Edexcel A-Level Physics: Gravitational Fields and Space

A star spends most of its life on the main sequence of the Hertzsprung-Russell diagram, fusing hydrogen in its core. When the core hydrogen is exhausted the star leaves the main sequence, and its final fate is decided by its mass.

Explain how a star like the Sun evolves once it leaves the main sequence, and explain how the evolution and final remnant of a star of much greater mass differs. In your answer you should refer to the balance between gravity and outward pressure, to the formation of a red giant or supergiant, and to the possible end-states (white dwarf, neutron star or black hole).

(6 marks)

Two planets, Planet X and Planet Y, can each be treated as uniform spheres whose entire mass acts at the centre. Their data are given below.

Quantity	Planet X	Planet Y
Mass, $M$M	$6.0 \times 10^{24}$6.0×1024 kg	$3.0 \times 10^{23}$3.0×1023 kg
Radius, $R$R	$6.4 \times 10^{6}$6.4×106 m	$2.4 \times 10^{6}$2.4×106 m

(Gravitational constant $G = 6.67 \times 10^{-11}$G=6.67×10−11 N m² kg⁻².)

(a) Calculate the gravitational field strength at the surface of Planet X. (2 marks)

(b) Calculate the gravitational field strength at the surface of Planet Y. (1 mark)

(c) A probe of mass 1200 kg rests on the surface of Planet X. Calculate the gravitational potential at the surface of Planet X, and hence the minimum work that must be done to move the probe from the surface to a point far away (effectively infinity). (3 marks)

An astronomer measures the recession speed of five distant galaxies and estimates their distance from Earth. The results are shown below.

Galaxy	Distance, $d$d / Mpc	Recession speed, $v$v / km s⁻¹
A	50	3 600
B	100	6 800
C	150	10 700
D	200	13 900
E	250	17 800

(Take 1 Mpc $= 3.09 \times 10^{19}$=3.09×1019 km.)

(a) State Hubble's law and explain how these data support it. (2 marks)

(b) Use the data to determine a value for the Hubble constant $H_0$H0​ in km s⁻¹ Mpc⁻¹. (1 mark)

(c) Hence estimate the age of the universe in seconds, and state one assumption your estimate relies on. (2 marks)

An Earth-observation satellite moves in a circular orbit at a radius of $r = 8.0 \times 10^{6}$r=8.0×106 m measured from the centre of the Earth. The mass of the Earth is $M = 6.0 \times 10^{24}$M=6.0×1024 kg and $G = 6.67 \times 10^{-11}$G=6.67×10−11 N m² kg⁻².

The gravitational force on the satellite provides the centripetal force needed for its circular orbit.

(a) Show that the orbital speed of the satellite is given by $v = \sqrt{\dfrac{GM}{r}}$v=rGM​​, and calculate its value. (3 marks)

(b) Hence calculate the orbital period of the satellite. Give your answer in minutes. (2 marks)

A star behaves as a black body. Its spectrum peaks at a wavelength of $\lambda_{max} = 290$λmax​=290 nm, and its radius is $R = 1.5 R_\odot$R=1.5R⊙​, where $R_\odot = 6.96 \times 10^{8}$R⊙​=6.96×108 m.

Use Wien's displacement law $\lambda_{max} T = 2.90 \times 10^{-3}$λmax​T=2.90×10−3 m K and the Stefan-Boltzmann law $L = 4\pi R^2 \sigma T^4$L=4πR2σT4, with $\sigma = 5.67 \times 10^{-8}$σ=5.67×10−8 W m⁻² K⁻⁴.

(a) Calculate the surface temperature of the star. (2 marks)

(b) Hence calculate the luminosity of the star. (2 marks)

This question is about two key definitions in the Gravitational Fields and Space topic.

(a) Define what is meant by the gravitational field strength at a point in a gravitational field, and state its SI unit. (2 marks)

(b) State Hubble's law and state what the Hubble constant $H_0$H0​ represents. (1 mark)