Binary Stars

Most star systems are at least binary stars. When these stars form, there is typically enough matter for two cores to condense and form separate stars. The binary stars then revolve about their common center of gravity in a strange celestial dance. Some stellar systems are made of more than two stars. For instance, the star Castor in Gemini is comprised of at least 6 stars! In this activity, you will find double stars and determine their angular separation in arc-seconds.

Procedure

  1. If clear go outside first and observe and draw two binary systems chosen by instructor. If cloudy see step 9 below about what to draw.
  2. Instead of making your own measurements you will be given data for two of the stars in the table below. Record these numbers in the Data Table. Calculate the average drift time.
  3. Use Voyager data panel to get the Dec (declination) for the two stars. Use VIEW/Find & Center command to find the star. Click on star to bring up Data Panel. For Dec convert minute and seconds to decimal fraction of degree.
  4. Use the average of these drift times and the DEC to calculate the east-west separation and then the actual separation in arc-seconds as described under the theory section. Record in Data Table.
  5. Then convert actual separation in arc-seconds to radians. To convert arc-seconds to radians, divide your actual separation by 206270.
  6. Given the distance to one of the double stars, you can calculate the ‘Projected Separation’ in AU’s. The distances in LY’s to each pair is given in Table 12.1. Use this with the equation, s = r. The ‘r’ will be the distance, and  is the angular separation in radians. The distance ‘s’ will be the ‘Projected Separation’ in LYs.
  7. Record projected separation in LYs in Results Table. Convert this answer to AU’s. Use text or Internet to find conversion factor between LY and AU. Put separation in AUs in Analysis Table.

8. Once you have gotten the separation in AU, use the Voyager program to find the

orbital period in years. Use Find & Center command to find

the star. Click on star to bring up data panel. Click Components on data panel.

9. If cloudy: Take time out from the calculations to draw the Voyager picture of the system

in the space provided on the handout.

10. Click Orbit button. Record period in Data Table. Given the orbital period in years,

calculate and record the mass of the binary star. Mass = a3 / p2. The mass is the binary

mass compared to the Sun’s mass.

11. Repeat steps above for the other star.

12. Do calculations on added page to get separate masses.

Table 12.1, Double Stars
Bayer Designation of the Binary Star / Distance / Correction Angle
Eta () Cas / 19 LY / 43
Delta () Cyg / 109 LY / 41
Xi () Cep / 100 LY / 86
Zeta Lyr / 154 LY / 30
Epsilon () Lyr / 130 LY / 8
Iota () Cas / 140 LY / 56

Theory

Binary Stars are actual star systems that orbit each other due to their mutual gravitational attraction. From Earth, these stars look like double stars where two stars are very close together. Using the drift-time technique with a higher power eyepiece, you can determine the east-west separation between these stars. A correction angle has been included so that you can find the actual diagonal separation (see the figure). How do we use drift time to find east-west separation? You know that objects on the celestial equator seem to rise and set at a rate of 15” (arc-seconds) per second of time.

  1. The drift rate will depend on the DEC of the object being observed.so you will have to correct for this in step 2.
  2. Calculate: East-west separation in seconds = drift time x 15 x cos (DEC)
  3. Finally, you need to calculate the actual separation in seconds using the correction angle (CA) and the sine function for triangles:

Note: Angle marked in triangle above should be lower right cornert.

Data you will need is given below.

Delta Cyg Drift Times (Sec)

0.2
0.19
0.18
0.21
0.22
0.18
0.2
0.21
0.22
0.19

Xi Cep Drift Times (Sec)

1.27
1.26
1.28
1.29
1.25
1.28
1.27
1.29
1.25
1.26