Doppler shift, redshift and the universe

An ambulance sounding its siren moves at constant speed directly towards a listener who is standing still.
Compared with the sound emitted by the siren, which statement describes the sound received by the listener?

A hydrogen line with a laboratory wavelength of 486.1 nm is observed at 488.5 nm in the spectrum of a galaxy.
What is the speed of the galaxy along the line of sight?

Which observation is evidence for the existence of dark matter?

A train sounds its horn at a constant frequency as it travels at constant speed along a straight track towards a passenger standing on a platform. The train then passes the platform and moves away.

A calcium absorption line has a laboratory wavelength of 393.4 nm. In the spectrum of a distant galaxy the same line is observed at 401.2 nm. The Hubble constant is 70 km s⁻¹ Mpc⁻¹.

Figure 1 shows the wavefronts of sound from a source S at one instant. S moves at constant speed along the line joining two stationary observers, P and R.
How do the frequencies heard by P and by R compare with the frequency emitted by S?

Figure 1 shows the position of a hydrogen absorption line in a laboratory spectrum and in the spectrum of a distant galaxy. The laboratory wavelength of the line is 656.3 nm.
What is the recession speed of the galaxy?

The bar chart shows the mean density of four model universes, W, X, Y and Z, compared with the critical density. All four are expanding now. Consider the effect of gravity alone.
Which universe or universes will eventually stop expanding and then contract?

Figure 1 shows wavefronts of sound spreading out from a stationary loudspeaker S. One grid square represents 0.20 m. A cyclist C rides directly towards S at a constant speed. The speed of sound in air is 340 m s⁻¹.

A satellite transmits radio waves of frequency 400 MHz. As it passes over a ground station, the station records the change Δf between the received frequency and 400 MHz. The graph shows Δf against time t; t = 0 is the moment of closest approach. The satellite moves at a constant speed of 7.5 km s⁻¹.

A galaxy is 85 Mpc from the Earth. The Hubble constant is 68 km s⁻¹ Mpc⁻¹.
What redshift z is expected in the light from this galaxy?

The Hubble constant is taken as 72 km s⁻¹ Mpc⁻¹. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.
Assuming the universe has always expanded at the same rate, what is its age?

Considering gravity alone, the mean density of a model universe is greater than the critical density.
What is the ultimate fate of this universe?

New measurements increase the accepted value of the Hubble constant by 10%.
The age of the universe is estimated as 1/H₀. By what factor does this estimate change?

A student analyses data for five galaxies. The distances were found using standard candles and the recession speeds from redshifts.

Cold hydrogen gas in space emits radio waves of frequency 1420 MHz. A radio telescope receives this emission from a distant galaxy at a frequency of 1385 MHz. The Hubble constant is 68 km s⁻¹ Mpc⁻¹. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.

A star orbits a companion star. Its orbit is circular and is seen edge-on from the Earth. Over several weeks, the wavelength of a line in the star's spectrum is measured; the laboratory wavelength of this line is 600.00 nm. The observed wavelength varies smoothly between a minimum of 599.96 nm and a maximum of 600.08 nm and repeats every 6.0 days.

The graph shows the recession speed v of nine galaxies plotted against their distance d, with a best-fit line through the origin. 1 Mpc = 3.09 × 10²² m.
What is the Hubble constant, in s⁻¹?

A star moves in an orbit, so its velocity along the line of sight from the Earth changes as shown in the graph. A positive velocity means the star is moving away from the Earth. A sodium line in the star's spectrum has a laboratory wavelength of 589.00 nm.
What is the shortest wavelength observed for this line?

A small loudspeaker emitting a note of constant frequency is fixed to the end of a rotating arm, so that it moves anticlockwise at constant speed around the circle shown in Figure 1. A listener L is a long way away, level with the centre of the circle.
At which position is the loudspeaker when it emits the sound that L hears with the highest frequency?

Figure 1 is a scale drawing of the wavefronts of sound from a source S that is moving at constant speed along the horizontal line. The wavefronts were emitted at intervals of one period of the source. One grid square represents 5.0 cm. The speed of sound in air is 340 m s⁻¹.

Figure 1 shows part of the emission spectrum of oxygen gas in a laboratory, and the same part of the spectra of two distant galaxies, P and Q. The laboratory wavelength of the emission line is 500.7 nm. The Hubble constant is 71 km s⁻¹ Mpc⁻¹.

An astronomer measures the redshift z and the distance d of nine galaxies and plots the graph shown, with distance in metres. The best-fit line through the origin passes through the gridline intersection at 8.0 × 10²⁴ m, z = 0.060. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.

A galaxy is seen edge-on. A spectral line with a laboratory wavelength of 500.0 nm is observed at 503.2 nm from one edge of the galaxy and at 502.0 nm from the opposite edge.
What is the orbital speed of the stars at the edges?

Astronomers measure the orbital speeds of gas clouds in a spiral galaxy from Doppler shifts. At 8.0 kpc from the centre the speed is 230 km s⁻¹; at 25 kpc it is 225 km s⁻¹. Almost all of the galaxy's visible stars lie within 8.0 kpc of the centre. Assume circular orbits. 1 kpc = 3.09 × 10¹⁹ m; G = 6.67 × 10⁻¹¹ N m² kg⁻².

Astronomers do not yet agree on the age of the universe or on its ultimate fate.

Two independent methods of measuring the Hubble constant give 67 km s⁻¹ Mpc⁻¹ and 73 km s⁻¹ Mpc⁻¹. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.

The graph shows the rotation curve of a spiral galaxy: the orbital speed v of stars and gas against distance r from the centre. Two points are marked on the curve. Assume circular orbits, so that the mass inside an orbit is M = v²r/G.
What is the ratio (mass inside the orbit at 30 kpc) ÷ (mass inside the orbit at 10 kpc)?

The graph shows how the separation of two distant galaxy clusters has changed with time in a model of the universe, together with the tangent to the curve at the present time. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.
What is the Hubble constant at the present time in this model?

The graph shows how the relative size of the universe changes with time in three models, X, Y and Z, considering gravity alone. In each model the universe is expanding at the same rate today. The dashed line shows a universe that has always expanded at this constant rate. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.

The chart shows values of the Hubble constant H₀ obtained by four different methods. Each value is shown with its uncertainty as an error bar. 1 Mpc = 3.09 × 10²² m. 1 year = 3.15 × 10⁷ s.

A spiral galaxy is seen edge-on. The graph shows the observed wavelength of the hydrogen-alpha line, measured at different positions along the galaxy's major axis. The laboratory wavelength of the line is 656.30 nm. Three points are marked on the curve. Assume the stars and gas move in circular orbits. 1 kpc = 3.09 × 10¹⁹ m.