By Carroll B.W., Ostlie D.A.

ISBN-10: 0321442849

ISBN-13: 9780321442840

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**Additional resources for An introduction to modern astrophysics: Solution manual**

**Sample text**

B) See Fig. 1. 2 and Fig. 1. (d) The surface value of the temperature obtained from Eq. 53) is certainly more valid (on physical grounds) than the surface boundary condition of T D 0 employed by StatStar. However, given the numerous other approximations involved, StatStar’s surface value of T D 0 is adequate for our computational purposes. 29 (a) See Fig. 2. (b) See Fig. 2. 28. Te D 5504 K. 8 Eq. 8651 The difference is greatest at mid angles (approximately 50ı ) and near 90ı . (d) Van Hamme’s formula best mimics the observational data for the Sun.

5 Beginning with Eq. 9) and substituting Eq. 6 From the non-relativistic expression for kinetic energy (E), r r 2E 2 1 vD and dv D dE: m 2 mE Using the relation nv dv D nE dE and making the appropriate substitutions in Eq. 1) leads directly to Eq. 28). 7 From Eq. 22), the gravitational potential energy of the Sun is approximately Ug D 2:3 1041 J. Using the virial theorem (Eq. 46), the thermal kinetic energy of the Sun is roughly 3N kT =2 D 1:2 1041 J, where N is the number of particles in the Sun.

Substituting, Â Ã a1 C a2 : r D r2 a2 Now, using Eq. 2 (a) 1 rp C ra D a1 C a2 : 2 The probability of detecting the radial velocity variations is greatest when the i D 90ı, while the probability goes to zero when i D 0ı . i / D sin i . 3 sin3 i sin i d i 0 D 3i 8 D 3 : 16 Ãˇ sin 2i sin 4i ˇˇ =2 C 4 32 ˇ0 For the smallest angle, a cos i D r1 C r2 , implying Â Ã 1 r1 C r2 i D cos : a (b) i D 88:5ı . 4 (a) 37 For p 00 D 0:3792100, the distance to Sirius is d D 1=p 00 D 2:63 pc. This means that the linear size of the semimajor axis of the reduced mass is approximately a D ˛d D 3:00 1012 m.

### An introduction to modern astrophysics: Solution manual by Carroll B.W., Ostlie D.A.

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