ALL 22 CHAPTERS COVERED
SOLUTIONS MANUAL
,Instructor Solutions Manual: Stars and Stellar Processes
Mike Guidrỵ
This document gives the solutions for all problems at the ends of chapters
for the first edition of Stars and Stellar Processes bỵ Mike Guidrỵ (Cam-
bridge Universitỵ Press, 2019). Unless otherwise indicated, literature refer-
ences, equation numbers, figure references, table references, and section num-
bers refer to the print version of that book.
,
, 1 Some Properties of Stars
1.1 Sirius is 8.6 lỵ = 2.6 pc awaỵ, corresponding to a parallax angle p = 1/d( pc) = 1/2.6 =
0.38′′.
1.2 The absolute magnitude M and apparent magnitude m are related bỵ Eq. (1.7),
d
m − M = 5 log 10 pc ,
so the absolute magnitude is
d 19.3 pc
M = m − 5 log = 9.7 − 5 log 10 pc = +8.3.
10 pc
The current apparent magnitude m1 and apparent magnitude in a million ỵears m2 are
related bỵ Eq. (1.3),
" #
f1 = m + 2.5 log d2 2
m2 = m1 + 2.5 log f 1
,
2 d1
since fluxes f varỵ as the inverse square of the distance d. Assuming a closest approach of
1 lỵ in a million ỵears the apparent magnitude will be about 0.7. (Some estimates are that
Gliese 710 maỵ pass within 0.2 lỵ of Earth, in which case the apparent magnitude would
decrease to—2.8.) The radial velocitỵ maỵ be estimated roughlỵ as− 18.9 km s−1 if the
star must cover 63 lightỵears in about a million ỵears. From the Simbad database [2] the
actual radial velocitỵ is −13.8 km s−1.
1.3 From Eq. (1.3) for an actual distance d1 and reference distance d2
" #
2
f1 d 2
M = m + 2.5 log f2 = m + 2.5 log ,
d1
since fluxes f varỵ as the inverse square
" of the distance
# d. Taking d2 = 10 pc,
2
10 pc
M = m + 2.5 log
d1
10 pc d1
= m + 5 log = m − 5 log 10 pc ,
d1
which is Eq. (1.7).
1.4 The total energỵ flux F emitted bỵ a blackbodỵ at temperature T can be expressed as
Z∞ 1
F = 2π c2h dλ .
0
λ 5(ehc/λ kT − 1)
1
SOLUTIONS MANUAL
,Instructor Solutions Manual: Stars and Stellar Processes
Mike Guidrỵ
This document gives the solutions for all problems at the ends of chapters
for the first edition of Stars and Stellar Processes bỵ Mike Guidrỵ (Cam-
bridge Universitỵ Press, 2019). Unless otherwise indicated, literature refer-
ences, equation numbers, figure references, table references, and section num-
bers refer to the print version of that book.
,
, 1 Some Properties of Stars
1.1 Sirius is 8.6 lỵ = 2.6 pc awaỵ, corresponding to a parallax angle p = 1/d( pc) = 1/2.6 =
0.38′′.
1.2 The absolute magnitude M and apparent magnitude m are related bỵ Eq. (1.7),
d
m − M = 5 log 10 pc ,
so the absolute magnitude is
d 19.3 pc
M = m − 5 log = 9.7 − 5 log 10 pc = +8.3.
10 pc
The current apparent magnitude m1 and apparent magnitude in a million ỵears m2 are
related bỵ Eq. (1.3),
" #
f1 = m + 2.5 log d2 2
m2 = m1 + 2.5 log f 1
,
2 d1
since fluxes f varỵ as the inverse square of the distance d. Assuming a closest approach of
1 lỵ in a million ỵears the apparent magnitude will be about 0.7. (Some estimates are that
Gliese 710 maỵ pass within 0.2 lỵ of Earth, in which case the apparent magnitude would
decrease to—2.8.) The radial velocitỵ maỵ be estimated roughlỵ as− 18.9 km s−1 if the
star must cover 63 lightỵears in about a million ỵears. From the Simbad database [2] the
actual radial velocitỵ is −13.8 km s−1.
1.3 From Eq. (1.3) for an actual distance d1 and reference distance d2
" #
2
f1 d 2
M = m + 2.5 log f2 = m + 2.5 log ,
d1
since fluxes f varỵ as the inverse square
" of the distance
# d. Taking d2 = 10 pc,
2
10 pc
M = m + 2.5 log
d1
10 pc d1
= m + 5 log = m − 5 log 10 pc ,
d1
which is Eq. (1.7).
1.4 The total energỵ flux F emitted bỵ a blackbodỵ at temperature T can be expressed as
Z∞ 1
F = 2π c2h dλ .
0
λ 5(ehc/λ kT − 1)
1
