This document discusses various units used to measure astronomical distances, including the astronomical unit (AU), light year, and parsec. It describes how trigonometric parallax can be used to determine the distance to stars by measuring their change in position over half a year. Standard candles, like Cepheid variables and Type Ia supernovae, which have known intrinsic luminosities, allow distances to be calculated using the inverse square law. The Hubble law relates a galaxy's redshift to its distance from Earth, showing the expansion of the universe.

1. Astronomical distance meassurements

2. Units
• A U (astronomical unit)
The distance between sun and earth.
aproximately 1.5X1015m

3. Light Year (L Y)
• Distance the light travels in one year
• 1 LY = 9.46X1015 m

4. Parsec
• This is the distance of a star with a parallax
angle of 1 arcsec.
• 1 parallax-second = 1 parsec = 3.08X1016m
• =206,265 au.
• 1 parsec = 3.26 LY

5. Trigonometric Parallax
- The stellar parallax is the apparent motion of a star due to our changing perspective as
the Earth orbits the Sun.
-parsec: the distance at which 1 AU subtends an angle of 1 arcsec.

6. 1/360 = 1 degree
1/60 degree = 1 arcminute
1/60 arcminute = 1 arcsecond

7. Stellar Parallax
• The Distance to a star is inversely proportional
to the parallax angle.
• There is a special unit of distance called a
parsec.
• This is the distance of a star with a parallax
angle of 1 arcsec.

8. How parallax measurements can be
used to determine the distances.?
• The star is viewed from two positions at 6
month intervals
• The change in angular position of the star
against backdrop of distant/fixed stars is
measured
• Trigonometry is used to calculate the distance
to the star The diameter/radius of the Earth’s
orbit about the Sun must be known

9. Luminosity
(L)
• Energy radiated from a star in all directions in
one second.
• It is similar to the power of a star.

10. Radiation flux (F)
• Radiation flux, is the amount of power radiated
through a given area, in the form of
electromagnetic radiations (photons) or other
elementary particles, typically measured in
W/m2

11. Inverse Square Law
• 𝐹 =
𝐿
4𝜋𝑑2
F= radiation flux
L= Luminosity
d= distance

12. Standard candle
• StandardCandles—astronomical objects with known
luminosity.
Main sequence stars.
Cepheid variables.
White dwarf supernovae.
Galaxies

13. Cepheid Variables
Cepheid variable stars are population I (metal-rich) yellow giant stars with periodic
luminosity variation….
• Their periods range from a few days to over 100 days,
• Their luminosities range from 1000 to 30,000 L⊙,
• The high luminosity makes it possible to identify them from a large distance…
• Their luminosity and period are strongly correlated. Therefore, we can determine their
luminosity by simply measuring their periods!
The luminosity of Cepheid
variabls are strongly
correlated to their
periodicity…

14. Tully-Fisher Relation
Although this is not discussed in our text
book, the luminosity of the spiral galaxies
are related to their rotational speed,. This
was discovered by B. Tully (of UH/IfA)
and J.R. Fisher in 1977. Therefore, the
luminosity of the spiral galaxies can be
determined simply by measuring their
rotational speed…
 Spiral galaxies are good standard
candles also!
 The slope of the luminosity-rotation
rate curve is different for different
type of spiral galaxies…

15. White Dwarf Supernova
Every time the hydrogen shell is ignited, the mass
of the white dwarf may increase (or decrease, we
don’t know for sure yet).
• The mass of the white dwarf may gradually
increase,
• At about 1 M⊙, the gravitation force
overcomes the electron degenerate pressure,
and the white dwarf collapses, increasing
temperature and density until it reaches
carbon fusion temperature.
• The carbon inside the white dwarfs are
simultaneously ignited. It explodes to form a
White dwarf supernova. (Type I).
• Nothing is left behind from a white dwarf
supernova explosion (In contrast to a
massive-star supernova, which would leave a
neutron star or black hole behind). All the
materials are dispersed into space.
White Dwarf Supernova is a
very important standard
candle for measuring
cosmological distance…

16. How a standard candle can be used to
measure distance.?
• Standard candles are astronomical objects of
known luminosity (L).
• Locate the standard candle.
• Measure the brightness/flux/intensity (F), of
the star
• Use inverse square law 𝐹 =
𝐿
4𝜋𝑑2
• calculate the distance d.

17. Distance and Redshift
In addition to distance, Hubble also measured the redshift of the galaxies…and when
combined with distances derived from observation of Cepheid variables and the brightest
stars in galaxies, Hubble found that, the more distant a galaxy, the greater its redshift is,
and hence the faster it is moving away from us…
→ the universe is expanding!

18. Doppler Shift Formula: (OK if v << c)
c
v
0





z
Radial velocity
(can be +ve or –ve)
Speed of light
Wavelength of light as
measured in the laboratory
Change in wavelength
(can be +ve or –ve)
redshift

19. Hubble’s Law
From the redshift and distance measurements,
we can express the recession speed V of a
galaxy located at a distant d away from us by
V = d  H0
The value of the Hubble’s Constant is
H0 = 20~24 [km/sec] / million light-year
Once the value of H0 is determined, we can
use measured recession speed to infer the
distance of galaxies using the formula
d = V / H0

20. H0 has units of (time)-1 – usually measured
in kilometres per second per Megaparsec
H0
-1 = Hubble time = timescale for the
expansion age of the Universe
Hubble’s Law
v = H0 d
Hubble’s constant
distance
Radial velocity
It tells us how fast the Universe is expanding

21. Thank you..