Hubble's law

The photograph below was taken by the James Webb Space Telescope (JWST) and shows a group of galaxies that formed shortly after the big bang, about 1310⁹ years ago.

Derive the equation T = 1/H₀ where T is the age of the universe.

State one assumption made in your derivation.

The parsec (pc) is a unit used for astronomical distances. 1 pc is 3.1×10¹⁶m.

The accepted range for the Hubble constant H₀ is (60–80) km s^–1 Mpc^–1. Deduce whether the observation by the JWST leads to a value of H₀ within the accepted range.

1 year = 3.1610⁷s

The light from one of the galaxies, called Maisie, has a redshift z of 14. The wavelength of light from Maisie detected at the telescope is 4.010^–6m and lies within the infrared section of the electromagnetic spectrum.

Calculate the wavelength of light emitted by Maisie.

Explain why the light emitted by Maisie arrives at the telescope as infrared.

One of the infrared detectors on the JWST is made from material with a work function of 0.30 eV.

Deduce whether this detector can detect the light from Maisie.

Astronomers observing stars at the centre of our galaxy have suggested that many of them are orbiting a supermassive black hole. The mass of this black hole is 9.2 10³⁶kg.

Calculate the orbital period for a star in a circular orbit at a distance of 1.9 10¹⁴m from a black hole of this mass.

The star S0-2 is in a highly elliptical orbit around the position of the black hole.

At its point of closest approach, S0-2 is at a distance of 1.8 10¹³m from the centre of the black hole.

At the most distant point of its orbit, S0-2 is 2.7 10¹⁴m from the black hole.

Show that the change in gravitational potential between the closest and most distant points in this orbit is about 3 10¹³J kg⁻¹.

At its point of closest approach, the star is travelling at a speed of 8.1 10⁶m s⁻¹.

Calculate the speed of S0-2 at the furthest point in its orbit using the change in gravitational potential.

mass of S0-2 = 2.4 10³¹kg

Trigonometric parallax and Hubble’s law are two methods used to determine astronomical distances. Explain whether either of these methods is suitable to determine the distance to S0-2.

There are several different methods that can be used to determine the distance from our solar system to astronomical objects. These include the measurement of red shift, trigonometrical parallax and the use of standard candles.

Which row of the table shows a suitable method for each of the objects named?

There are several different methods that can be used to determine the distance from our solar system to astronomical objects. These include the measurement of red shift, trigonometrical parallax and the use of standard candles.

Which row of the table shows a suitable method for each of the objects named?

In 1990, the Hubble Space Telescope (HST) was launched into a low Earth orbit above the Earth’s atmosphere.

HST orbits the Earth in a circular orbit with a speed of 7.59 km s^–1.

mass of Earth = 5.97 × 10²⁴ kg radius of Earth = 6.37 10⁶ m

Show that the height of HST above the surface of the Earth is about 6 × 10⁵ m.

Calculate the increase in the gravitational potential energy as HST is raised, from its initial position at the Earth’s surface, to its orbital height.

mass of HST = 11 600 kg

A student suggests that giving HST more energy than that required in (ii) would result in the satellite orbiting at a greater height and with a greater speed.

Assess the validity of the student’s suggestion.

The transmission of electromagnetic radiation through the atmosphere is shown on the graph.

State one advantage shown by this graph of positioning a telescope above the atmosphere.

High resolution images from HST allow astronomers to make detailed measurements of very distant galaxies. The graph shows how the recessional velocities of distant galaxies depend on their distance from Earth.

Determine an age for the universe.

The distance to astronomical objects relatively close to the Sun is determined using trigonometric parallax. For objects beyond a certain distance standard candles are used.

State what is meant by a standard candle.

Explain why trigonometric parallax is not used beyond a certain distance.

Describe how distances too large for the use of standard candles can be determined.