Lecture 5  Visual Binary Systems (1/26/99)
Mechanics   
Binaries II
Reading:
Chapter 15, 122 (ZG4)
Prelude P1, P2 (ZG4)
Notes:
pages 16  19
HST FOC image of binary star Gliese 623. The companion
is Gl623b, with a mass of 0.1 Msun, in a 2AU orbit with a 4 year period
around the brighter primary Gl623a. (Courtesy
STSCI)

Key Question: 
What are the conserved integrals
of motion in a twobody system?


Key Principle: 
Kepler's Laws of Motion


Key Problem: 
Determine masses and luminosities
of Sirius A & B.

Investigations:
 Orbital Mechanics continued
 Why are energy and angular momentum integrals of the
motion?
 How do energy and angular momentum generalize to systems with
more than 2 bodies?
 What is the virial theorem?
 How does the total energy determine the semimajor axis of the
orbit?
 How does the total angular momentum determine the eccentricity
and relate to Kepler's 2nd Law?
 What is Kepler's 3rd Law in its final centerofmass form?
 What two equations give the total mass and mass ratio for
the binary system?
 What are the limitations for using visual binary systems to
determine masses for a large number of stars?
 Visual Binaries  A Primer
 What are periastron and apastron?
 What are the primary and secondary in a binary?
 What is the line of apsides and how does its inclination
affect how the orbit appears on the sky?
 How do you determine the inclination of a visual binary orbit?
 Why must a binary orbit be confined to a plane?
 What input do you need to determine the mass using Kepler's 3rd
Law?
 Example (see homework 1):
Sirius A & B  Masses and Luminosities
 System Data 
Period:  49.94 years 
Parallax:  0.377" 
Apparent Magnitudes (bol): 
1.55, +5.69 
Apparent SemiMajor Axis: 
7.62" 
Ratio of Orbits a_A/a_B:  0.466 
Inclination:  ~0 
 What is the distance to Sirius in parsecs?
 What are the absolute bolometric magnitudes for Sirius A,B?
 What are the luminosities of Sirius A,B?
 What is the orbital semimajor axis in AU?
 What is the mass ratio m_A/m_B?
 What is the total mass M = m_A + m_B?
 What are the individual masses m_A, m_B?
 What are the masstolight ratios M/L of Sirius A,B?
 How do Sirius A, B compare with the Sun?
Binary Stars with HST:
Some binary stars and related objects reported in Hubble Space Telescope
press releases include:
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Steven T. Myers