**Hands-On Universe http://hou.lbl.gov**

# What are the Apparent Magnitudes of the Three Stars Next to Alcyone?

Lesson Draft (2/14/97) by Vivian Hoette, vhoette@hou.lbl.gov

Alcyone Image, Yerkes Observatory in cooperation with Rhodri Evans,
Ph.D.

# Goals:

A)  Use **image processing tools** to display and analyze a CCD image of
    Alcyone and three other stars. taken through a professional
    telescope. Alcyone is the brightest star of the Pleiades Star
    Cluster.

B)  Use the photometry tool, **Auto Aperture**, to determine the
    brightness counts for four stars.

C)  Use an astronomy formula and a scientific calculator to find
    apparent magnitudes of stars.

D)  Calculate **brightness ratios** of Alcyone compared to three other
    stars.

E)  Calculate the **apparent magnitude** of three stars when given the
    apparent magnitude of Alcyone.

# Strategy:

## A) Prepare image of Alcyone and other stars for analysis work. 

1)  Open image (etatau3.fts).

2)  Flip image vertically.

3)  Position image so that all four stars can be seen.

![](media/image1.emf){width="2.7736111111111112in" height="2.125in"}

Etatau3.fts, Yerkes Observatory, October 31, 1996

## B) Use Auto Aperture to find the brightness counts of each star. 

1\) On the tool bar there is an icon which looks like a bull's eye. This
is the auto aperture tool.

-   Click on auto aperture and then move the cursor to the center of the
    star that you wish to measure. Click on the mouse.

-   A number will appear next to the star and also in the results box.
    This number is the brightness counts for the star. (If you wish to
    move the results box out of the way, click on the title bar of the
    image and drag the box to the side.)

2.  Record the Brightness Counts results in Data Table for Etatau3.fts.
    (Image, flipped vertically.) Alcyone is the brightest star in the
    image. The other stars do not have names.

## C) Use the formula astronomers use to find apparent magnitudes. 

When astronomers know the apparent magnitude of one star, they use this
formula to find the apparent magnitude of other stars in the same image.

[Formula for Comparing Apparent Magnitudes:]{.underline}

Apparent Magnitude of Unknown Star - Apparent Magnitude of Known Star =
2.5 log (Brightness Counts of Alcyone / Brightness Counts of Unknown
Star)

[Using Algebra, rewrite this formula as:]{.underline}

Apparent Magnitude of Unknown Star = 2.5 log (Brightness Counts of Known
Star / Brightness of Unknown Star) + Apparent Magnitude of Known Star

### **1. How much brighter is Alcyone compared to each of the other stars.**

> In this section you are solving the following part of the formula:
> [(Brightness Counts of Alcyone / Brightness Counts of Unknown
> Star)]{.underline}.

Calculate the ratio: Alcyone's brightness counts / Unknown Star's
brightness counts. Round your answers to whole numbers. Record your
answers for each star in the Data Table, **Brightness Ratio: Alcyone /
Star.**

**First Calculator Steps:**

> Start with the brightness counts for Alcyone
>
> Press /
>
> Key in the brightness counts for the unknown Star
>
> Press =

### **What is the magnitude difference of the stars?**

> **2.5 log** (Brightness Counts of **Alcyone /** Brightness of Unknown
> **Star**) is the part of the formula that allows you to find the
> difference in apparent magnitude between Alcyone and an unknown star.
>
> Record your answers for each star in the data table under **Difference
> in Apparent Magnitude.**
>
> **Second Calculator Steps:**
>
> Start with the Ratio of Alcyone / Star
>
> Press the log button
>
> Press \*
>
> Key in 2.5
>
> Press =

### **What are the apparent magnitudes of the three unknown stars?** 

> Add the difference in apparent magnitudes of the an unknown star and
> Alcyone, to the apparent magnitude of Alcyone. Record your answers for
> all three stars under **Apparent Magnitude**.
>
> **Third Calculator Steps:**
>
> Start with the difference in Apparent Magnitudes
>
> Press +
>
> Key in 2.90
>
> Press =

-   
-   

**Hands-On Universe http://hou.lbl.gov**

# What are the Apparent Magnitudes of the Three Stars Next to Alcyone?

Record Sheet Draft (2/1/97) by Vivian Hoette, vhoette@hou.lbl.gov

Alcyone Image, Yerkes Observatory in cooperation with Rhodri Evans,
Ph.D.

**Your Name
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
The Date \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_**

![](media/image1.emf){width="2.7736111111111112in" height="2.125in"}

Etatau3.fts, Yerkes Observatory, October 31, 1996

[**Data Table for Etatau3.fts** (flipped vertically)]{.underline}

+----------------+----------+--------------+------------+------------+
| ##             | ##       | ##           | #          | ### **     |
| # **Image Posi | # **Brig | # **Brightne | ## **Diffe | Apparent M |
| tion of Star** | htness C | ss Ratio: Al | rence in A | agnitude** |
|                | ounts**  | cyone/Star** | pparent Ma |            |
|                |          |              | gnitude**  |            |
+----------------+----------+--------------+------------+------------+
| Alcyone (x:    |          |              |            | 2.90       |
| 31, y: 26)     |          |              |            |            |
+----------------+----------+--------------+------------+------------+
| Star at (x:    |          |              |            |            |
| 141, y: 71)    |          |              |            |            |
+----------------+----------+--------------+------------+------------+
| Star at (x:    |          |              |            |            |
| 161, y: 155)   |          |              |            |            |
+----------------+----------+--------------+------------+------------+
| Star at (x:    |          |              |            |            |
| 201, y: 117)   |          |              |            |            |
+----------------+----------+--------------+------------+------------+

1.  
2.  

Look at the brightness counts, ratios of brightness counts, differences
in apparent magnitudes and the apparent magnitudes of all the stars.
What do you notice about how the brightness changes compared to how the
magnitude values change.

**Hands-On Universe http://hou.lbl.gov**

# What are the Apparent Magnitudes of the Three Stars Next to Alcyone?

Record Sheet Draft (2/1/97) by Vivian Hoette, vhoette@hou.lbl.gov

Alcyone Image, Yerkes Observatory in cooperation with Rhodri Evans,
Ph.D.

![](media/image1.emf){width="2.7736111111111112in" height="2.125in"}

Etatau3.fts, Yerkes Observatory, October 31, 1996

[**Data Table for Etatau3.fts** (flipped vertically)]{.underline}

+----------------+----------+--------------+------------+------------+
| ##             | ##       | ##           | #          | ### **     |
| # **Image Posi | # **Brig | # **Brightne | ## **Diffe | Apparent M |
| tion of Star** | htness C | ss Ratio: Al | rence in A | agnitude** |
|                | ounts**  | cyone/Star** | pparent Ma |            |
|                |          |              | gnitude**  |            |
+----------------+----------+--------------+------------+------------+
| Alcyone (x:    | 3        | 1            | 0.00       | 2.90       |
| 31, y: 26)     | ,014,177 |              |            |            |
+----------------+----------+--------------+------------+------------+
| Star at (x:    | 126,057  | 24           | 3.45       | 6.35       |
| 141, y: 71)    |          |              |            |            |
+----------------+----------+--------------+------------+------------+
| Star at (x:    | 21,924   | 137          | 5.34       | 8.24       |
| 161, y: 155)   |          |              |            |            |
+----------------+----------+--------------+------------+------------+
| Star at (x:    | 15,915   | 189          | 5.69       | 8.59       |
| 201, y: 117)   |          |              |            |            |
+----------------+----------+--------------+------------+------------+

3.  

Compare these calculated answers to the V magnitudes as listed in the
SIMBAD catalog of stars.

  -------------------- ---------------------- ---- --------------------- ------------------------------
  [Star]{.underline}   [Simbad]{.underline}        [Brightness           [Calculated Apparent
                                                   Counts]{.underline}   Magnitude]{.underline}

  Alcyone, 23630, 25   2.90                        3,014,177             2.90 (given)
  Tau                                                                    

  23629, 24 Tau        6.29                        126,057               6.35

  23607                8.26                        21,924                8.25

  23608                8.72                        15,915                8.59
  -------------------- ---------------------- ---- --------------------- ------------------------------

-   This research has made use of the SIMBAD Database operated at CDS,
    Strasbourg, France.

```{=html}
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-   Consultation for data analysis with Mike Smutko, University of
    Chicago Graduate Student, Astrophysics.

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-   Image etatau3.fts taken by Vivian Hoette for Jacqueline Whitler and
    other HOU teachers with Rhodri Evans and Dave Rapchun of Yerkes
    Observatory.