Student Solutions Manual for Stars and Stellar Processes 1st Edition by Mike Guidry

Student Solutions Manual for Stars and Stellar Processes
1st Edition by Mike Guidry




Student Solutions Manual for Stars and Stellar Processes
1st Edition by Mike Guidry

,Student Solutions Manual: Stars and Stellar Processes

Mike Guidry


This document gives the solutions for select problems (those marked with
***) at the ends of chapters for the first edition of Stars and Stellar Processes
by Mike Guidry (Cambridge University Press, 2019). Unless otherwise indi-
cated, literature references, equation numbers, figure references, table refer-
ences, and section numbers refer to the print version of that book.

,Student Solutions Manual for Stars and Stellar Processes 1st Edition by Mike Guidry




Student Solutions Manual for Stars and Stellar Processes 1st Edition by Mike Guidry

, 1 Some Properties of Stars


1.1 Sirius is 8.6 ly = 2.6 pc away, corresponding to a parallax angle p = 1/d( pc) = 1/2.6 =
0.38′′.
1.4 The total energy flux F emitted by a blackbody at temperature T can be expressed as
∫ ∞
2 1
F = 2π c h dλ.
0 λ 5(ehc/λ kT − 1)

Using the substitutions
−hc
u = hc/λ kT λ = hc/ukT dλ = du,
u2kT
the integral can be evaluated giving
4∫ ∞
2 kT u3
F = 2π c h du
hc 0 eu − 1
2π c2hk4T 4
= ζ(4)Γ(4)
h4c4
2π 5k4 4
= T ≡ σ T 4,
15h3c2
where the properties of the Riemann zeta function ζ(x)
∫ ∞
1 ux−1
ζ(x) ≡ eu − 1
du
Γ(x) 0

and the gamma function Γ(x) have been used, and σ is the Stefan–Boltzmann constant.
1.7 From the following diagram,

F v
F1 2
2


v1 r1 CM r2


circular motion about the center of mass requires that
m1v2 m2v2 Gm1m2
|F1| = 1 = Gm1m2 2 |F2| = 2 = 2
.
r1 (r1 + r2) r2 (r1 + r2)
The angular velocity is ω = |ω| = v/r and the period is P = 2π/ω = 2π r/v, from which
v2 = 4π 2r2/P2. Insert this into the above equation for |F 1| and solve for P2,
2 4π 2 2 r1
P = (r1 + r2) .
G m2
1