How Long Does an Interstellar Cloud Take to Contract?

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SUMMARY

An interstellar cloud with a radius of 10 parsecs and a mass of 10,000 solar masses will take approximately 29.6 million years to contract under the assumption of zero initial velocity and constant density. The calculation utilizes the formula for free-fall time, which is derived from the gravitational constant and the mass of the cloud. The parameters provided indicate that the cloud is slightly above the average interstellar medium density, yet the calculations remain valid for the specified conditions.

PREREQUISITES
  • Understanding of gravitational physics and free-fall dynamics
  • Familiarity with the concept of interstellar clouds and their properties
  • Knowledge of astronomical units (AU) and solar mass (Msun)
  • Basic proficiency in mathematical calculations involving square roots and powers
NEXT STEPS
  • Research the gravitational constant (G) and its role in astrophysical calculations
  • Explore the dynamics of interstellar medium (ISM) and its average density
  • Learn about the implications of free-fall time in astrophysics
  • Investigate the effects of external forces on the contraction of interstellar clouds
USEFUL FOR

Astronomers, astrophysicists, and students studying cosmic structures and gravitational dynamics will benefit from this discussion.

knhlove
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Problem:"An interstellar cloud with a radius of 10parsecs and a mass of 10000 Msun is contracting. How long does this take? (The cloud itself has no pressure)
 
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knhlove said:
Problem:"An interstellar cloud with a radius of 10parsecs and a mass of 10000 Msun is contracting. How long does this take? (The cloud itself has no pressure)

Assuming it begins at zero velocity and constant density then its freefall time is ~sqrt(R^3/GM) but the size you've quoted sounds a tad excessive for the mass you quote if it's a gravitationally bound mass. The cloud is only about double the average ISM. But let's use those numbers because it's going to collapse at some temperature assuming no other masses interfering with it. So the radius is 2062648 AU and the mass is 10,000 suns. Thus free-fall time in Gaussian years is sqrt(2062648^3/10,000) = 29.6 million years.
 

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