Understanding Parallax and Parsecs

Hello and welcome to today's lesson looking at the concepts of parallax and parsecs in astrophysics. So in today's lesson we're going to try and understand these concepts of parallax and parsecs. We're going to try and understand parsecs and light years as distance measurements, define the parsec and the light year and calculate different astronomical distances in different distance units which falls into the following part of the AQA A-level physics specification for astrophysics. So the next part of this course is going to look at stars and stellar physics. Now our galaxy we think may contain over 250 billion stars and we can classify stars based on their distance from the Earth. Now in today's lesson we're going to look at how we can measure the distances between different stars and the Earth. So as you'll be aware we live in the Milky Way galaxy which is a collection of approximately 250 billion stars. So in comparison to our own solar system, the Milky Way is vast. So for example, the Kepler search was a 10-year mission to find exoplanets, and you can see in the concept of the entire Milky Way galaxy, we've barely covered it at all. Now, in this small area of space, we observed over 530,000 stars in this small area of the Milky Way alone. So again, that included 2,662 planets. Now... In this particular methodology, we use something called the transit method to detect these exoplanets. Now, the transit method is where the exoplanet moves in between the star and the Earth's common plane, causing the star to be dimmed from the perspective of the Earth. Now, the transit method only actually works for stars in the same plane, i.e. edge-on, as the Earth. Now, in comparison to other galaxies, our Milky Way is an above-average galaxy, but it's not the biggest galaxy. Now, whilst the space in between galaxies, known as voids, is even bigger than the galaxies themselves, now we can even try and measure the entire observable universe, which is the region of space we can observe via electromagnetic radiation, such as visible light. Now, so far, we've observed no spatial edge to the universe. We have, however, observed a temporal edge to the universe, and there was no time, which was observable... before this temporal edge, so we call the event which produced this the Big Bang. Now this means outside the observable universe exists the entire universe. So to put it bluntly, space is big, it's very very big. Now astronomical distances are extremely big and therefore we've got to use several different units of distance to make these numbers smaller and more easier to manage. So what units do we use to measure distance in astronomy? Well there are three main units used to measure distances in astronomical objects. The first unit is the light year. Now the light year is used in many particular science fiction shows such as Star Trek where they discuss distances between stars. You've got the parsec which was famously used in Star Wars by Han Solo. It's a famous scene as it implies the parsec is a speed when it's actually in fact a distance. So it says in the particular Star Wars scene that it's a ship that made the Kessel Run in less than 12 parsecs. That would be like saying I once ran a marathon in 18 miles because parsecs is a measure of distance. And the third unit which we can measure distance is the Astronomical Unit or the AU. Now the AU is used predominantly when looking at distances inside our solar system. Now the first unit we're going to focus on is the astronomical unit, the AU. Now the astronomical unit is the mean distance between the Earth and the Sun. Now the mean distance must be used as the distance between the Earth and the Sun varies throughout the year as the Earth's orbit is an ellipse and not a circle. So as a result you will see that as the Earth orbits the Sun, the distance between the Earth and the Sun is changing, so therefore we have to use the mean distance. Now counter-intuitively, the northern hemisphere is closer to the Sun during the winter months compared to the summer months, which is actually one reason why our summers in the northern hemisphere are milder than those in the southern hemisphere. Now, we are using the average distance between the Sun and the Earth to determine the astronomical unit. Now, Copernicus defined the concept of the astronomical unit, but didn't know the value of this term. Now, the size of the astronomical unit... was found in 1769 when it was carefully measured during a transit of Venus, which is when Venus passes between the Earth and the Sun from the perspective of the Earth. Now one astronomical unit is the mean distance from the Sun to the Earth and we have a value of 1.5 million times the distance between the Sun and the Earth. value of 1.5 times 10 to the 11 meters. Now the next unit we're going to look at is the light year. Now the light year is the distance travelled by an electromagnetic wave in a vacuum in one Earth year. Now we use electromagnetic waves to detect the different objects in the universe. So how do you know things such as stars and galaxies and quasars exist? We know that because they emit electromagnetic radiation. So therefore the distance from an object in light years tells you how long ago that radiation was emitted or set off from that object. In essence, it's telling you what the image of the object is, when it's from, and how long it was ago. So if an object is 10 light years away, you are observing it as it was 10 years ago. So, for example, because the moon is 1.3 light seconds from the Earth, When you observe the Moon, you observe the Moon as it was 1.3 seconds ago. The same for the Sun, but it's 8.3 minutes. The same for Alpha Centauri, the nearest star to the Earth, which is not the Sun, which is 4.3 light years away. So therefore, you observe Alpha Centauri as it was 4.3 years ago. You observe the Hercules-Gobleta Cluster as it was 25,000 years ago. And you observe the Andromeda Galaxy. the nearest galaxy to us which is not the Milky Way, as it was 2.5 million years ago, as it's 2.5 million light years away. Now this property of the universe allows us to examine the evolution of the universe over time, but the issue is it doesn't allow us to see how distant galaxies compare in composition to our present day galaxies, only what distant galaxies were like a very long time ago. So the light year is the distance travelled by light, or any electromagnetic radiation in a vacuum in one Earth year. And they can be easily converted into meters by multiplying the speed of light in a vacuum, 3 times 10 to the 8 meters per second, by the number of seconds in a year, to get our value of 9.46 times 10 to the 15 meters. Now the last unit we need to look at is the parsec. Now the parsec is the most commonly used astronomical unit, but it is also the most difficult unit to define. Now one parsec is the distance which causes a parallax angle of one arc second to be observed. Now the idea of astronomical parallax is similar to the idea of experimental parallax. Now an astronomical parallax is the relative change in position of an object due to the motion or the angle of the observer. So the distance to nearby stars can be calculated by observing how much they move relative to stars at a distance. so they appear not to move at all, the background stars. Now this is done by comparing the position of a nearby star in relation to the background stars at different parts of the Earth's orbit. So consider you are moving and you observe the night sky. So if you have a movement in a particular direction, the stars appear to move in the night sky. Now the closer the star is to the observer, the greater this movement. So you'll observe that a near star... will move a lot more than a far star, which will move a lot more than a distant galaxy. So that's a very important idea. Now the nearest star moves a great deal in the night sky, the far star moves a little in the night sky, and the distant galaxy remains approximately fixed. Now the maximum distance where you can observe this movement is approximately 350 light years away. Now, the stars therefore appear to move in the night sky. This concept is observed in the night sky as the Earth is moving around the Sun in orbit. So you'll notice that there is this apparent movement. So we can observe this change in position due to the fixed positions of the distant galaxies which appear not to move. So these galaxies are also moving slightly due to the parallax, however it's such a small effect we can't detect it. So over the course of the year, the stars move backwards and forwards in the night sky as the Earth is orbiting the Sun in an ellipse. So the stars appear to move in the night sky, so over the Earth year, the following movement will be observed. It goes from position 1 to position 2, then back to position 3 from position 2. So the changing angle observed by the observer is called the angle of parallax. So if you observe the position of a star at either end of the Earth's orbit, so when they're six months apart from each other, the angle of the parallax is half the angle that the star moves in the night sky. in relation to the background stars. Now the greater the angle of parallax the closer the star is to the observer. So we can consider a right angle triangle that forms over half the Earth's orbit. So we can observe it as this right-angled triangle. So we know that from mathematics, from SOHCAHTOA, from trigonometry, that tan theta is equal to the opposite side of the right-angled triangle divided by the adjacent side of the right-angled triangle, which in this particular right-angled triangle is the radius of the orbit divided by the distance between the Earth and that particular star. So in this particular idea, we'll call that r in d. So tan theta is equal to r over d. Now here, r is the mean distance between the sun and the earth. So r is one astronomical unit. So therefore, we know that theta is approximately equal to r over d when using the small angle approximation, which states that tan theta is approximately theta when we are using the angle in radians. So all angles measured in astronomy are going to be less than 10 degrees, so this particular approximation is always followed. Now remember, when you give an answer and you use this in an examination, please state that you are using the small angle approximation as an assumption. So we can now define a parsec as the distance between the Earth and the star when the parallax angle is exactly 1 arc second. Now just to clarify... There are 60 arc minutes in one degree and there are 60 arc seconds in one arc minute. So therefore, the definition of an arc second is it's 1 3,600th of a degree as there are 3,600, 60 times by 60, arc seconds in a degree. Now the definition of the parsec must include you drawing this triangle to show the different values. So most examination mark schemes... show this particular orientation in the definition of your particular parsec. So one arc second is an extremely small change in the position of a star from the Earth. Now parallax angles of less than 0.01 arc seconds are actually very difficult to measure from the Earth because of the smearing effect of the Earth's atmosphere, which limits Earth-based telescopes to measure distances to stars to approximately 100 parsecs away. Space-based telescopes can get an accuracy to 0.001, which is an increasing number of stars whose distance can be measured via this parallax methodology. However, most stars, even in our own galaxy, are much further away than 1,000 parsecs, since the Milky Way is about 30,000 parsecs across. So we must use a different method to the parallax methodology to measure those distances. Now we measure distances greater than 300 parsecs with a method called the standard candle. Now we'll look at these ideas of standard candles later in the course. Now there's also a shortcut method to working out the distance between objects if you have an angle of parallax. So if we define the angle of parallax to be theta we can actually say the distance between the sun and the nearby star which we're measuring is equal to one over theta. Now this formula is derived from a complex mathematical formula in relationships you have not covered yet. But this formula works when the angle is in arc seconds. And this gives you a distance in parsecs. Now this equation is not given to you on your examination sheet. You are expected to memorise it. So to clarify, this is the same diagram here which is shown previously but in the opposite orientation. So we can remember that 1 parsec is the distance which causes a... parallax angle of one arc second to be observed. So the parsec is an important unit because of the way distances to nearby stars can be determined by using something called trigonometrial parallax. Now this involves measuring how the apparent position of a star against the much more distant background star changes as the earth goes around the Sun and one parsec is approximately 3.26 light years. So let's have a look at an example question which uses the concept of parallax. So a star in orbit around the Earth has a radius of 6.6 metres. Given that it's in orbit 569 kilometres from the Earth, find the angle subtended by it as it's viewed from the Earth. Well, so you use the equation to find half the angle subtended, which is theta is approximately equal to r over d. Remember, we can drop the tan theta aspect because we're using a small angle approximation. You then convert your kilometers into meters, so you get an angle of 1.159 times 10 to the minus 5, and it's in radians because that's the unit we use in this particular methodology. So therefore, if you want to find the total angle subtended, you then double it because you've just found out half the angle subtended. So, what have we learned in today's lesson? One astronomical unit, 1 AU, is the distance between the Earth and the Sun. One light year is the distance travelled between light or any electromagnetic radiation in one year. And one parsec is the distance at which the observed parallax angle is equal to one arc second. So the second of one arc, which is one three thousand six hundredth of a degree. So if you have been successful and you've learned in today's lesson, you should be able to understand what parsecs and light years are as distance measurements, define the light year, define the parsec and calculate different. astronomical distances in different distance units. Hope you've enjoyed today's lesson on parallax and parsecs and have a lovely day.

So the next part of this course is going to look at stars and stellar physics. Now our galaxy we think may contain over 250 billion stars and we can classify stars based on their distance from the Earth. Now in today's lesson we're going to look at how we can measure the distances between different stars and the Earth.

So as you'll be aware we live in the Milky Way galaxy which is a collection of approximately 250 billion stars. So in comparison to our own solar system, the Milky Way is vast. So for example, the Kepler search was a 10-year mission to find exoplanets, and you can see in the concept of the entire Milky Way galaxy, we've barely covered it at all.

Now, in this small area of space, we observed over 530,000 stars in this small area of the Milky Way alone. So again, that included 2,662 planets. Now...

In this particular methodology, we use something called the transit method to detect these exoplanets. Now, the transit method is where the exoplanet moves in between the star and the Earth's common plane, causing the star to be dimmed from the perspective of the Earth. Now, the transit method only actually works for stars in the same plane, i.e. edge-on, as the Earth.

Now, in comparison to other galaxies, our Milky Way is an above-average galaxy, but it's not the biggest galaxy. Now, whilst the space in between galaxies, known as voids, is even bigger than the galaxies themselves, now we can even try and measure the entire observable universe, which is the region of space we can observe via electromagnetic radiation, such as visible light. Now, so far, we've observed no spatial edge to the universe.

We have, however, observed a temporal edge to the universe, and there was no time, which was observable... before this temporal edge, so we call the event which produced this the Big Bang. Now this means outside the observable universe exists the entire universe. So to put it bluntly, space is big, it's very very big.

Now astronomical distances are extremely big and therefore we've got to use several different units of distance to make these numbers smaller and more easier to manage. So what units do we use to measure distance in astronomy? Well there are three main units used to measure distances in astronomical objects.

The first unit is the light year. Now the light year is used in many particular science fiction shows such as Star Trek where they discuss distances between stars. You've got the parsec which was famously used in Star Wars by Han Solo.

It's a famous scene as it implies the parsec is a speed when it's actually in fact a distance. So it says in the particular Star Wars scene that it's a ship that made the Kessel Run in less than 12 parsecs. That would be like saying I once ran a marathon in 18 miles because parsecs is a measure of distance. And the third unit which we can measure distance is the Astronomical Unit or the AU. Now the AU is used predominantly when looking at distances inside our solar system.

Now the first unit we're going to focus on is the astronomical unit, the AU. Now the astronomical unit is the mean distance between the Earth and the Sun. Now the mean distance must be used as the distance between the Earth and the Sun varies throughout the year as the Earth's orbit is an ellipse and not a circle.

So as a result you will see that as the Earth orbits the Sun, the distance between the Earth and the Sun is changing, so therefore we have to use the mean distance. Now counter-intuitively, the northern hemisphere is closer to the Sun during the winter months compared to the summer months, which is actually one reason why our summers in the northern hemisphere are milder than those in the southern hemisphere. Now, we are using the average distance between the Sun and the Earth to determine the astronomical unit.

Now, Copernicus defined the concept of the astronomical unit, but didn't know the value of this term. Now, the size of the astronomical unit... was found in 1769 when it was carefully measured during a transit of Venus, which is when Venus passes between the Earth and the Sun from the perspective of the Earth.

Now one astronomical unit is the mean distance from the Sun to the Earth and we have a value of 1.5 million times the distance between the Sun and the Earth. value of 1.5 times 10 to the 11 meters. Now the next unit we're going to look at is the light year.

Now the light year is the distance travelled by an electromagnetic wave in a vacuum in one Earth year. Now we use electromagnetic waves to detect the different objects in the universe. So how do you know things such as stars and galaxies and quasars exist?

We know that because they emit electromagnetic radiation. So therefore the distance from an object in light years tells you how long ago that radiation was emitted or set off from that object. In essence, it's telling you what the image of the object is, when it's from, and how long it was ago. So if an object is 10 light years away, you are observing it as it was 10 years ago. So, for example, because the moon is 1.3 light seconds from the Earth, When you observe the Moon, you observe the Moon as it was 1.3 seconds ago.

The same for the Sun, but it's 8.3 minutes. The same for Alpha Centauri, the nearest star to the Earth, which is not the Sun, which is 4.3 light years away. So therefore, you observe Alpha Centauri as it was 4.3 years ago. You observe the Hercules-Gobleta Cluster as it was 25,000 years ago. And you observe the Andromeda Galaxy.

the nearest galaxy to us which is not the Milky Way, as it was 2.5 million years ago, as it's 2.5 million light years away. Now this property of the universe allows us to examine the evolution of the universe over time, but the issue is it doesn't allow us to see how distant galaxies compare in composition to our present day galaxies, only what distant galaxies were like a very long time ago. So the light year is the distance travelled by light, or any electromagnetic radiation in a vacuum in one Earth year. And they can be easily converted into meters by multiplying the speed of light in a vacuum, 3 times 10 to the 8 meters per second, by the number of seconds in a year, to get our value of 9.46 times 10 to the 15 meters.

Now the last unit we need to look at is the parsec. Now the parsec is the most commonly used astronomical unit, but it is also the most difficult unit to define. Now one parsec is the distance which causes a parallax angle of one arc second to be observed. Now the idea of astronomical parallax is similar to the idea of experimental parallax.

Now an astronomical parallax is the relative change in position of an object due to the motion or the angle of the observer. So the distance to nearby stars can be calculated by observing how much they move relative to stars at a distance. so they appear not to move at all, the background stars.

Now this is done by comparing the position of a nearby star in relation to the background stars at different parts of the Earth's orbit. So consider you are moving and you observe the night sky. So if you have a movement in a particular direction, the stars appear to move in the night sky. Now the closer the star is to the observer, the greater this movement.

So you'll observe that a near star... will move a lot more than a far star, which will move a lot more than a distant galaxy. So that's a very important idea.

Now the nearest star moves a great deal in the night sky, the far star moves a little in the night sky, and the distant galaxy remains approximately fixed. Now the maximum distance where you can observe this movement is approximately 350 light years away. Now, the stars therefore appear to move in the night sky.

This concept is observed in the night sky as the Earth is moving around the Sun in orbit. So you'll notice that there is this apparent movement. So we can observe this change in position due to the fixed positions of the distant galaxies which appear not to move.

So these galaxies are also moving slightly due to the parallax, however it's such a small effect we can't detect it. So over the course of the year, the stars move backwards and forwards in the night sky as the Earth is orbiting the Sun in an ellipse. So the stars appear to move in the night sky, so over the Earth year, the following movement will be observed.

It goes from position 1 to position 2, then back to position 3 from position 2. So the changing angle observed by the observer is called the angle of parallax. So if you observe the position of a star at either end of the Earth's orbit, so when they're six months apart from each other, the angle of the parallax is half the angle that the star moves in the night sky. in relation to the background stars. Now the greater the angle of parallax the closer the star is to the observer.

So we can consider a right angle triangle that forms over half the Earth's orbit. So we can observe it as this right-angled triangle. So we know that from mathematics, from SOHCAHTOA, from trigonometry, that tan theta is equal to the opposite side of the right-angled triangle divided by the adjacent side of the right-angled triangle, which in this particular right-angled triangle is the radius of the orbit divided by the distance between the Earth and that particular star.

So in this particular idea, we'll call that r in d. So tan theta is equal to r over d. Now here, r is the mean distance between the sun and the earth. So r is one astronomical unit. So therefore, we know that theta is approximately equal to r over d when using the small angle approximation, which states that tan theta is approximately theta when we are using the angle in radians.

So all angles measured in astronomy are going to be less than 10 degrees, so this particular approximation is always followed. Now remember, when you give an answer and you use this in an examination, please state that you are using the small angle approximation as an assumption. So we can now define a parsec as the distance between the Earth and the star when the parallax angle is exactly 1 arc second. Now just to clarify... There are 60 arc minutes in one degree and there are 60 arc seconds in one arc minute.

So therefore, the definition of an arc second is it's 1 3,600th of a degree as there are 3,600, 60 times by 60, arc seconds in a degree. Now the definition of the parsec must include you drawing this triangle to show the different values. So most examination mark schemes... show this particular orientation in the definition of your particular parsec. So one arc second is an extremely small change in the position of a star from the Earth.

Now parallax angles of less than 0.01 arc seconds are actually very difficult to measure from the Earth because of the smearing effect of the Earth's atmosphere, which limits Earth-based telescopes to measure distances to stars to approximately 100 parsecs away. Space-based telescopes can get an accuracy to 0.001, which is an increasing number of stars whose distance can be measured via this parallax methodology. However, most stars, even in our own galaxy, are much further away than 1,000 parsecs, since the Milky Way is about 30,000 parsecs across.

So we must use a different method to the parallax methodology to measure those distances. Now we measure distances greater than 300 parsecs with a method called the standard candle. Now we'll look at these ideas of standard candles later in the course.

Now there's also a shortcut method to working out the distance between objects if you have an angle of parallax. So if we define the angle of parallax to be theta we can actually say the distance between the sun and the nearby star which we're measuring is equal to one over theta. Now this formula is derived from a complex mathematical formula in relationships you have not covered yet. But this formula works when the angle is in arc seconds. And this gives you a distance in parsecs.

Now this equation is not given to you on your examination sheet. You are expected to memorise it. So to clarify, this is the same diagram here which is shown previously but in the opposite orientation. So we can remember that 1 parsec is the distance which causes a...

parallax angle of one arc second to be observed. So the parsec is an important unit because of the way distances to nearby stars can be determined by using something called trigonometrial parallax. Now this involves measuring how the apparent position of a star against the much more distant background star changes as the earth goes around the Sun and one parsec is approximately 3.26 light years.

So let's have a look at an example question which uses the concept of parallax. So a star in orbit around the Earth has a radius of 6.6 metres. Given that it's in orbit 569 kilometres from the Earth, find the angle subtended by it as it's viewed from the Earth.

Well, so you use the equation to find half the angle subtended, which is theta is approximately equal to r over d. Remember, we can drop the tan theta aspect because we're using a small angle approximation. You then convert your kilometers into meters, so you get an angle of 1.159 times 10 to the minus 5, and it's in radians because that's the unit we use in this particular methodology.

So therefore, if you want to find the total angle subtended, you then double it because you've just found out half the angle subtended. So, what have we learned in today's lesson? One astronomical unit, 1 AU, is the distance between the Earth and the Sun. One light year is the distance travelled between light or any electromagnetic radiation in one year. And one parsec is the distance at which the observed parallax angle is equal to one arc second.

So the second of one arc, which is one three thousand six hundredth of a degree. So if you have been successful and you've learned in today's lesson, you should be able to understand what parsecs and light years are as distance measurements, define the light year, define the parsec and calculate different. astronomical distances in different distance units. Hope you've enjoyed today's lesson on parallax and parsecs and have a lovely day.

Transcript for:Understanding Parallax and Parsecs

Transcript for:
Understanding Parallax and Parsecs