Welcome to AS Astronomy!
Welcome to one of the most exciting topics in your Physics course: Astronomy! In this module, we step away from the lab bench and turn our focus to the entire cosmos. You will explore how physicists measure unimaginable distances, uncover why distant galaxies are racing away from us, and discover the evidence that proves our Universe had a fiery beginning in the Big Bang.
Don't worry if the scale of space feels overwhelming at first! We will break down every concept step-by-step using everyday analogies, simple calculations, and memorable tips to help you master this topic for your CCEA AS 2 exam.
1. The Scale and Structure of the Universe
Before we calculate distances, let's understand the cosmic hierarchy from smallest to largest:
• Planetary Systems: A central star (like our Sun) orbited by planets, moons, asteroids, and comets.
• Galaxies: Colossal collections of billions of stars, gas, and dust held together by gravity. Our home is the Milky Way.
• Galaxy Clusters & Superclusters: Galaxies clump together into clusters, which in turn form massive superclusters spanning hundreds of millions of light-years.
Astronomical Distance Units
Kilometres and metres are far too small for cosmic scales. Physicists use three standard astronomical units:
1. The Astronomical Unit (\(\text{AU}\))
The mean (average) distance between the centre of the Earth and the centre of the Sun.
\(1\text{ AU} \approx 1.50 \times 10^{11}\text{ m}\)
Best used for: Distances within our Solar System.
2. The Light-Year (\(\text{ly}\))
The distance that light travels through a vacuum in one Earth year (\(365.25\text{ days}\)).
Using \(\text{distance} = \text{speed} \times \text{time}\):
\(1\text{ ly} = (3.00 \times 10^8\text{ m s}^{-1}) \times (365.25 \times 24 \times 60 \times 60\text{ s}) \approx 9.46 \times 10^{15}\text{ m}\)
Best used for: Distances between nearby stars and across galaxies.
3. The Parsec (\(\text{pc}\))
The standard unit used by professional astronomers, derived from parallax and arcseconds.
\(1\text{ pc} \approx 3.09 \times 10^{16}\text{ m} \approx 3.26\text{ ly}\)
Larger multiples include the kiloparsec (\(1\text{ kpc} = 10^3\text{ pc}\)) and megaparsec (\(1\text{ Mpc} = 10^6\text{ pc}\)).
Key Takeaway: \(\text{AU}\) is for solar systems, \(\text{ly}\) and \(\text{pc}\) are for stars and galaxies. Remember: \(1\text{ pc} > 1\text{ ly} > 1\text{ AU}\).
2. Stellar Parallax
What is Parallax?
Hold your thumb out in front of your face. Close your left eye and look with your right eye. Now switch eyes. Your thumb appears to shift position against the distant background. This apparent shift in position of a nearby object against a distant background due to a change in the observer's viewing position is called parallax.
Measuring Parallax in Space
As the Earth orbits the Sun, astronomers observe a nearby star at six-month intervals (when Earth is on opposite sides of its orbit, creating a baseline of \(2\text{ AU}\)). The nearby star appears to shift slightly against very distant "fixed" background stars.
• Parallax Angle (\(p\)): Half the total angular shift measured over six months.
• Angles in astronomy are tiny, so degrees are subdivided:
\(1\text{ degree} = 60\text{ arcminutes } (60')\)
\(1\text{ arcminute} = 60\text{ arcseconds } (60'')\)
Therefore, \(1\text{ arcsecond } (1'') = \left(\frac{1}{3600}\right)^\circ\).
The Definition of a Parsec
One parsec (\(1\text{ pc}\)) is defined as the distance to a star that has a stellar parallax angle of exactly one arcsecond (\(1''\)) using a baseline radius of \(1\text{ AU}\).
The Parallax Equation
When the angle \(p\) is given in arcseconds (\(''\)), the distance \(d\) in parsecs (\(\text{pc}\)) is simply:
\(d = \frac{1}{p}\)
Example: Proxima Centauri has a parallax angle of \(0.768''\).
\(d = \frac{1}{0.768} \approx 1.30\text{ pc}\)
Limitations of Stellar Parallax
• As distance increases, the parallax angle \(p\) becomes vanishingly small.
• Ground-based telescopes are limited by atmospheric turbulence ("blurring"), restricting ground measurements to stars within roughly \(100\text{ pc}\). Space telescopes (like Gaia) can measure much further because they are above Earth's atmosphere.
Key Takeaway: Parallax only works for relatively nearby stars. The smaller the angle \(p\), the farther away the star is (\(d \propto \frac{1}{p}\)).
3. Luminosity, Radiant Flux Intensity, and Standard Candles
Luminosity vs. Radiant Flux Intensity
It is crucial not to confuse these two terms:
• Luminosity (\(L\)): The total power emitted by a star across all wavelengths. It is measured in Watts (\(\text{W}\)) or \(\text{J s}^{-1}\). This is an intrinsic property of the star—it doesn't change no matter how far away you stand.
• Radiant Flux Intensity (\(F\)): The radiant power received per unit area perpendicular to the direction of the light. It is measured in \(\text{W m}^{-2}\). This is the observed "brightness".
The Inverse Square Law
As light travels outward from a star, it spreads uniformly across the surface of an expanding sphere with surface area \(A = 4\pi d^2\), where \(d\) is the distance to the star.
\(F = \frac{L}{4\pi d^2}\)
Where:
• \(F\) = Radiant flux intensity (\(\text{W m}^{-2}\))
• \(L\) = Luminosity of the star (\(\text{W}\))
• \(d\) = Distance from the star to the observer (\(\text{m}\))
What is a Standard Candle?
A standard candle is an astronomical object that has a known, fixed luminosity (\(L\)).
How astronomers determine distance using a Standard Candle:
1. Identify a standard candle (such as a Cepheid variable star or a Type Ia Supernova).
2. Determine its known luminosity \(L\).
3. Measure its observed radiant flux intensity \(F\) at Earth using a telescope.
4. Rearrange the Inverse Square Law to calculate the distance \(d\):
\(d = \sqrt{\frac{L}{4\pi F}}\)
Key Takeaway: If you know how intrinsically bright an object is (\(L\)) and how bright it looks (\(F\)), you can calculate its distance (\(d\)).
4. The Doppler Effect and Redshift
The Doppler Effect for Light
You have experienced the Doppler effect with sound: when an ambulance drives past, its siren sounds higher-pitched as it approaches and lower-pitched as it speeds away. The same effect happens with light:
• Blue Shift: When a light source moves towards the observer, the observed wavelength is compressed (shortened), shifting spectral lines towards the blue/violet end of the spectrum.
• Redshift: When a light source moves away from the observer, the observed wavelength is stretched (lengthened), shifting spectral lines towards the red end of the spectrum.
The Redshift Equation
For celestial bodies moving at speeds \(v\) much less than the speed of light \(c\) (\(v \ll c\)):
\(z = \frac{\Delta \lambda}{\lambda_0} = \frac{\lambda - \lambda_0}{\lambda_0} = \frac{v}{c}\)
Where:
• \(z\) = Redshift (a dimensionless quantity)
• \(\Delta \lambda\) = Change in wavelength (\(\text{m}\))
• \(\lambda_0\) = Emitted (rest) wavelength measured in a laboratory (\(\text{m}\))
• \(\lambda\) = Observed wavelength from the distant object (\(\text{m}\))
• \(v\) = Recessional velocity of the galaxy (\(\text{m s}^{-1}\))
• \(c\) = Speed of light in a vacuum (\(3.00 \times 10^8\text{ m s}^{-1}\))
Common Mistake to Avoid: Make sure \(\lambda_0\) is always in the denominator, not the observed wavelength \(\lambda\)!
Key Takeaway: Redshift means an object is moving away from us. Greater redshift means greater recessional speed.
5. Hubble's Law and the Expanding Universe
Edwin Hubble's Discovery
In 1929, Edwin Hubble measured the distances and spectral shifts of distant galaxies. He discovered two crucial facts:
1. Almost all distant galaxies show redshift, meaning they are moving away from us.
2. The recessional speed \(v\) of a galaxy is directly proportional to its distance \(d\) from Earth.
Hubble's Law Equation
\(v = H_0 d\)
Where:
• \(v\) = Recessional velocity of the galaxy (\(\text{km s}^{-1}\) or \(\text{m s}^{-1}\))
• \(d\) = Distance to the galaxy (\(\text{Mpc}\) or \(\text{m}\))
• \(H_0\) = Hubble Constant (the gradient of the velocity vs. distance graph)
Units of the Hubble Constant (\(H_0\))
• In astronomical units: \(H_0 \approx 70\text{ km s}^{-1}\text{ Mpc}^{-1}\)
• In SI units: Convert \(\text{km}\) to \(\text{m}\) and \(\text{Mpc}\) to \(\text{m}\) to give \(H_0\) in units of \(\text{s}^{-1}\).
Estimating the Age of the Universe
If galaxies are moving apart today, running time backwards means all matter was once concentrated at a single point. Assuming the expansion rate has been roughly constant:
\(\text{Time } t = \frac{\text{Distance}}{\text{Velocity}} = \frac{d}{v}\)
Substituting Hubble's Law (\(v = H_0 d\)):
\(t \approx \frac{d}{H_0 d} = \frac{1}{H_0}\)
Therefore, the approximate age of the Universe is given by the Hubble Time: \(T \approx \frac{1}{H_0}\) (when \(H_0\) is expressed in \(\text{s}^{-1}\)).
Did you know? Current estimates place the Hubble age of the Universe at roughly \(13.8\text{ billion years}\).
6. The Big Bang Theory and Supporting Evidence
The Big Bang Theory states that the Universe began as an extremely hot, infinitely dense point (a singularity) roughly 13.8 billion years ago, and has been expanding and cooling ever since.
Key Observational Evidence
1. Galactic Redshift and Hubble's Law
The observed expansion of the Universe implies that all matter originated from a single hot, dense starting point in the past.
2. Cosmic Microwave Background Radiation (CMBR)
• In 1965, Penzias and Wilson detected a uniform, faint microwave radiation coming from every direction in the sky.
• This is the cooled relic radiation produced shortly after the Big Bang.
• Originally extremely high-energy, short-wavelength gamma radiation, the expansion of space has stretched these wavelengths over billions of years into the microwave region.
• The CMBR corresponds to blackbody radiation at a temperature of approximately \(2.7\text{ K}\), is remarkably isotropic (the same in all directions), and exhibits tiny fluctuations that explain how matter clumped together to form galaxies.
3. Relative Abundance of Hydrogen and Helium
Nuclear fusion during the first few minutes after the Big Bang (Big Bang nucleosynthesis) predicted that the Universe should consist of roughly \(75\%\) Hydrogen and \(24\%\) Helium by mass, with trace amounts of Lithium. Modern observations match this prediction with remarkable precision.
Quick Review Summary Box
• Parallax formula: \(d = \frac{1}{p}\) (Distance in \(\text{pc}\), angle in \(\text{arcseconds}\)).
• Inverse Square Law: \(F = \frac{L}{4\pi d^2}\) (Brightness decreases with distance squared).
• Standard Candle: An object of known luminosity \(L\) used to find cosmic distances.
• Doppler Redshift: \(z = \frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}\) (Light from receding objects stretches to longer wavelengths).
• Hubble's Law: \(v = H_0 d\) (Distant galaxies move away faster).
• Age of Universe: \(T \approx \frac{1}{H_0}\).
• Pillars of Big Bang Theory: Hubble expansion/redshift, Cosmic Microwave Background Radiation (\(2.7\text{ K}\)), and the \(3:1\) mass ratio of Hydrogen to Helium.