U Cephei is an eclipsing binary system consisting of two stars that orbit their common centre of mass - AQA - A-Level Physics - Question 2 - 2022 - Paper 4
Question 2
U Cephei is an eclipsing binary system consisting of two stars that orbit their common centre of mass. The primary star is class B; the secondary star is class G.
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Worked Solution & Example Answer:U Cephei is an eclipsing binary system consisting of two stars that orbit their common centre of mass - AQA - A-Level Physics - Question 2 - 2022 - Paper 4
Step 1
Explain the shape of the graph in Figure 1.
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Answer
The minima occur when one star passes in front of the other, causing a reduction in observed brightness. The rhythm of the graph suggests that the system is periodically eclipsing, leading to the observed drops in apparent magnitude.
Step 2
State why the average of the values in Table 1 is different from the laboratory value.
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Answer
The average values in Table 1 differ from the laboratory value due to the Doppler effect; the stars are moving in relation to the observer, which causes shifts in the measured wavelengths.
Step 3
Show that the orbital speed of the primary star is about 250 km s^-1.
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Using the formula for Doppler shift:
u}{
u_0} = rac{v}{c}$$
where the change in wavelength,
$$ riangle
u =
u_{ ext{max}} -
u_{ ext{min}} = 486.498 ext{ nm} - 486.136 ext{ nm} = 0.362 ext{ nm},$$
we find the speed as follows:
$$v = c imes rac{ riangle
u}{
u_0}$$
Substituting known values yields:
$$v ext{ (in km/s)} = 3 imes 10^8 m/s imes rac{0.362 imes 10^{-9}}{486.136 imes 10^{-9}} \\ = 250 ext{ km/s}.$$
Step 4
Calculate the orbital radius of the primary star.
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To calculate the orbital radius, we can use Kepler's third law. Given the period can be derived from the light curve, if we assume it is approximately 2.5 days:
T=2.5extdays=2.5imes24imes3600extseconds,
we find
r = rac{(G imes M imes T^2)^{1/3}}{2 imes rac{ ext{period}}{2 ext{π}}},
substituting values for gravitational constant G and solar mass M gives us the radius in meters.
Step 5
Which absorption lines would be most prominent in the spectrum of the primary star? Tick (✓) one box.
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The most prominent absorption lines in the spectrum of the primary star would be from hydrogen and helium.
Step 6
Discuss how astronomers could confirm this.
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Astronomers could confirm the presence of a white dwarf and a neutron star through observational techniques such as detecting X-rays from the neutron star, analyzing the spectra of the stars to identify their composition, and observing the gravitational effects of one star on the other, which could indicate their masses.
