This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Binary Stars Key Characteristics
About half of all stars are binary or multiple star systems Key Fundamentals
Used to determine stellar masses
Used to determine stellar diameters Major Types of Binary Stars
Visual Binaries Spectroscopic Binaries Eclipsing Binaries Visual Binaries Visual Binaries Visual Binaries are Resolved
Skinny Triangle Approximation
D = d tan Resolution = 2.5 x 105 / D
Example: GT 16-inch telescope = 2.5 x 105 (500 x 10-9 m) / (0.4 m) = 0.3 arcsec
The atmosphere limits all telescopes to a resolution of ~1.0 arcseconds. Shapes of Orbits
First Kepler tried circles, equants, ovals, etc. Finally, after years,
he tried an ellipse. Found that the orbit of Mars is an ellipse with
the Sun at a focus.
The sum of the distances to the two foci is always constant for all
points on the ellipse. Ellipses are described by their semi-major
axis and by their eccentricity.
e = ( foci / major axis) Kepler’s Three Laws
1. All planets have elliptical orbits
with the Sun at a focus (conic
sections). 2. Law of Equal Areas:
Equal areas are swept out in
equal time intervals. Kepler’s Second Law Interactive Kepler’s Three Laws
3. Harmonic Law (published in The Harmony of the Worlds):
P2 = k a3,
where k = 1 if P is in earth years and a is in AUs. Modification of Kepler’s Laws All orbiting bodies have a conic-section orbit,
with the massive body (i.e., the Sun) at a focus. Modification of Kepler’s Laws Law of Equal Areas: Equal areas are swept out in equal time intervals.
This is explained by Conservation of Angular Momentum.
r1 v1 = r2 v2 Modification of Kepler’s Laws The Third Law needs to have the sum of the masses included.
(M + m) P2 = k a3,
where k = 1 if P is in earth years, a is in AUs, and (M + m) is in solar masses.
For objects orbiting the Sun, (M + m) = 1. Visual Binaries
Kepler’s 3rd Law
(M1 + M2) P2 = a3
M is in solar masses
P is in years, and
a is in Astronomical Units
(1 AU = mean Earth-Sun distance) Kepler's Third Law Interactive PRS Question
1. If two stars with the mass of the Sun had a circular orbit (radius =
5 AU), the orbital period would be about
a. 4.0 years
d. 12.0 years
b. 5.5 years
e. 16.0 years
c. 8.0 years Resolution Improvements
Resolutions to 0.02 arcsec Interferometric Techniques
Resolutions to 0.001 arcsec Spectrum Binaries Spectroscopic Binaries Spectroscopic Binaries
Conservation of Angular Momentum
M1 / M2 = v2 / v1 = r2 / r1 Doppler Shift = v / c Radial Velocity Interactive PRS Question
2. If the orbital velocity of Star A is 5 times that of Star B, then Star A is
how many times as massive as Star B?
a. The same
d. 1/5 times
b. 5 times
e. 1/25 times
c. 25 times Eclipsing Binaries Eclipsing Binaries
Unresolved – appear as a single star
Orbital plane lies close to our line-of-sight Partial Eclipse Binary Star Interactive Phase
Observed Time – Reference Time
XX . XXXX
Phase Textbook Binary
HD 71636 Partial P = 5.0 days
a = 17.4 R
M1 = 1.5 M M2 = 1.3 M R1 = 1.4 R R2 = 1.6 R Diameters of Stars
L = 4 R2 T4
L R2 T4 PRS Question
3. Two stars in a binary system have the same temperature but the
diameter of Star A is twice that of Star B. How many times brighter
is Star A than Star B?
a. 1 X
d. 16 X
b. 2 X
e. 32 X
c. 4 X Mass-Luminosity Relationship L M 4.0
0.08 solar < M < 50 solar ...
View Full Document
- Spring '12