Astronomical distances are measured using stellar parallax (D = 1/P in parsecs) and Hubble's Law (v = H₀D), where the age of the universe is calculated as 1/H₀; the cosmic microwave background radiation, released during recombination and uniformly distributed at 2.7 Kelvin, provides strong evidence for the Big Bang theory, while hydrogen spectral lines are commonly used for velocity measurements due to hydrogen's abundance in the universe.
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OCR Paper 1 A Level Physics RevisionAdded:
Let's all solve some OCR A level physics paper one revision questions. The first question is about the stellar parallax.
State and explain how the stellar parallax is used to measure distances in space. Okay, so the stellar parallax is caused by the relative motion of the Earth around the Sun, which allows us to measure the parallax angle. And we do that with respect to the background of fixed stars.
Once we have the parallax angle, we can calculate the corresponding distance using D is equal to 1 over P, which will give us the distance in parsecs.
Next one, figure 23.1 gives some data and we have some wavelengths of hydrogen and this is on the Andromeda galaxy and on the Virgo Cluster.
The Virgo Cluster is 16.5 megaparsecs from the Earth. Estimate the age of the universe using the data. So, it's a good time.
It's still pretty amazing that we can estimate the age of the universe using some data, so let's do that. So, to calculate the age of the universe, we are going to use Hubble's constant. Now, the Hubble's law says that the speed is equal to the recession velocity given by H0 multiplied by D. We know what the distance in megaparsecs is. What we need to do is work out the speed. So, the only way to work out the speed in this case would be to The only way to work out the speed from these wavelengths would be to use the Doppler shift equation. So, I'm just going to use that delta lambda over lambda is about equal to V over C, meaning that V is going to be equal to delta lambda over lambda multiplied by C. Okay, so the fractional change in wavelength, that's going to be I'm just going to work in nanometers, so that'll be 489.8 take away 486.1. Then I'm going to divide this by 486.1.
Multiply this by the speed of light, which is uh what is it? 3.0 * 10 to the 8 m/s.
Now, this here will just give me around 2.28 * 10 to the power of 6 m/s.
Okay, we have the speed, so let's work out H0. So, I'm going to bring this expression I'm going to plug that into here. So, I'm going to say that H0 uh is going to be given by V over D. And then the age of the universe is 1 over H0.
So, that's just going to be D over V.
So, that's going to be 16.5 megaparsecs. That's 10 to the power of 6 multiplied by 1 parsec, which is 3.1 multiplied by 10 to the power of 16.
Divide that by the speed, which is 2.28 times by 10 to the power of 6, giving us right around 2.24 * 10 to the power of 17 seconds.
And this is a very large number as you would expect, 2.24 * 10 to the power of 17. Perfect. Suggest why hydrogen spectral lines might often be used to measure the star's relative velocity.
Well, it is the most abundant element in the universe.
Okay, next one. The Big Bang theory is an explanation for the start of the universe. Explain how the cosmic microwave background radiation supports the Big Bang theory for the start of the universe. Comment on the relevance of the data in figure 23.1.
The first thing that I'm going to do is cover some points for the cosmic microwave background radiation.
So, the CMBR was released during the what is known as recombination time. You don't really need to know this uh for the specification, but it was uh to the beginning of the universe as gamma as in very very intense gamma radiation, which has then been red shifted to microwaves.
Its intensity is uniform in all directions, and it has a corresponding temperature of 2.7 Kelvin.
Now, how does that support the Big Bang theory? Well, the Big Bang theory is the theory of the expansion of the universe from a very very small point. So, if the initial gamma rays have been stretched to in all directions to that corresponding temperature, this is one piece of major evidence for the Big Bang theory.
What else do we need to do? We need to comment on the relevance of the data concerning the Big Bang theory. Well, the data is showing two things. Number one, that there is a recessional velocity, and we've actually calculated that for the Virgo Cluster. With the Andromeda Galaxy, very interestingly though, it's the only galaxy that is moving towards us. It's about to combine with our galaxy into one super galaxy I think in the next 500 million years. So, this galaxy actually shows an evidence of blue shift. So, I can say that the figure shows that the far away Virgo galaxy is receding away from the Earth, and the Andromeda is blue shifted because it is approaching Earth.
And one thing with six-markers is if there's a calculation that can be done, I would also probably include it. to guarantee myself the full marks, I would also calculate the speed at which Andromeda is actually approaching. So, I can just use the same expression that delta lambda over lambda is about equal to V over C. So, let's label this as the blue shift velocity.
In other words, uh V will just be given by delta lambda over lambda multiplied by C. And our delta lambda will be given by 485.6 take away 486.1. This will be negative now because it's in the other direction multiplied by the speed of light, which is 3.0 * 10 ^ 8. This here is just going to give us around three minus 3.1 * 10 ^ 5 uh m/s. And I've covered quite a lot of points. I've calculated everything that can be calculated. So, I'm feeling pretty good about the six-marker. If you're revising for paper one OCR, you should also check out this question over here, which might be really useful for you in astrophysics. Good luck revising.
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