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1) How does the sun make the planets orbit?
The planets are far away across empty space. Can you pull on something without touching it? You are going
to explore this problem with some spacetime fabric. Your group will be given a large piece of stretchy
fabric and you want to get a ball to orbit around it many times.
a) How must you launch the ball?
Predict and Explain:
Observe:
b) How will a year (the time for one orbit) change if it orbits closer to the centre?
Predict and Explain:
Observe:
c) How will a year change if the center is pulled down further?
Predict and Explain:
Observe:
d) How will a year change if the orbiting body is more massive?
Predict and Explain:
Observe:
e) Suppose you were a bug living in this system and had no concept of up and down. You experience a
two-dimensional world of left-right and forward-back. You observe the motion of circles orbiting the
central point. What are two different ways that you could explain the motion?
f) Watch Dr. Quantum in Flatland on youtube.com. How did Dr. Quantum convince the circle that
there is a third dimension? How can you convince someone in our world that there is a fourth
dimension?
2) How can we detect the curvature of space?
Einstein’s general theory of relativity says that we live in a four-dimensional universe. We can see three
dimensions easily: there is up/down, east/west and north/south. However, we can’t picture the fourth
dimension. How can we detect it? Imagine that you are Albert Amoeba and you live on the surface of a
balloon. You suspect that your two-dimensional world is actually curved into a third dimension and you
want to convince the other amoebas of your theory. What measurements could you make to do this?
a) Do the angles in a triangle add up to 180o? Draw a triangle with three 90o angles. Explain below
how you did this. (What is the answer to this riddle? On the Earth you walk 10 km south, 10 km
west and then 10 north and end back where you started. What colour is the bear?)
b) Does the circumference, C= 2r? Draw a very large circle and measure the radius along the curve
of the surface. r = ______Calculate the circumference (Show your steps.)
Measure the circumference. C = ______ Why is the calculated circumference different?
c) Is it true that parallel lines never meet? Draw two short parallel lines by tracing either side of a
ruler. Extend one line by rolling the edge of the ruler gently along the balloons surface and tracing
the edge as you go. Repeat for the other line. Sketch your observations below:
d) What happens if you draw a rectangular orbit? Draw a 15-cm line on your balloon. At right
angles to that, draw another 15-cm line. Repeat a few more times. What do you get?
3) What is the Effect of a Curved Space on Light?
Light travels in straight lines. However, in a curved space light can’t travel in a regular straight line so it
travels in the straightest line possible for that space. These lines are called geodesics.
a) Turn a shallow bowl upside down on a whiteboard. This represents the curved space caused by a
mass. Draw a star far from the mass. Use a long piece of masking tape to represent light going from
the star toward one edge of the bowl. When the tape reaches the edge, stick it as smoothly as
possible onto the bowl, along the curved sides and then onto the table again. Sketch what the path
looks like. Suppose you saw this light. Where would you think it was coming from? Add this to your
sketch with a dotted line that extends back from the light that reaches you.
b) This bending of light is called gravitational lensing. Light can also reach you by bending around the
other side. Where will you see the star?
c) The curving of light was tested during an eclipse in 1919. Stars with light passing near the sun
appeared to be shifted. Explain why it was tested during an eclipse.
d) This flat world only lets us show light coming from one side or the other – a wine glass can show
what light coming from all directions will look like. Place the wine glass over the spot below and
look down through the glass. Sketch what it looks like. Sketch what it looks like with the spot
slightly off-centre. You can see some real images from gravitational lenses at
http://hubblesite.org/newscenter/archive/releases/1996/10/image/a/
e) A black hole is an astronomical object so dense that light can`t escape from it, so we can’t see it
directly. Light that passes near it will be bent a lot. You can see a simulation of what Earth orbiting a
black hole would look like at http://jila.colorado.edu/~ajsh/insidebh/lensearth_640x480.gif How is an
astronomical black hole different from a hole in a box that looks black? (Hint: How is the light
around the black hole affected? What will it look like from the other side? What is inside the black
holes?)
4) How do we know the Universe started in a Big Bang?
Astronomers have measured the distances to many galaxies and they have measured their velocities. Over
99% of the galaxies are moving away from us. You have a friend who thinks this is because we have some
kind of galactic bad breath. Albert Amoeba also discovered that the galaxies in his world were all moving
away from him. He was able to explain this by imagining that his space was able to expand.
a) Albert’s universe is one-dimensional. It consists of spiral galaxies (paper clips) connected by space
(elastic bands). The coloured paper clip is Albert’s galaxy. The other paper clips are a nearby galaxy
B and a further one C. Stretch your universe until it is 30 cm long. Measure and record the three
distances in the table below. Stretch it until it is the other lengths shown and record the new distances.
AB
AC
BC
30 cm
40 cm
50 cm
60cm
b) Use the table above to discuss whether galaxies B and C are moving away from Alfred.
c) Astronomers have discovered that galaxies that are farther far from Earth are moving away faster than
closer galaxies. Use the table to show whether this is happening in Albert’s world as well.
d) Use this model to explain to your friend why the galaxies are moving away from us.
e) Astronomers think that our universe was incredibly small, dense and hot and then started expanding
about 13.8 billion years ago – in the Big Bang. How could they figure out the age of the universe
using the galaxy’s distances and speeds?
f) Suppose a galaxy is 7 billion light-years away from us. How fast is it moving compared to light?
g) The objects in the room are emitting infrared light with a wavelength around 1/1000th of a millimetre.
However, in every direction space is emitting microwaves with a wavelength that is two thousand times
bigger. This bigger wavelength corresponds to a temperature of -270o C. Space is really cold but it
wasn’t always like that. Open your mouth wide and blow on your hand. What does it feel like? Make a
small opening with your lips and blow again. What has changed? Expansion of gases causes them to
cool. Expansion of space also causes cooling. How can you use a slinky to explain why we know that
space used to be much hotter?