## How Big is That Star?

# How Big is That Star?

## Measuring Binary Stars

Name: __________________________________

Date: ______

Class: _______________________

You are going to be measuring the sizes of stars in binary systems.

## Background

Look at the sample light curves below. They show the brightness of a binary system as a function of time.

Illustration of the relationship between the dips in the light curve and the stars in a binary. The large red circle represents the larger star in the binary system and the smaller circles represent the smaller star as it moves through its orbit.

- In a sentence, describe the relationship
between t
_{1}and d_{1}. What does d1 represent? - In a sentence, describe the relationship
between t
_{2}and d_{2}. What does d2 represent? - Using this information, data from real binary systems, and the equation d=v × t (distance equals velocity times time), you’ll calculate the sizes of a few stars.

## HT Cas

Work through this example along with your teacher.

Light curve for binary system HT Cas.

- Using the graph above, determine and record the following (be sure to include units):
- t
_{1}: __________________ - t
_{2}: __________________

- t
- The orbital velocity of HT Cas is known to be 390 km/sec.
- Using d=v × t, determine the size of each star in HT Cas. Show your work below, or on additional paper, if you need more room.
- Write the size of each star below (make sure to include units):
- d
_{1}: __________________ - d
_{2}: __________________

- d

## X0748-676

Light curve for binary system X0748-676.

- Using the graph above, determine and record the following (be sure to include units):
- t
_{1}: __________________ - t
_{2}: __________________

- t
- The orbital velocity of X0748-676 is known to be 500 km/sec.
- Using d=v × t, determine the size of each star in X0748-676. Show your work below, or on additional paper, if you need more room.
- Write the size of each star in X0748-676 below (make sure to include units):
- d
_{1}: __________________ - d
_{2}: __________________

- d

## Vela X-1

Light curve for binary system Vela X-1.

- Using the graph above, determine and record the following (be sure to include units):
- t
_{1}: __________________ - t
_{2}: __________________

- t
- The orbital velocity of Vela X-1 is known to be 280 km/sec.
- Using d=v × t, determine the size of each star in Vela X-1. Show your work below, or on additional paper, if you need more room.
- Write the size of each star in Vela X-1 below (make sure to include units):
- d
_{1}: __________________ - d
_{2}: __________________

- d