By B. Carroll, D. Ostlie
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Additional info for An Introduction to Modern Astrophysics 2nd ed - SOLUTIONS MANUAL
1: The relationship between effective temperature and mass for main sequence stars. 10 Massive planets with short orbital periods exert a greater force on the parent star, thus producing higher radial velocities of the stars themselves. In addition, shorter periods imply that a greater number of orbital periods can be measured over a given length of time. 11 From Eq. 7), it is evident that only m sin i can be determined, unless the angle of inclination can be determined independently (meaning that the system must be eclipsing).
5 shows that nearly all of the calcium atoms are in the form of Ca II, available for forming the H and K lines. 14 The Saha equation, Eq. 8), is NiC1 2ZiC1 D Ni ne Zi Â 2 me kT h2 Ã3=2 e i = kT : Stars of the same spectral type have the atoms in their atmospheres in the same states of ionization and excitation. The left-hand side of the Saha equation will therefore have the same value for atoms of the same element. The right-hand side increases monotonically as T increases, and decreases monotonically as ne increases.
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. 28. 2: A comparison between the limb darkening formulae of Van Hamme and the Eddington approximation (Eq. 58). 1 From Eq. 15), dr D d =Ä . Substitution into Eq. 6) leads immediately to the final result. 1 (see also Fig. 8). In this case however, r < r1 and r1 < R < r2 . R C r /2 . R r /2 After integrating over u, exact cancellation occurs, giving F D 0.
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