Stellar Mass

Ursa Major

Alcor

Mizar

(Binary star)

Gravitational Orbits Animation

Binary star (system): two stars orbiting a commoncenter of mass (CM).

CM

1

2

r1 r2

1

2

2

1

r

r

M

M

r2 = 3 AU, r1 = 1 AU 3 AU 1

AU 3

M

M

2

1

Kepler’s laws apply here . . .

Yuk!

21

32

M M

a P

P: yearsa: AUM: Solar Masses

32

2 a m) G(M

4 P

a = r1 + r2 = 4 AU

Suppose: P = 8 yrs . . .

8

4

P

a M M

2

3

2

3

21 1 M

“Seeing” Binary Stars

1. Visual Binary: Two stars seen in telescopee.g., Mizar

Albireo

Sirius A & B

AB

Kruger 60

Distance = 13 ly

A

B

L M

A

B

0.01 L

0.0034 L

P = 44.6 yrsa = 9.5 AU

0.28 M

0.16 M

2. Spectroscopic Binary: Motion of starsdetected via Doppler shift of spectrum lines.

Mizar

Each star is itself binary!

Earth

* Doppler shift

* No Doppler shift

Spectroscopic Binary Animation

3. Eclipsing Binary: Stars mutually eclipseeach other.

Earth

* No eclipse

* Eclipse

Binary ‘light curve’B

righ

tnes

s

Time

½ orbit period

Eclipsing Binary Animation

Binary Statistics

* At least 50% of all stars reside in binaries.

* The sun is apparently a loner!