Astrophysics and CosmologyEdexcel International A Level Physics: Topic test

20 questions, 54 marks

Edexcel International A Level Physics

Astrophysics and Cosmology topic test

Total 54 marks

Name

Class

Date

1
Mars has a mass of 6.42 × 10²³ kg and a radius of 3.39 × 10⁶ m. Treat Mars as an isolated uniform sphere. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the gravitational field strength at the surface of Mars?
[1 mark]
A1.26 × 10⁷ N kg⁻¹
B0.93 N kg⁻¹
C5.6 × 10¹⁰ N kg⁻¹
D3.73 N kg⁻¹
(b)
What is the gravitational potential at the surface of Mars?
[1 mark]
A−1.26 × 10⁷ J kg⁻¹
B+1.26 × 10⁷ J kg⁻¹
C−3.73 J kg⁻¹
D−4.28 × 10¹³ J kg⁻¹
(c)
Calculate the minimum work that must be done to move a lander of mass 1500 kg from the surface of Mars to a point very far from Mars.
[2 marks]
Total for question 1: 4 marks
2
Io, a moon of Jupiter, moves in a circular orbit of radius 4.22 × 10⁸ m about the centre of Jupiter, whose mass is 1.90 × 10²⁷ kg. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the orbital speed of Io?
[1 mark]
A3.0 × 10⁸ m s⁻¹
B1.73 × 10⁴ m s⁻¹
C2.45 × 10⁴ m s⁻¹
D0.71 m s⁻¹
(b)
What is the orbital period of Io?
[1 mark]
A2.4 × 10⁴ s
B7.7 × 10⁴ s
C1.53 × 10⁵ s
D9.6 × 10⁵ s
(c)
Show that, for a satellite in a circular orbit about Jupiter, the square of the orbital period is proportional to the cube of the orbital radius.
[2 marks]
Total for question 2: 4 marks
3
A red dwarf star has a surface temperature of 3000 K and a radius of 1.0 × 10⁸ m. Treat it as a black body radiator. The Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴, Wien's constant is 2.898 × 10⁻³ m K and the luminosity of the Sun is 3.85 × 10²⁶ W.
(a)
Calculate the wavelength at which the red dwarf emits the maximum intensity of radiation, and state in which region of the electromagnetic spectrum this lies.
[3 marks]
(b)
Calculate the luminosity of the red dwarf, and compare it with the luminosity of the Sun.
[4 marks]
Total for question 3: 7 marks
4
A star S has a parallax angle of 0.050 arcseconds when observed from Earth. The intensity of the radiation from S measured at Earth is 1.0 × 10⁻⁹ W m⁻², and the wavelength at which its radiation has maximum intensity is 483 nm. Treat S as a black body radiator. 1 pc = 3.09 × 10¹⁶ m; σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien's constant is 2.898 × 10⁻³ m K. The Sun is a main sequence star with a surface temperature of 5800 K, a luminosity of 3.85 × 10²⁶ W and a radius of 6.96 × 10⁸ m.
(a)
Calculate the distance to S in metres, and the luminosity of S. State how the luminosity of S compares with that of the Sun, and why trigonometric parallax would be unsuitable if S were 2000 pc away.
[6 marks]
(b)
The luminosity of S is 4.8 × 10²⁷ W. Calculate the surface temperature and the radius of S, and explain what its position on a Hertzsprung–Russell diagram, compared with the Sun, suggests about its stage of evolution.
[6 marks]
Total for question 4: 12 marks
5
A Cepheid variable star in a nearby galaxy is used as a standard candle. It has a known luminosity of 5.0 × 10³⁰ W and the intensity of its radiation measured at Earth is 2.0 × 10⁻¹⁶ W m⁻². 1 pc = 3.09 × 10¹⁶ m.
(a)
What is the distance to the Cepheid variable star?
[1 mark]
A4.5 × 10²² m
B1.6 × 10²³ m
C2.0 × 10⁴⁵ m
D8.9 × 10²² m
(b)
The same star would be moved to a distance four times greater. What would be the intensity measured at Earth?
[1 mark]
A8.0 × 10⁻¹⁶ W m⁻²
B5.0 × 10⁻¹⁷ W m⁻²
C3.2 × 10⁻¹⁵ W m⁻²
D1.25 × 10⁻¹⁷ W m⁻²
(c)
Explain why trigonometric parallax could not be used to find the distance to this galaxy.
[2 marks]
Total for question 5: 4 marks
6
A white dwarf has a luminosity of 3.0 × 10⁻³ times that of the Sun and a surface temperature of 25 000 K. The luminosity of the Sun is 3.85 × 10²⁶ W and the Stefan–Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Treat the white dwarf as a black body radiator.
(a)
On a Hertzsprung–Russell diagram, with luminosity increasing upwards and surface temperature increasing to the left, where is the white dwarf?
[1 mark]
Atop left
Btop right
Cbottom left
Dbottom right
(b)
What is the radius of the white dwarf?
[1 mark]
A7.2 × 10⁶ m
B2.0 × 10⁶ m
C5.1 × 10¹⁰ m
D4.1 × 10¹² m
(c)
Describe how a star similar in mass to the Sun evolves from the main sequence to become a white dwarf.
[2 marks]
Total for question 6: 4 marks
7
Light from a galaxy in a distant cluster is observed to have a lower frequency than when it was emitted, with |Δf|/f = 0.0150. Take c = 3.00 × 10⁸ m s⁻¹, the Hubble constant H₀ = 2.3 × 10⁻¹⁸ s⁻¹, 1 year = 3.16 × 10⁷ s and 1 Mpc = 3.09 × 10²² m.
(a)
State whether the galaxy is moving towards or away from Earth, with a reason, and calculate its speed relative to Earth.
[3 marks]
(b)
Use Hubble's law to calculate the distance to the galaxy in megaparsecs, and use H₀ to estimate the age of the universe in years.
[4 marks]
Total for question 7: 7 marks
8
A star orbits the centre of a spiral galaxy in a circular orbit of radius 2.5 × 10²⁰ m at a speed of 2.2 × 10⁵ m s⁻¹. The mass of visible matter (stars and gas) inside the orbit is estimated to be 5.0 × 10⁴⁰ kg. Treat the mass inside the orbit as a point mass at the centre of the galaxy. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
Calculate the mass inside the orbit of the star that is needed to produce this orbital speed, and explain what the result suggests about the matter in the galaxy.
[6 marks]
(b)
Explain how the possible existence of dark matter, and the uncertainty in the value of the Hubble constant, lead to controversy over the age and the ultimate fate of the universe.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).