Dimensional analysis to estimate gas clounds collapse

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SUMMARY

The discussion focuses on using dimensional analysis to estimate the collapse time of interstellar gas clouds with a given density of ρ = Mo pc-3, where Mo = 1.9898e33 g. Participants clarify the process of dimensional analysis, emphasizing the need to manipulate units of density (M L-3), gravity (M L-1 T-2), and momentum (M L T-1) to isolate time. The conversation highlights the importance of understanding these relationships to derive the collapse time without specific mass or length values.

PREREQUISITES
  • Understanding of dimensional analysis principles
  • Familiarity with physical quantities such as density, gravity, and momentum
  • Basic knowledge of astrophysics, particularly star formation processes
  • Proficiency in manipulating units and dimensions in equations
NEXT STEPS
  • Study dimensional analysis techniques in physics
  • Research the role of gravitational collapse in star formation
  • Learn about the equations governing gas dynamics in astrophysics
  • Explore examples of dimensional analysis applied to other physical phenomena
USEFUL FOR

Students in physics or astrophysics, educators teaching dimensional analysis, and researchers interested in the dynamics of star formation and gravitational collapse.

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Homework Statement


stars form by gravitational collapse of interstellar gas clouds. use dimensional analysis to estimate how long it takes for a cloud with a density p=Mo pc^-3 to collapse

Mo= 1.9898e33 g

Homework Equations





The Attempt at a Solution


I just have no idea how to use dimensional analysis, and how I would use it to solve the problem. My book has nothing about it. So if someone can explain to me how I use dimensional analysis step by step solve this problem.

Thanks
 
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Hey
after reading I have better idea on what to do. Here is what i got.

PgML/po I have to try to get the signs to cancle out and just to be left with time right?

so P= ML-3 for density g= M-1 L3 T-2 for gravity. po = MLT-1 for momentum so all of the cancel and you are left with time. Is that the right formula? Hmmm but how am i suppose to find how long it will take without the mass length or momentum? or did i do something wrong?
 

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