Practise Edexcel A-Level Physics astrophysics and cosmology through gravitational fields, stellar radiation laws, HR diagrams, parallax, redshift and Hubble’s law.
The dwarf planet Ceres is the largest object in the asteroid belt.
Ceres has a mass of . Ceres has a circular orbit of radius around the Sun.
Show that the gravitational force exerted on Ceres by the Sun is about .
Determine the time T, in years, for Ceres to make one complete orbit about the Sun.
1 year
Mercury is the smallest planet in our solar system. The gravitational field strength at the surface of Mercury is .
It is claimed that the gravitational field strength at the surface of Ceres is less than 5% of .
Evaluate whether this claim is accurate.
radius of Ceres
Weather satellites may be in an equatorial orbit or a polar orbit, as shown.
A weather satellite in a polar orbit circles the Earth at a height of 8.50 × 10^5 m above the surface of the Earth.
Show that the gravitational potential at this height is about −5.5 × 10^7 J kg^-1.
mass of Earth = 5.98 × 10^24 kg
radius of Earth = 6360 km
Hence calculate the increase in gravitational potential energy when the satellite is placed in orbit.
satellite mass = 4990 kg
gravitational potential at the Earth’s surface = −6.27 × 10^7 J kg^-1
Increase in gravitational potential energy =
It is claimed that a satellite in orbit at a height of would make 15 orbits of the Earth every 24 hours.
Assess the validity of this claim.
It is suggested that the satellite could be placed in an equatorial orbit at a radius of 42200 km . With this radius the satellite would have an orbital period equal to 24 hours.
Give one advantage and one disadvantage of placing a weather satellite in a polar orbit rather than in the suggested equatorial orbit.
Electrostatic forces and gravitational forces can both be modelled by the idea of a field. Give one similarity and one difference between electric fields and gravitational fields.
Similarity
Difference
The dwarf planet Ceres is the largest object in the asteroid belt.
Ceres has a mass of . Ceres has a circular orbit of radius around the Sun.
Show that the gravitational force exerted on Ceres by the Sun is about .
The dwarf planet Ceres is the largest object in the asteroid belt.
Ceres has a mass of . Ceres has a circular orbit of radius around the Sun.
Mercury is the smallest planet in our solar system. The gravitational field strength at the surface of Mercury is .
It is claimed that the gravitational field strength at the surface of Ceres is less than 5% of .
Evaluate whether this claim is accurate.
radius of Ceres
The Sun is a main sequence star.
As the Sun continues its evolution, its mass will decrease. It is estimated that at its largest radius, the mass of the Sun will have decreased significantly.
Explain how the orbital period of a planet would change as the mass of the Sun decreases.
Assume that the radius of the planet’s orbit about the Sun does not change.
The Sun is a main sequence star.
The Sun will eventually leave the main sequence and become a red giant star.
luminosity of Sun = 3.83 × 10^26 W
At this stage of its evolution the Sun will be classified as a red giant star. The wavelength of red light is between 6.2 × 10^-7 m and 7.8 × 10^-7 m.
Comment on the value for λ_max and this classification of the Sun.
The Sun is a main sequence star.
The Sun will eventually leave the main sequence and become a red giant star.
luminosity of Sun = 3.83 × 10^26 W
Show that the current radius of the Sun is about 7.0 × 10^8 m.
surface temperature of Sun = 5780 K
The Sun is a main sequence star.
The Sun will eventually leave the main sequence and become a red giant star.
luminosity of Sun = 3.83 × 10^26 W
As a red giant star, the radius of the Sun will be about 150 times its current radius. Its luminosity will be about 1600 times its current luminosity.
λ_max is the wavelength at which peak power radiation occurs.
Show that when the Sun is in its red giant stage, λ_max is about 1 × 10^-6 m.
current radius of Sun = 7.0 × 10^8 m
Cepheid variable stars are used by astronomers as standard candles.
The luminosity of Cepheid variable stars varies periodically.
There is a linear relationship between the period and the mean luminosity of a Cepheid variable star, as shown.
When viewed from Earth, the mean intensity of this Cepheid variable star is 5.1 × 10^-4 W m^-2.
Determine the distance of this Cepheid variable star from Earth.
Distance of this Cepheid variable star from Earth =
The astronomer Hertzsprung used parallax to determine the distances to some of the variable stars known as Cepheids.
Using parallax measurements, astronomers can determine distances to all stars with a parallax angle larger than .
The variable star Alpha Cephei is from the Earth.
Deduce whether the distance to Alpha Cephei could be determined from parallax measurements.
distance from Earth to Sun
The astronomer Hertzsprung used parallax to determine the distances to some of the variable stars known as Cepheids.
Cepheids are a type of standard candle.
Describe how standard candles can be used to determine distances to stars.
The astronomer Hertzsprung used parallax to determine the distances to some of the variable stars known as Cepheids.
The Sun is a yellow star with a surface temperature of about 6000 K . In the 20th century, astronomers discovered a large variety of stars in our galaxy. Hertzsprung and Russell developed the Hertzsprung-Russell (HR) diagram as a way of classifying stars.
An HR diagram is shown below.
Label the x-axis of the HR diagram. You should include approximate values.
There are five zones, Z 1, Z 2, Z 3, Z 4 and Z 5, identified on the HR diagram. Complete the following table. You should match one zone with each description.
The astronomer Hertzsprung used parallax to determine the distances to some of the variable stars known as Cepheids.
The Sun is a yellow star with a surface temperature of about 6000 K . In the 20th century, astronomers discovered a large variety of stars in our galaxy. Hertzsprung and Russell developed the Hertzsprung-Russell (HR) diagram as a way of classifying stars.
An HR diagram is shown below.
The position of a star on the HR diagram changes as the star evolves. Explain how a star like the Sun evolves as it progresses from zone Z3 to its final position on the HR diagram.
A massive planet orbits the red dwarf star Gliese 876. The planet was discovered after wavelength shifts in spectral lines were seen in the light received from the star.
Explain how a massive planet orbiting a star can cause a change in the wavelength of light received from the star.
The spectrum of light emitted by the star Chi Lupi provides evidence of mercury atoms in the outer layers of the star. The light emitted from the star is compared with light emitted from a mercury lamp on Earth.
One line in the spectrum of light from Chi Lupi has a wavelength of 576.933 nm . The equivalent line in a mercury spectrum produced on Earth is 576.959 nm .
A student concluded from this data that Chi Lupi is moving towards the Earth, and that the relative velocity of Chi Lupi is about .
Deduce whether the student's conclusions are correct.
The ultimate fate of the universe is uncertain.
Which of the following would result in an open universe?
The average density of the universe is equal to the critical density of the universe.
The average density of the universe is less than the critical density of the universe.
The mass of the universe is equal to the critical mass of the universe.
The mass of the universe is greater than the critical mass of the universe.