a) The time it takes for part of a cloud 100,000 AU in radius to collapse to for

Question

a) The time it takes for part of a cloud 100,000 AU in radius to collapse to form a new star turns out to be about half the time it would take an object to orbit the star on an elliptical orbit with a semi-major axis of 50,000 AU. Use this information and Kepler’s Third Law to find the collapse time, assuming the star has the same mass as the Sun, and put your answer in years. What fraction of the age of the Sun (4.5 billion years) is this?

b) In an example in the text, an interstellar cloud having a diameter of 10^16 m and a rotation period of 10^6 yr collapses to a sphere the size of the Sun (1.4×10^9 m in diameter). If all of the cloud’s angular momentum stayed in that sphere, verify that the sphere would have a rotation period of only 0.6 s.

c) Because angular momentum is a quantity that is conserved, we can get an idea how the angular momentum of the original gas cloud was shuffled around. Look at the equations in “Working It Out” 7.1. Which planet has the second largest amount of orbital angular momentum, and how does it compare to Jupiter’s? If you look at the planet characteristics in Appendix 4 and you understand what makes orbital angular momentum large, you should be able to narrow things down so that you don’t have to calculate Lorbital for all of the planets.

d) Which planet has the most spin angular momentum? How does it compare to the Sun’s spin angular momentum? Again, you don’t have to calculate the Lspin for every planet if you can use the equation for Lspin and Appendix 4 to narrow your search.

Explanation / Answer

solving first question

(a)By keppler third law

time taken =T

T^2=4(pi)^2*R^3/GMsun

R=50000 AU =50000*1.5*10^11 m

Msun=1.989*10^30 kg

we got T=3.5*10^14 sec=1.11*10^7 years

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