
away
○ Orbits of planets extend about 50 m from Sun
○ Proxima Centauri is another marble 270 km away (about the
distance to Columbus or Harrisburg)
○ The space between the outer planets and the nearest star is
basically empty

Stars
The Inverse Square Law
★ Luminosity: the total amount
of energy a star radiates
per second
I = L/(4πR²)

Stars
★ The amount of energy emitted over time is spread out over a
larger and larger sphere as light travels away from a star
★ If we know a star’s apparent brightness and its distance from
us, we can calculate its luminosity
★ Stars with the same brightness may be at different distances
and have different luminosities

Stars
★ Stars with the same brightness may be at different distances
and have different luminosities

Top Hat Question

Stars
★ We will typical talk about luminosity, mass, etc. of stars
relative to the Sun
○ Solar luminosity (Lₛ)
○ Solar mass (Lₛ)
○ Solar Radius (Lₛ)
★ Most stars are less
luminous than the Sun

Stars
★ Recall that the color of stars is related to its Temperature
○ Cooler stars are redder
○ Hotter stars are bluer

Stars

Stars
★ Recall Stefan’s Law and Wien’s Law

Stars
★ There are seven general categories of stars, defined based
on their spectra:

Stars
★ Gas above the photosphere
of a star will absorb light
at particular wavelengths
based on elements in the
atmosphere
★ Strength of the absorption
depends on elemental
composition, density, and
temperature

Stars
★ The Sun’s composition appears to
be fairly typical, but older stars
contain less of the elements
beyond Helium

Stars
★ Observing the size of a star is
not done easily
★ A few very large, nearby stars
can be imaged directly
★ The rest are too small on
★ the sky for even the Hubble
★ Space Telescope to resolve
Betelgeuse is ~600 times larger than the Sun →

Stars
★ For the vast majority of stars that cannot be imaged
directly, size must be calculated from other measurements

Stars
★ The size or radius of a star must be calculated from its
luminosity and temperature (at the photosphere)
★ The Luminosity-Radius-Temperature relation or LRT relation:
○ This combines Stefan's Law and the surface area of a sphere

Stars
★ Invert this relation to solve for radius:
★ Using this relation to calculate the size of a few sample
stars from their temperatures and luminosities:

Stars
★ Stellar radii can vary widely
compared to our Sun

Stars
★ Star formation happens when part of a molecular cloud begins
to shrink under its own gravitational force
○ These are cold, dense parts of the ISM

Stars
★ Interstellar Medium (ISM): the gas in between
stars, made mostly of hydrogen and helium
★ As the molecular cloud collapses, the center
becomes hotter and denser, eventually forming
an opaque object: a protostar
★ It takes about 100,000 years to form a
protostar

Stars
★ A protostar has an identifiable "surface" or photosphere
like a star, but obtains its energy from collapsing rather
than from fusion
★ We consider a star to have been born when nuclear fusion
begins in its core
★ Protostars have cool surfaces, but are large and luminous