Download Schools @ Lord`s Bridge - University of Cambridge

Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
Resolution
Astronomers need to be able to look at objects in the sky with high precision. Resolution,
or ‘resolving power’, is a measure of how well an eye, or a telescope, can do this. It is
measured by observing whether a telescope can see two very distant, very close together
objects as separate from each other. For example: a car has two headlights. If the car is
too far away then your eye will not be able to separate the two headlights and will see
them as one lamp.
Figure 1: This is an example from NASA. On the left is a photo taken at the Las
Campanas observatory, and, on the right, one taken by the Hubble Space Telescope of
the same object:
Question 1: Which telescope has the highest resolution, the one at Las Campanas or the
Hubble Space Telescope?
ANSWER: The Hubble Space Telescope as it can see the two stars as two separate
objects.………………………………………………………………………………………………
Figure 2: One way of assigning a numerical value to resolution is to measure the smallest
angle of separation between two objects that an observer can distinguish as separate:
This angle, θ, is known as the angular resolution of a telescope. It has a particular value
for a given telescope. The smaller the angle, the better the resolution.
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
Angular Resolution
Figure 3: Two factors affect the angular separation of objects:
i) How far apart are the objects?
ii) How far away from the observer are the objects?
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
Angular Resolution
A good example of angular resolution is whether you can distinguish car headlights as
separate light sources over a large distance.
Question 2: How far away do you think a car would need to be before you can only make
out one, overall source of light, coming from both headlights? (Make a guess, then read
on to find out the correct answer…)
………………………………………………………………………………………………………
………………………………………………………………………………………………………
………………………………………………………………………………………………………
Question 3: Do you think the human eye has a better or worse angular resolution than an
optical telescope? Why?
ANSWER: Worse. This is one of the main reasons why we use telescopes.
………………………………………………………………………………………………………
………………………………………………………………………………………………………
………………………………………………………………………………………………………
Angular resolution depends on two factors: the size of the aperture of the telescope (in the
case of an eye this is the size of the pupil) and the wavelength of the electromagnetic
waves being detected. The formula is:
θ = 1.22λ
D
Where λ is the wavelength of the electromagnetic waves in metres, D is the diameter of
the aperture of the telescope, also in metres, and θ is the angular resolution of the
telescope in radians.
NOTE: A radian is a measure of an angle, just like a degree. There are 2π
(=6.2821318) radians in a circle, rather than 360 degrees. We use radians because
they are very useful. For example, the length of an arc is simply equal to the angle of
the arc in radians multiplied by the radius of the arc. This can easily be seen by
considering an arc that forms a whole circle. The circumference of a circle is 2πr,
which is equal to the angle of the circle, 2π, multiplied by the radius of the circle, r.
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
A Challenging Calculation
For a human eye:
• the size of the pupil is about 2 mm (2 x 10-3 m)
• the average wavelength of visible light is about 5 x 10-7 m
The resolution of the human eye, θ, can be calculated using the formula:
θ = 1.22λ
D
θ = 1.22 x 5 x 10-7
2 x 10-3
θ = 3 x 10-4 radians
For the human eye to resolve a pair of car headlights:
• the angular resolution of the human eye is 0.0175˚
• the separation of the car headlights is about 1 m
The distance of the car headlights away for the observer, d, is given by the formula:
d = __1___
θ
d = _____1_____
3 x 10-4
d = 3,333 m
Therefore, the human eye can resolve a pair of car headlights when the car is about 3.3
km away from the observer.
Question 4: Radio waves have a much longer wavelength than light (100,000 times
longer). Do you think that the human eye has a better or worse angular resolution than a
single radio dish? (HINT: think about the first formula you used above. Remember: the
smaller the value of θ, the better the resolution).
ANSWER: The human eye has much better angular resolution than a single radio dish.
You would need a very large dish to obtain comparable resolution (see
below).………………………………………………………………………………………………
Question 5: Remember, the angular resolution of the human eye is about 3 x 10-4
radians. For a wavelength of 0.5 m, what approximate value of D would give a radio dish
with the same resolution as the human eye? (HINT: use the formula!)
ANSWER:
D = 1.22 x 0.5
D = 2,033 m
θ = 1.22λ
So, D = 1.22λ
-4
3 x 10
D
θ
Question 6: What does this tell you about the size of radio telescopes if they are to be
any use for observing?
ANSWER: They need to be as big as possible to produce the best images.
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
The Electromagnetic Spectrum and Astronomy
Often we cannot see objects with visible light. It may be that an object, such as a star, is
very dim because it is too small, less intense or very far away. Stars may emit
electromagnetic radiation of other wavelengths however, and we can observe them using
the correct wavelength telescope. Most of the telescopes at Lord’s Bridge observe objects
using radio-waves and microwaves which often allow us to see objects that would be
invisible to us at optical wavelengths.
Figure 4: The electromagnetic spectrum
Radio
Microwave
>10-1 m 10-2 m
Infra-red
10-4 m
Visible
Ultra-violet
10-6 m
10-8 m
Wavelength
X-ray
10-10 m
Gamma ray
10-12 m <10-13 m
Did you know?
•
•
•
•
Microwaves are short wavelength radio waves.
Microwave ovens work by producing intense microwaves with a wavelength of
about 10 cm, which excite water molecules in food.
The front grill on microwave cookers has regular holes a few millimetres across.
These allow visible light waves to pass through so that you can see your
cooking, but not the longer microwaves, which are dangerous to humans.
The first artificial radio waves were produced in 1885, by Heinrich Hertz, although
their existence had been predicted by James Clerk Maxwell in 1864. Hertz, who
has the unit of frequency named after him, created the radio waves using a spark
between two metal balls held close to one another with a large voltage across
them.
As an example of using different wavelengths of electromagnetic waves to study the
universe, we can look at the binary star T Tauri, in the constellation of Taurus. Binary star
systems consist of two stars (bi means two or double) very close together in the sky, so
we need a high level of resolution to observe them separately. The two stars in the T Tauri
binary system are known as T Tau N (the northern most star) and T Tau S (the southern
most star).
Question 7: T Tauri is too faint to see with the naked eye, so we need telescopes to view
it. Can you think of the reason why telescopes can see dimmer objects than our eyes?
(Hint: think about the size of the telescope apertures)
ANSWER: Telescopes have much wider apertures than out eyes, so they can collect
more light. This allows them to see dimmer objects that don’t produce enough light
to stimulate our eyes. ……………………………………………………………………………..
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
Optical Wavelengths
T Tauri is more complicated than many other binary star systems, however, as one of the
two stars is very bright at optical wavelengths and the other is very dim.
Figure 5: Here is image of T Tauri, viewed at optical wavelengths (i.e. 5 x 10-7 m):
There is a cloud of dust on the right hand side of the binary star. This is known as a
nebula. We can see it because it reflects light from T Tauri. Note how there appears to be
only one star rather than two. Indeed, astronomers believed that there was only one star
until it was viewed using radio waves in 1981.
Radio Wavelengths
Figure 6: Here is a radio picture of the binary star at wavelength 0.02 m:
Here you can clearly see that there are two stars in the system. Declination (latitude) and
Right Ascension (longitude) are astronomical measures of position in the sky, similar to
latitude and longitude on the Earth.
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
The Electromagnetic Spectrum and Astronomy
Question 8: Which of the two stars in the binary system, T Tau N or T Tau S, emits the
most radio wavelength radiation?
ANSWER: T Tau S emits more radio wavelength radiation than T Tau N. Each
contour on the plot represents an increment in intensity, so the more contours there
are, the higher the intensity. …………………………………………………………………
Question 9: Which telescope, the radio one or optical one, had the better resolution when
these images were taken? Why?
ANSWER: The radio telescope had better resolution than the optical telescope. The
two stars are clearly seen as separate objects in the radio image, whereas only one is
seen in the optical image. ………………………………………………………………………
Question 10:
a) Look at Figure 6. Each graduation on the vertical axis is 0.2 arc seconds. Arc seconds
are a measurement of angle, like degrees, only much smaller. Using the vertical axis as a
scale, measure approximately how far apart the two stars are from one another. Record
your answer here.
ANSWER: 0.65 arc seconds. ………………….……………………………………………..…
……………………………………………………………………………………………….………
b) To convert the angle you measured in part a) from arc seconds into degrees, multiply
the number by 0.00028 (Remember, a degree is divided into minutes and seconds: 1 arc
second = 0.00028 degrees). Record your answer here.
ANSWER: 0.000182 degrees. ………………….…………………………………………..…
………………………………………………………………………………………………………
c) Your answer to part b) is the angular separation of the two stars in degrees. So, we can
say that the telescope that took the image shown in Figure 6 must have at least this value
of angular resolution. For comparison, the angular resolution of the human eye is about 1
arc minute, or 0.017 degrees). Taking your answer to part b) as the angular resolution of
the telescope, how many times better than the eye is this telescope at resolving objects?
ANSWER: 0.017 / 0.000182 = 93.4
This telescope is about 90 times better at resolving objects than the human eye. ….
d) The wavelength of the radio waves used to make the image in Figure 6 was 2 cm (0.02
m). How large (approximately) was the aperture diameter of the telescope? (HINT: use the
formula given earlier to calculate D)
ANSWER (Remembering to convert from radians to degrees):
D = 1.22 x 0.02 x 57
D = 7,642 m
θ = 1.22λ
So, D = 1.22λ
D
θ
0.000182
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
The Electromagnetic Spectrum and Astronomy
In fact, the telescopes used to take the image in Figure 6 was not this big (for Question
10, part d) you should have got an answer of about 8,000 m!). The telescope that took the
image was the Very Large Array (VLA) in New Mexico, USA, shown in Figure 7.
Figure 7: The Very Large Array (VLA) is a collection of radio dishes arranged to perform a
technique called Aperture Synthesis – just like the telescopes at Lord’s Bridge. Each
individual dish in the VLA is 25 m in diameter.
The VLA consists of a number of smaller telescopes that sweep out an effective area of a
larger telescope using the Earth’s rotation. Like the telescopes at Lord’s Bridge, the VLA
uses a technique known as aperture synthesis to achieve the highest resolution possible.
This technique involves combining the signals from an array of telescopes and adding
them together to form a better image.
The maximum diameter of the VLA is 36km, so it was very easy for it to obtain the image
in Figure 6. In the array configuration used to obtain the image, the resolution was
actually an incredible 0.00004°. An optical telescope with this angular resolution could
resolve a pair of car headlights at about 1,400 km away!
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
Using more of the electromagnetic spectrum
We have now looked at images of T Tauri using radio waves and light waves. What other
types of electromagnetic radiation could we use? We could use a smaller wavelength
wave like Ultraviolet waves or X-Ray waves. This would require using a satellite-based
telescope as these wavelengths of electromagnetic radiation do not penetrate our
atmosphere. It turns out, however, that it is much more interesting to view the pair using
Infra-red radiation, which has a wavelength that falls between radio waves and visible
waves in the electromagnetic spectrum.
Did you know?
•
Infra-red radiation can be used to “see” in the dark. Everything, including
you, emits Infra-red radiation. The wavelength of the radiation depends
on the temperature of the object. Infra-red sensors can “see” humans
and other warm objects against a background of colder objects.
When we look at the T Tau binary star system using the Infra-red section of the
electromagnetic spectrum this is what we see:
This picture of T Tau was taken using an Infra-red camera called MIRLIN (Mid-Infra-red
Large-well Imager) at the Hale telescope on Mt. Palomar in California, USA. Infra-red
radiation cannot penetrate our atmosphere very well so observations have to be made
from high up mountains or, ideally, in space. The wavelength of the Infra-red
electromagnetic radiation used to make this image was 1x10-5m.
Question 11: Which star, T Tau N or T Tau S emits the most Infra-red radiation?
ANSWER: T Tau S emits the most Infra-red radiation. The brighter the image, the
more intense the emitted radiation.…………………………………………………………
© University of Cambridge, Cavendish Laboratory, 2004.
Schools
@
Lord’s Bridge
RESOLUTION, ELECTROMAGNETIC WAVES AND BINARY STARS –
TEACHER NOTES (KS5)
Question 12: Consider your answers to Question 8 and Question 11. Now, which star
do you think is the brightest in the visible region of the electromagnetic spectrum?
………………………………………………………………………………………………………
………………………………………………………………………………………………………
You may be surprised to discover that it is actually T Tau N that is the brighter optical star,
despite the fact that the radio plot and the Infra-red photo shows T Tau N as the lesser of
the two sources.
We can summarise all these results in a table:
Radio Wavelength (λ = 0.02 m)
Infra-red Wavelength (λ = 1 x 10-5 m)
Optical Wavelength (λ = 5 x 10-7 m)
T Tau N
Dimmer
Dimmer
Brighter
T Tau S
Brighter
Brighter
Dimmer
What is the explanation for this? Well, stars emit electromagnetic waves at all
wavelengths. However, depending on the temperature of the star there will be a more
intense section of the electromagnetic spectrum where the star radiates, usually in the
Infra-red, Visible or Ultraviolet regions. The hotter the star, the shorter the dominant
wavelength of radiation emitted. It is like the flame from a Bunsen burner: blue flames are
hotter than yellow flames. The temperature governs the wavelength of light coming from
the flame.
Question 13: Our sun emits most of its light in the visible region of the spectrum. So too
does T Tau N. T Tau S, on the other hand, emits most of its radiation in the Infra-red
region of the spectrum. Therefore, which star is hotter, Tau N or Tau S?
ANSWER: T Tau N is hotter than T Tau S, because T Tau N emits most of its
radiation at shorter wavelengths than T Tau S does. ……………………………………
KEY WORDS:
•
•
•
•
•
Resolution (resolving power): How well a telescope can distinguish two objects
as separate
Angular Resolution: The smallest angle of separation between two objects that
can be resolved by a telescope.
Binary Star: Two stars very close together in the sky. They can be close
together in space, like T Tau, or they can be far apart in space, but along the
same line of sight for the observer – making them appear close in the sky.
Declination: A measure of an object’s elevation in the sky. The astronomical
equivalent of latitude.
Right Ascension: The astronomical equivalent of longitude. Along with
declination, right ascension pinpoints an object’s position in the sky.
© University of Cambridge, Cavendish Laboratory, 2004.