Cosmology

What is the doppler effect?

The apparent change in the frequency and wavelength of waves received from an object moving relative to an observer compared to what would be observed without relative motion

What is pitch?

The frequency of sound waves

Explain red shift

If the galaxy is moving away from the Earth ('receding') the absorption lines will be red-shifted - they all move towards the red end of the spectrum, because the wavelength appears stretched.

Explain blue shift

If the galaxy is moving towards the Earth the absorption lines will be blue-shifted - they move towards the blue end of the spectrum, because the wavelength appears shorter.

State the Doppler equation and the meaning of each symbol and their units

• λ is the source wavelength (measured in a lab on earth) and Δλ is the change in wavelength recorded by the observer. Units of both are m (metres)

• f is the source frequency (measured in lab on earth) and Δf is the change in frequency recorded by the observer. Unit of both is Hz (Hertz)

• v is the magnitude of the relative velocity between the source and observer, and c is the speed of light through a vacuum (3.00 x 10⁸ ms^-1). Unit of both is ms^-1 (metres per second)

The Doppler equation can only be used in which situations?

The Doppler equation can only be used for objects with speeds far less than the speed of light.

What is the Astronomical Unit (definition, symbol, conversion, when the unit is used)?

• The mean distance from the Earth to the Sun

• Symbol AU

• 1 au = 150 million km = 1.50 x 10¹¹m

• Most often used to express the average distance between the Sun and other planets in the Solar System.

What is the light year (definition, symbol, conversion, when the unit is used)?

• The light-year is the distance travelled by light in a vacuum in a time of one year.

• Symbol ly

• 1 ly = 9.46×10¹⁵m

• The light-year is often used when expressing distances to stars or other galaxies.

Describe a practical to determine the wavelength of light with a diffraction grating (diagram with labelled equipment, method, analysis, uncertainties, safety)

Method:

• Record the number of lines per mm on your diffraction grating.

• Set up the apparatus as shown in the diagram so that you can see two bright spots on either side of the central bright spot.

• Measure the distance D from the grating to the screen using a metre rule

• Measure the distance x₁ from the central bright spot to the first bright spot on the left, n = 1, using a metre rule

• Measure the distance x₂ from the central bright spot to the second bright spot on the left, n = 2, using a metre rule

Analysis:

• number of lines per m = number of lines per mm × 10^-3

• Calculate slit seperation using d = 1 / number of lines per m

• Angle θ_n = arctan( x_n / D ). Use this equation to calculate θ₁ and θ₂ from the recorded data

• nλ = d × sin θ. Rearranging this gives λ = ( d × sin θ ) / n. Use this to calculate the values of wavelength for θ₁ and θ₂

Uncertainties:

• The percentage uncertainty of λ can be reduced by increasing D and/or by measuring the distance between the central bright spot and a higher order bright spot

Safety:

• Never look directly into the laser

• Switch lasers off when not in use

• Ensure the screen is a matt surface with no potential for reflection

Explain the name ‘Annual parallax method’

Is called ‘annual’ as measurements are taken at 2 times over a year.

Is called ‘parallax’ as nearby stars appear at different positions depending on where you view them from

Explain the annual parallax method

The distance to nearby stars can be found using the annual parallax method

To do this angular displacements ‘A’ between a star and a distant star are measured, when the Earth is at opposite extremities of its orbit around the sun (eg. January and July)

The parallax angle ‘p’ is the average of A.

The angles are small so often stated in arc seconds. 1 arc sec = 1/3600 degrees

Distance D in m = 1.5 x 10¹¹ / tan(p°)

to be finished

What is the relationship between the degree, arcminute and arcsecond?

There are 60 arcminutes in 1°, and 60 arcseconds in each arcminute.

Define the arcminute

(1/60)°, a minute of arc

Define the arcsecond

(1/3600)° = 1/60 arcminutes, a second of arc

Define the parsec and draw a diagram to aid this definition

• Distance at which 1AU subtends an angle of 1/3600th degree (=1 parsec)

• 1 pc = 1 AU / tan(1/3600°) ≈ 3.1 × 10¹⁶ m

What is the parallax equation and the meaning and unit of each term?

• p = 1/d

• p is the parallax angle in arcsec

• d is the distance to a nearby star (< 100 pc away) in parsec (pc)

State Hubble’s Law

The recessional speed v of a galaxy is almost directly proportional to its distance d from the Earth

What is the equation relating the recessional speed of distant galaxies to their distance from us, and the meaning and unit of each term?

• v = H₀d 

• v is the recessional speed

• H₀ is the hubble constant

• d is the ditant of the galaxy from us

What is the Cosmological Principle?

The assumption that, when viewed on a large enough scale, the Universe is homogeneous and isotropic, and the laws of physics are universal

What is mean by homogeneous (in the context of cosmology)?

Uniform in terms of the distribution of matter across the Universe when viewed on a sufficiently large scale

What is meant by isotropic?

The same in all directions (for example the Universe, appearing the same to any observer regardless of position)

What is cosmic background radiation (CMBR)?

The microwave signal of uniform intensity detected from all directions of the sky, which fits the profile for a black body at a temperature of 2.7K

Which objects did Edwin Hubble take pictures of? What measurements did he take?

He photographed nebuli, and measure the variation in birghtness of the stars within them.

List Hubble’s findings

• The distance to the Andromeda galaxy was ∼2 million ly, much farther than anyone expected. This showed the universe was much larger than we had innitialy thought.

• Showed the universe was expanding

What does Hubble’s Law indicate about the size of the universe?

The universe is expanding

What does Hubble’s Law indicate about origin of the universe?

It suggests that all matter originated from a single point in the past, commonly referred to as the Big Bang

If everything is moving away from us are we the centre of the universe?

No, as there is no centre from which everything expands.

Describe the big bang

A moment in the past when all the matter in the Universe was contained in a singularity (a single point), the beginning of space and time, that expanded rapidly outwards

What experimental evidence supports the Big Bang?

• Hubble's law shows that the Universe is expanding. It follows that, if we could run time backwards, the Universe would be much smaller, denser, and hotter, and would eventually reach a single point.

• Physicist have detected a uniform microwave signal they could not account for. They had accidentally discovered the microwave background radiation that could only be explained by the Big Bang and the expansion of space.