When objects are far away it is sometimes difficult to determine their shape. You may only see one side of the object or from a direction that doesn't give enough information to determine the objects true shape.

Astronomers are constantly trying to determine the shape of objects in the sky. They take images of galaxies or the planet discs that are created from new stars that only give clues as to the true shapes of these objects in the sky. Astronomers then need to infer from the images given to determine the actual shape of the celestial bodies they study.

In the lesson you will be given information and skills that astronomers use to determine the shape of objects in the night sky.

Astronomers use images in 2 dimensions and infer the objects shape into 3 dimensions. They utilize the information around and inside the object to infer the orientation (how it sits in space) of the object.

How do you know where the door to your school building is? Before you think this is such a simple answer, let's complicate the issue. Imagine trying to explain it to someone who has never been to your school--and they plan on parachuting from an airplane to get to your school. Now they can't see the door. How would you describe which side of the building the door is on now?

You will have to utilize the information around the building to find its orientation to our friend the parachuter. We will put some axes down to mark the sides of the building. Let's put the x-axis through the sides of the building and the y-axis through the front and back of the building.

Let's also mark the sides and the front and back of the building with positive and negative signs to mark the difference between left and right. Positive and negative signs also help give a sense to how an object is oriented with having to worry about left or right.

Where would the optimal (best) place to put the positive and negative signs for our axes?



Now we are ready to help our parachuter find the door to our school. We can direct them to the negative y side of the building. You may not be able to see the door from the roof but we can now infer which side the door is on by utilizing the way we oriented the axes on our building.

If we set our axes on an celestial body, we can do more then just determine where objects are in that space: we can determine the actual shapes that these objects take in the larger space around them. The shapes these objects take tell us a good bit about how they were formed and their age.

Let's revisit our school building. The 3 dimensional shape of the building would be a cube. If we rotate the building around the x- and y-axis, the sides would look the same, a square, but the object takes up more space than we see.

To be 3 dimensions we need to have 3 axes that we can rotate our object around. If we have already set 2 of the axis in the object an x and y. If we were to place a third, which we will call z, where would it be?



Now that we have all of our axes set for our object, we can rotate the object along all three of our axes.

What if our object is not as uniform as our cubical school building? What if we rotated the objects around its axes and the pictures of the object wouldn't repeat? How could we figure out what shape it is?

Astronomers will look at a single object in the sky and have many 2 dimensional images as they move in the sky and infer their 3 dimensional shape. As the objects move in the sky their 2 dimensional images also changes. By carefully examining the changes in the 2 dimensional images they are able to determine the overall 3 dimensional shape.

We are going to study three different 3 dimensional shapes and discuss how their 2 dimensional image change as they rotate and move in space. Our three objects will be a soccer ball, a football, and a Frisbee.

First, let's look at a soccer ball. Its three-dimensional shape is a sphere. When we place our axes on the ball, we notice that rotating the ball in any direction will get us the same two-dimensional image.

What kind of 2D images would you have to have to know the shape of the object is a sphere?



Can you determine a way to show that the ball is spinning? Write your answer below.



Next we will look at a football.

A football is most like a 3 dimensional ellipse in its shape. A 2 dimensional ellipse is a shape much like a circle. It has curves just like a circle but looks as if it has been squished in the middle. The amount of "squish" is determined by its eccentricity (the measured ratio of distance between the foci and width of the ellipse) that the ellipse possesses.


A diagram of the parts of an oval. An oval is sitting so its longest side is horizontal. The side that goes along the length of the oval side-to-side is called the major axis; half of that is the semi-major axis. The side going along the width of the oval top-to-bottom is called the minor axis; half of that is the semi-minor axis. The foci (sing: focus) are located at particular points along the major axis; a longer distance between foci means a greater eccentricity. Linear eccentricity is the distance from one of the foci to the center of the oval. Eccentricity (not linear, just generally) is the linear eccentricity divided by the semimajor axis.



When we rotate an object that is an ellipse what shapes are the 2 dimensional images?



Astronomers have a complicated problem in determining the 3 dimensional shapes of objects due to the multiple images that one object can have as it moves through space. This issue is observed in trying to determine if an object is an ellipse or not. This is why there is more than one way to determine shape. As more testing points toward an object being elliptical in shape the more confident the astronomer can be in their inferences.

Now lets put in our 3rd axis to rotate our ellipse. Look at the following images, which can be rotated.

Lastly let's look at a Frisbee:

This last shape is of important interest to astronomers. The Frisbee shape is defined as the elliptic. This shape when rotated gives an assortment of different elliptical shapes and these elliptical shapes can vary in size based on how it rotates. In other words the squish changes as it moves. It can be difficult to infer the actual shape of the object from just one or two pictures. Astronomers take **thousands** of measurements to in to determine the actual shape of an elliptic. Watch the Frisbee rotate around the axis and think about how many pictures you would need to figure out that you were looking at a Frisbee.

When we rotate an object that is an elliptical what shapes are the 2 dimensional images?




Find an object in the room that everyone in your class would recognize. Write about the different shapes you would see if you rotated around three axes?



Below is an image of the young star HD 181327 as observed by the Hubble Space Telescope. With the star in the center digitally masked by a black disk, you can see the circle-shaped pattern surrounding the star.

HD 181327 in all its disky glory. The disk looks like a big, circular ring around the center star.

What are possible 3 dimensional shapes that could look like the above circle shaped pattern that you are seeing in just 2 dimensions?



The true 3 dimensional shape of this pattern around HD 181327 is a circular ring, similar in shape to a ring you might put on your finger. It is believed that infant planets may be forming inside of this ring-shaped disk around the star. From your two dimensional snapshot, it is difficult or impossible to tell whether it is a ring shape, sphere shape, or other shape. Below is an image of another young star, Fomalhaut, observed by the Herschel Space Telescope.

Fomalhaut surrounded by its super big disk. We're looking at an angle about 60 degrees up, and it's also angled away from us a little bit. It looks like a really elongated ovalar ring, like if you stretched out a rubber band. It is distinctly a ring; there is a definite gap between the outer ring material and the inner star.

What are possible 3 dimensional shapes that could resemble the 2 dimensional oval-shaped feature that you see surrounding the star above?



The true 3 dimensional shape of this oval around Fomalhaut is a circular ring, similar to the ring around the previous star you examined. But in this case, the ring looks more oval-shaped because you are looking at it from a different angle. From your 2 dimensional image, the true shape could have been either a circular ring or an oval shaped object, depending on its orientation relative to your point of view. This ring shaped disk is also believed to be a birthplace of infant planets. Below is a more complicated object observed by the Hubble Space Telescope.

The more complicated object. It's a sort of squat oval closer to a circle, about the shape of a tennis racket. It's tilted about 130 degrees, like if you held the tennis racket comfortably in your right hand. It also doesn't look like a ring; it looks like it's a cloud surrounding the star.

Based on your limited 2 dimensional view, what could be the true 3 dimensional shape of the above object?



It is difficult to tell from your two-dimensional perspective, but this object's true shape is similar to that of an elongated bubble. The object's name is is IC 418. Rather than being the birthplace of planets, this bubble shape is the glowing gas and dust that has been ejected from a dying star.