> **Where Are You?**

**STUDENT ACTIVITY---SCALE MODELING OF VESTA AND CERES IN THE SOLAR
SYSTEM**

If you were to look through the most powerful telescope from the 19^th^
century on a clear, cloudless night, an asteroid such as Ceres or Vesta
would appear only as a tiny point of light.¹ You may wonder: *How big
are these asteroids really? How far away are they from Earth? And how
can I get a better view of these points of light?* In this activity, you
will create a model to help you answer these questions. This model will
help you to develop an understanding of both the size and distance of
Ceres and Vesta relative to Earth.

***Part 1: Size to Scale***

1.  Using food items, you will create a scaled-down model of a portion
    of our Solar System. The table below lists several planets and
    asteroids along with their approximate diameters measured in
    kilometers. Your job will be to convert the diameter to the scale of
    **1 centimeter (cm) = 500 kilometers** (km) Then based on your
    calculations, assign foods to represent the Solar System objects.
    Mercury has been completed for you as an example.

+---------+--------+----------------------------+-----------+---------+
| **Solar | **Diam | **Convert to Scale**       | **Sc      | **Food  |
| System  | eter** |                            | aled-down | Item**  |
| B       |        | **1 cm = 500 km**          | Size in   |         |
| odies** | **in   |                            | cm**      |         |
|         | km**   |                            |           |         |
+---------+--------+----------------------------+-----------+---------+
| ***Mer  | ***4,  | ![](media/image1.jpeg){wi  | *         | ***Or   |
| cury*** | 880*** | dth="1.6666666666666667in" | **9.76*** | ange*** |
|         |        | heig                       |           |         |
|         |        | ht="1.3597222222222223in"} |           |         |
+---------+--------+----------------------------+-----------+---------+
| ***E    | ***12, |                            |           |         |
| arth*** | 756*** |                            |           |         |
+---------+--------+----------------------------+-----------+---------+
| ***     | ***6,  |                            |           |         |
| Mars*** | 794*** |                            |           |         |
+---------+--------+----------------------------+-----------+---------+

***¹ See vignette "[What Can You See with a
Telescope?](../../../../../DawnCommunity/flashbacks/fb_07.pdf)"***

+---------+--------+----------------------------+-----------+---------+
| **Solar | **Diam | **Convert to Scale**       | **Sc      | **Food  |
| System  | eter** |                            | aled-down | Item**  |
| B       |        | **1 cm = 500 km**          | Size in   |         |
| odies** | **in   |                            | cm**      |         |
|         | km**   |                            |           |         |
+---------+--------+----------------------------+-----------+---------+
| ***V    | ***    |                            |           |         |
| esta*** | 525*** |                            |           |         |
+---------+--------+----------------------------+-----------+---------+
| ***C    | ***    |                            |           |         |
| eres*** | 933*** |                            |           |         |
+---------+--------+----------------------------+-----------+---------+

> Gather the foods you have selected as representations of Earth, Mars,
> Vesta, and Ceres. Use observation to respond to the questions below.

2\. What features do these model planets and asteroids have in common?
What differences can you find? Note the similarities and differences in
the Venn diagram below.

> **PLANETS ASTEROIDS**

3\. The first and oldest theory of the origins of asteroids suggested
that asteroids were pieces of an exploded planet. Another theory
proposed that asteroids were free solar system material that never fully
developed into planets. How does the model you created support or oppose
these theories?

4\. If you were to expand this model, the next planet would be Jupiter.
Jupiter is so massive that its gravitational pull is what interrupted
the development of asteroids in the asteroid belt into fully formed
planets. Jupiter's diameter is 142,984 km. Using the same scale (1 cm =
500 km), how large should a model Jupiter be? What object could you use
to model Jupiter?

***Part 2: Distance to Scale***

The table below shows the approximate distances of Earth, Mars, Vesta,
and Ceres from the Sun. Refer to the table as you answer the questions
below.

  ---------------------- -------------------- ----------------------------
  **Solar System         **Diameter in km**   **Distance from the Sun in
  Bodies**                                    km**

  ***Earth***            ***12,756***         ***149,597,890***

  ***Mars***             ***6,794***          ***227,936,640***

  ***Vesta***            ***525***            ***353,400,000***

  ***Ceres***            ***933***            ***413,900,000***
  ---------------------- -------------------- ----------------------------

5\. If you were to model the distances of these four Solar System bodies
in relation to each other using a standard 100-yard football field,
could you use the same scale for both size and distance (1 cm = 500 km)?
Explain.

6\. To describe the distances of solar system bodies, astronomers use a
special unit of measurement called ***Astronomical Unit*** or ***AU***
for short. AU indicates a planet's or asteroid's mean distance from the
Sun. The approximate distances from the Sun (rounded to the hundredths)
in AU are:

> **Earth 1.0 AU Vesta 2.36 AU**
>
> **Mars 1.52 AU Ceres 2.77 AU**
>
> Why do you think AU is the preferred unit of measurement for distance
> in our Solar System?

7\. Now you along with three of your classmates will model the distances
between Earth, Mars, Vesta, and Ceres, using the approximate scale of
**1 AU = 20 meters (or 2000 centimeters)** Rather than measure out 20
meters for each AU, you will measure in walking strides. To do this, you
should first measure the length of each person's stride in centimeters.
Record each stride measurement in the table below. Complete the table to
determine how many regular walking paces each person in your group will
need to take to show the distance of their assigned solar system body
from the Sun.

  ---------------- --------------- -------------- ------------- ------------
  **Student Name** **Measurement   **Solar System **Distance    **Number of
                   of one stride   Bodies**       from the Sun  Strides**
                   in                             in AU**       
                   centimeters**                                

                                   ***Earth***    ***1.0***     

                                   ***Mars***     ***1.52***    

                                   ***Vesta***    ***2.36***    

                                   ***Ceres***    ***2.77***    
  ---------------- --------------- -------------- ------------- ------------

8\. Each person should get the food item that represents his/her planet
or asteroid. Find a large open space such as a gymnasium, football
field, or long hallway for this activity. Designate a line to represent
the Sun. Holding the food item, each person should walk the appropriate
number of strides to show the distance of his/her planet or asteroid
from the Sun or starting line. When each person arrives at his or her
designated spot, stop and hold the food item up for others to see. After
you have had the opportunity to observe the model, discuss and respond
to the questions below with members of the group.

9\. Were Ceres and Vesta visible from Earth in your model? Describe your
observations.

10\. The model you just created uses two different scales. The foods
were sized to a scale of 1 cm = 500 km. The distances reflect the scale
of 1 AU = approximately 20 meters. Try to use the same scale for both
size and distance.

a.  Begin by converting the distance scale into kilometers and
    centimeters. 1 AU equals approximately 150,000,000 km, whereas 20
    meters is the same as 2000 centimeters. How many kilometers would be
    represented by one centimeter in this scale?

b.  If you were to substitute the old size scale (1 cm = 500 cm) with
    the new scale (in a above), what portion of the food items would
    most appropriately represent the sizes of the solar system bodies?

11\. Do you feel this was a helpful model of the portion of our Solar
System that includes the asteroid belt? Explain your response based on
your experience.

12\. How could this model be improved so that it more accurately
reflects the size and distance scale of Earth in relation to the
asteroid belt?

13\. In order to study asteroids like Vesta and Ceres up close, what
technology would astronomers need?