Name:________________________________

ID number:____________________________

Course (circle one): A01 or A20

## Lab Sheet: Determining the Extragalactic Distance Scale

### I. Find the Cepheids!

#### A. Record all the grids you visited:

```  26, 47
___________________________________________________________
___________________________________________________________
```

#### B. Cepheid information

Find a minimum of 8 Cepheids.
```Cepheid name   Grid #   Avg mV   P(days)    Mv     mV-Mv

C46           47      25.3     25.3
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______
____________   ______   ______   _______  ______  ______

```

#### C. Other objects of interest:

```Grid #   (x,y)coordinates                Comments
26        178, 113         Blip in lower right section
______   ________________   _______________________________________
______   ________________   _______________________________________
______   ________________   _______________________________________
______   ________________   _______________________________________
______   ________________   _______________________________________

```

### II. The distance to M100

#### A. The P-L relation

Calculate the absolute magnitudes for each Cepheid in Part I, Section B using the equation

```    MV = - [2.76 (log10(P) - 1.0)] - 4.16,
```

where P is the period of the Cepheid in days from column 4. Enter your results in column 5.

#### B. The average distance modulus

Calculate the distance modulus (mV-Mv) for each Cepheid in Part I, Section B and write your results in column 6.

Sum all the distance moduli and divide by the number of Cepheids to get the average distance modulus.

```    Average distance modulus: mV-Mv =  __________
```

#### C. The distance to M100

Calculate the distance to M100, using the average distance modulus in the equation

```    d(pc) = 10[0.2(mV-Mv+5)]

d = __________ pc,      or      d = __________ Mpc.
```

### III. Estimate the Hubble Constant

Write the value of v (from the lab pages) here:
```    v = ________  km/sec
```

Copy the average distance to M100 from Section II, Part C here:

```
d = __________ Mpc.
```

Now calculate the current Hubble constant:

```    Ho = v/d =___________  km/sec/Mpc
```

How does this compare to the value of Ho that you learned in class or from your text?

___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________

### IV. Estimate the Age of the Universe

#### A. Assume the universe has been expanding at a constant rate

Use the value of Ho from Part III to calculate the age of the universe for the case when Ho represents the expansion of the universe for all time:
```                     1   sec Mpc (3.09 x 1019 km)     (1 year)
Age of universe = ---- ------- ----------------- ----------------
Ho    km         1 Mpc        (3.15 x 107 sec)

Age of universe = ________________ years.
```

Does your answer seem reasonable? How does this compare to the presumed ages of the oldest globular clusters?

___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________

#### B. Assume the expansion has been slowing over time

Calculate the age of the universe taking into account the slowing of the expansion with time, assuming o = 1.
```                        2
Age of universe  = ----.     (o = 1)
3 Ho

Age of universe = ________________ years.   (o = 1)

```

How does this compare to the presumed ages of the oldest globular clusters?

___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________

What can you infer about the actual value of o by comparing the two ages you have calculated? How does your evaluation of o compare to what you learned in class?

___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________

### V. Feedback

#### A. Science

Do you feel that this lab improved your understanding of how the extragalactic distance scale and the Hubble constant is determined? If so, how? In not, why?

___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________

___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________

```
```