Download Light of Distant Stars - Glasgow Science Centre

The Light of Distant Stars – Activity Guide
Learning Objectives
1. To understand how a graph showing light against time works.
2. To know that planets orbit distant stars and that these planets are called
‘extrasolar planets.’
3. To be able to explain how we gain information about extrasolar planets
from starlight.
4. To critically analyse the transit method used to find exoplanets and find
flaws with it.
5. To gain insight into the importance of the electromagnetic spectrum in
astronomy.
6. To know that it is possible to use Kepler’s Laws and Newton’s Laws to
learn about extrasolar planets.
Learning Experiences
SCN 3-06a
MTH 3-06a
SCN 4-06a
MTH 4-06a
SCN 3-08a
MNU 3-20a
MNU 4-20a
Leader Guide
This is an involved lesson using physics and mathematics to demonstrate one of the methods
used by scientists in the search for planets orbiting distant stars.
What you will need: low power bulb (star), beads of varying sizes (planets)
Optional: light sensor and computer with sensor interface and graphic function
Start with introducing the idea of a transit – where a planet passes in front of a star. It is
comparable in many ways to a solar eclipse, except that the effect is significantly lessened by
the distance of the planets. Included in this document is an account from Jeremiah Horrocks
on the transit of Venus.
We will then consider how to use a graph to show the change of light over time, and see how it
can be used to show an object causing a star to appear to dim.
Following this, we will use actual data to look for planets orbiting other stars.
Using Kepler’s laws, we will try and take away some information about these planets, just from
exploring the dimming effect on stars.
Finally, we will discuss the limitations of this method of observation, and consider how Newton’s
laws might help us discover even more extrasolar planets.
The Transit of Venus —Jeremiah Horrocks
Jeremiah Horrocks was an English astronomer who lived in the 17th century. He wrote
about the first observed transit of Venus. Here is his account of the event, as taken from
his book Venus in Sole Visa:
When the time of the observation approached, I retired to my apartment, and having closed the windows
against the light, I directed my telescope, previously adjusted to a focus, through the aperture towards the Sun
and received his rays at right angles upon the paper ... I watched carefully on the 24th from sunrise to nine
o'clock, and from a little before ten until noon, and at one in the afternoon, being called away in the intervals
by business of the highest importance which, for these ornamental pursuits, I could not with propriety
neglect ... About fifteen minutes past three in the afternoon, when I was again at liberty to continue my labours,
the clouds, as if by divine interposition, were entirely dispersed ... I then beheld a most agreeable spectacle, the
object of my sanguine wishes, a spot of unusual magnitude and of a perfectly circular shape, which had already
fully entered upon the Sun's disk on the left ... Not doubting that this was really the shadow of the planet, I
immediately applied myself sedulously to observe it ... although Venus continued on the disk for several hours,
she was not visible to me longer than half-an-hour, on account of [the Sun] so quickly setting ... The inclination
was the only point upon which I failed to attain the utmost precision; for, owing to the rapid motion of the
Sun, it was difficult to observe with certainty to a single degree ... But all the rest is sufficiently accurate, and as
exact as I could desire.
Light
After discussing Horrocks observations, set up the bulb at the front of the class, dim the lights.
Explain that the light bulb is a star. Children are all planets, able to get the stars light as long
as it is uninterrupted. Draw a graph on the board of light against time. Light should be
constant.
Time
Light
A planet is orbiting the star. This planet is a large textbook. It passes in front of the star,
dimming its light to all the children. Ask the class if anyone thinks they can draw the graph
of light against time for when the planet moved in front of the star. Anything showing a
dimming effect raising back to full is essentially correct. Ask a number of kids up to see what
each comes up with and get them to explain their reasons. Be a devils advocate, pushing
them to understand the results. Vote on their final answer.
Time
Ask what would happen to the transit graph if the planet were smaller. Take a number of
ideas (if provided) and put them up on the board.
Take the largest bead, and pass it in front of the bulb. Ask group what has happened.
Dimming effect is less.
Tell them that the time it is taking to pass by the star is remaining the same, but that it would
look different on the graph. Ask for volunteers to try and draw the change. Anything
where light doesn’t dim as much as with the book, but dims for the same duration, should be
considered correct.
Take the next largest bead and repeat. Ask for another volunteer to the new graph.
Anything where light doesn’t dim as much as previous bead, but dims for the same duration,
should be considered correct.
Time
Light
Light
Light
Repeat this all the way to the smallest bead. By now group should have an understanding
of how the graph represents light intensity. And you should have seen a trend of graphs
looking like this:
Time
Time
This should be building the group into understanding the reduced size of the planet affects
the stars light less, and to understand the way in which the graph shows this information.
The Transit of Beads – Moving Faster
Time
Light
Light
Light
Pick one of the bead sizes. Get the group to discuss what would happen to the transit
graph if the planet were to move faster. Ask someone to come up and draw it on the
board. If the light drops by the same amount, but for a shorter time, they are correct. Ask
someone else to draw it faster again. And someone else to draw it faster again. A sample
of graphs might look like this:
Time
Time
You can repeat this with other beads on another graph, perhaps testing the groups
understanding by asking them to interchange drawing a new graph with a bigger/smaller
planet which orbits faster/slower. This will thoroughly test the groups understanding of the
graphs which we will continue using throughout the activity.
The Transit of Extrasolar Planets
Light
After deciding on a ‘correct’ planetary transit, ask them to think about what it might look like
over time. Tell them that their planet goes around that star every two days, and you would
like to see what it would look like on the graph over a fortnight. Ask some of the group to try
drawing it. The result should look something like this:
Time
When a distant star dims for a period of time (anything from a few minutes to a few days), it
means nothing at all. When the dimming repeats in a very regular manner, for a similar
amount for a similar time for a long period of observation, that is when astronomers will start
to believe that there might be a planet.
In the next set of activities, we are going to look at some actual data from these stars. Using
this data, and following the same path as scientists, we will investigate what we can learn
from this light about the orbiting planets.
The Transit of Extrasolar Planets – Kepler’s Laws
Johannes Kepler came up with a number of simple rules to describe how a planet would orbit a star.
1.
2.
3.
The path of the planets about the Sun is elliptical in shape, with the centre of the Sun being located
at one focus. A circle is a special kind of ellipse where the two foci occupy the same space, so you
can simplify the statement to “The path of the planets about the Sun is circular with the centre of the
Sun in the centre of the circle”.
An imaginary line drawn from the centre of the Sun to the centre of a planet will draw out equal
areas in equal intervals of time.
The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their
average distances from the Sun.
The third law is the one which we will be using to help us determine the distance of the planet from the
star based on the period of its orbit.
Using the data provided, the group can find the period of the exoplanets.
Then, using graphs, they will use the data they have input to get the distance that the planet is orbiting
from the star.
Print out enough of the data sheets for groups to have one of each. They can then work on different
exercises and collaborate to complete the results sheet.
The Transit of Extrasolar Planets – Real Data
The Transit of Extrasolar Planets – Turning Data into Information
What the graphs of changing brightness provide is raw data. The next thing for us to do is
convert this data into something usable and understandable: information. An example of
the difference between data and information is the number 21122125. That is utterly
meaningless to us in that format. However if we were to write it 21-12-2125, then we know it
is a date. Use the following graphs to find the orbital distance and follow the instructions in
the table to find the radius of the planet in terms of the size of Earth.
Planetary Information
Planet
Name
HAT-P-11b
Kepler 4b
HAT-P-7b
Mystery b
Mystery c
TrES-2b
Kepler 5b
Period
(days)
Change in
Brightness Drop of
Z (%)
Calculated Information
Orbit Distance
(AU)
√Z
Radius (in Earth
radii) = 10 × √Z
The Transit of Extrasolar Planets – Sample Answer Sheet
This gives an idea of what the answers might look like. Depending on how the group members interpret
the data, they may read off information slightly differently to how it has been interpreted here. So long as
the reading makes sense and the maths that follows is handled correctly, it should be considered correct.
Planetary Information
Calculated Information
Planet
Name
Period
(days)
Change in
Brightness Drop of
Z (%)
Orbit Distance
(AU)
√Z
Radius (in Earth
radii) = 10 × √Z
HAT-P-11b
5
0.2
0.06
0.45
4.5
Kepler 4b
3
0.16
0.04
0.4
4
HAT-P-7b
2
2.4
0.03
1.5
15
Mystery b
240
0.16
0.75
0.4
4
Mystery c
360
0.01
1.0
0.1
1
TrES-2b
5
0.2
0.06
0.45
4.5
Kepler 5b
3
2.4
0.04
1.5
15
If you want you can ask the group which planets they think are made of rock and which ones are made of
gas. Kepler 5b and HAT-P-7b should be the ones considered Gas Giants because of their size. Mystery c is
the one most like Earth, and if it were orbiting a yellow-white star like the Sun, it would likely fall in the
habitable zone (where liquid water can exist).
The Transit of Extrasolar Planets – Turning Data into Information
Now that the data has been extracted and is useful information, we’re going to use it to find
out additional things about the planet. Kepler’s Third Law lets us draw graphs of orbital
distance against orbital period. Using the most suitable of the graphs provided, convert the
orbital period into the distance of the planet from the star. Note that not all of the charts
need to be used, and that approximations will need to be made.
Kepler’s Third Law Chart for Outer Solar System
350
Orbital Period (Earth Years)
300
Pluto
250
200
Neptune
150
Uranus
100
50
Jupiter
Saturn
0
0
5
10
15
20
25
Distance (AU)
30
35
40
45
50
The Transit of Extrasolar Planets – Turning Data into Information
This graph is best for planets which would fall between the orbits of Mercury and Earth.
Kepler's Third Law Chart for Inner Solar System
2.5
Mars
Orbital Period (Earth Years)
2
1.5
Earth
1
Venus
0.5
Mercury
0
0
0.2
0.4
0.6
0.8
1
Distance (AU)
1.2
1.4
1.6
1.8
The Transit of Extrasolar Planets – Turning Data into Information
This graph is best for planets that would fall within the orbit of Mercury.
Kepler's Third Law Chart for Orbital Periods less than
100 Days
120
Mercury
Orbital Period (Earth Days)
100
80
60
40
20
0
0
0.05
0.1
0.15
0.2
0.25
Distance (AU)
0.3
0.35
0.4
0.45
The Transit of Extrasolar Planets – Turning Data into Information
This graph the one to use for planets orbiting particularly quickly about the star.
Note: 1AU ≈ 150,000,000km
Kepler's Third Law Chart for Orbital Periods less than 15
Days
14
Orbital Period (Earth Days)
12
10
8
6
4
2
0
0
2
4
6
8
10
Distance (Million Kilometres)
12
14
16
The Transit of Extrasolar Planets – The Light of Distant Stars
At this point, we have taken the light emissions of a faraway star, and used that light to tell us about
possible planets orbiting that star.
The only way to know for certain that it’s a planet is to go to these stars, which could be thousands
of light years away, and check.
However, one last thing to do would be to indulge in a thought exercise. This is just one way of
searching for extrasolar planets, and, despite it having revealed a number of planets, it’s actually
the worst way of doing it.
Ask the group to discuss why they think this is a particularly poor way of searching for planets.
Hopefully someone will hit along the idea that the probability of a planet passing between a star
and us is very slim. It essentially requires the star systems that we are investigating to be lined up in
a way which benefits us. One precise alignment, when it is much easier for the planets to orbit in a
way where we can never see them passing in front of their star.
What we need is a method of looking for stars where the way the star system is oriented is of little or
no importance. This system uses Isaac Newton’s third law of motion. “Every action has an equal
and opposite reaction.” It means that when a planet is orbiting a star, the star is not just tugging
the planet around in its orbit, but the planet is tugging (much less due to its lower mass) on the star.
And this pulls the light a little bit one way and a little bit the other way. It causes a Doppler effect
to light, and we can measure that. The period in which the light moves this way and that gives us
the distance of the planet, and the amount the light moves tells us the mass (not the size) of the
planet. And this works for star systems at almost any angle with respect to us.