How Massive Must a Neutron Star Be to Keep Its Surface Intact While Rotating?

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SUMMARY

To determine the minimum mass required for a neutron star with a radius of 20 km to maintain surface integrity during rotation at 1.0 revolutions per second, the centripetal acceleration must be calculated. The correct centripetal acceleration value is approximately 7.89 x 10^8 m/s². Using the gravitational force equation F = GMm/r², the accurate mass of the neutron star is calculated to be approximately 4.7322 x 10^24 kg. Discrepancies in results among participants indicate a potential error in the centripetal acceleration value used by some contributors.

PREREQUISITES
  • Understanding of centripetal acceleration and its calculation
  • Familiarity with gravitational force equations, specifically F = GMm/r²
  • Basic knowledge of neutron star properties and astrophysics
  • Proficiency in unit conversion and scientific notation
NEXT STEPS
  • Study the derivation of centripetal acceleration in astrophysical contexts
  • Explore gravitational force calculations involving massive celestial bodies
  • Research neutron star formation and characteristics
  • Investigate the effects of rotation on stellar stability
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in the mechanics of neutron stars and their rotational dynamics.

wood_magpies
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certain neutron stars rotate at about 1.0 revolutions per second. If such a star has a raduis of 20km, what minimum mass must it have so that material on its surface doesn't fly off during the rapid rotation?


ive tried working out the centripetal acceleration, being 7.89 X10^8
then subbed into the equation, assuming that m=1:
ive made m=the material on the surface and given it a value of 1
M= mass of neutron star
G= gravity constant = 6.674 x 10^-11

F = GMm/r^2


the answer i got turned out to be 4.7322 x10^24kg
but a few of my friends got 2.236x10^24 kg

can anyone help please?
 
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With the given values, I get same result as you. You do seem to have a type in the magnitude of the centripetal acceleration, though.
 

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