Foundations of Astronomy, Enhanced
Foundations of Astronomy, Enhanced
13th Edition
ISBN: 9781305980686
Author: Michael A. Seeds; Dana Backman
Publisher: Cengage Learning US
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Chapter 11, Problem 6RQ
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What prevents a giant molecular cloud fragment from collapsing to zero radius and what happens to the density, pressure, and temperature to slow the continued collapse. What happens to the given temperature outside of the core as the core of the fragment slows its insider-out collapse.

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1) a) Calculate the Jeans length for the dense core of a giant molecular cloud with T=10 K, n = 1010/m³, and µ=2. b) Estimate the adiabatic sound speed for this core, using y=5/3. c) Use this speed to find the amount of time required for a sound wave to cross the cloud t3=2Rj/vs. d) Compare your answer with the free-fall scale and comment your results.
1.  A planetary nebula has an angular diameter of 76 arc seconds and a distance of 5100 ly. What is its linear diameter (in ly)?  Hint:  Use the small-angle formula:  angular diameter (in arc seconds) 2.06 ✕ 105 = linear diameter distance   2.  Suppose a planetary nebula is 3.2 pc in diameter, and Doppler shifts in its spectrum show that the planetary nebula is expanding at 31 km/s. How old is the planetary nebula in yr? (Note: 1 pc = 3.1 ✕ 1013 km and 1 yr = 3.2 ✕ 107 s.)
A planetary nebula expanded in radius 0.3 arc seconds in 30 years.  Doppler measurements show the nebula is expanding at a rate of 35 km/s.  How far away is the nebula in parsecs? First, determine what distance the nebular expanded in parsecs during the time mentioned.  Δd = vpc/sTs So we first need to convert the rate into pc/s and the time into seconds: vpc/s = vkm/s (1 pc / 3.09 x 1013km) vpc/s = ? Ts = (Tyr)(365 days/yr)(24 hrs/day)(3600 s/hr) Ts = ? s Δd= vpc/sTs Therefore, Δd = ? pc
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