Calculating the radius of a HII region - worked out but just need you to check

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SUMMARY

The discussion focuses on calculating the radius of a spherical HII region located 500 parsecs away, which subtends an angle of 20 arcminutes. The formula used is L = D(theta), where L represents the angular size, D is the distance, and theta is the angle in radians. The calculation yields a radius of 1.5 parsecs, acknowledging potential precision limits in the distance measurement, particularly with a possible error margin of ±50 parsecs.

PREREQUISITES
  • Understanding of angular measurements in astronomy, specifically arcminutes and radians.
  • Familiarity with the concept of parsecs as a unit of distance in astrophysics.
  • Basic knowledge of spherical geometry and its applications in astrophysical contexts.
  • Proficiency in using mathematical equations for distance and angular size calculations.
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  • Research the implications of distance measurement errors in astrophysical calculations.
  • Explore the significance of HII regions in the context of star formation and galactic evolution.
  • Learn about the conversion between arcminutes and radians for astronomical applications.
  • Investigate the methods used to estimate the sizes of astronomical objects based on angular size.
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Astronomy students, astrophysicists, and anyone interested in the calculations related to HII regions and their properties.

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Homework Statement


Estimate the radius of a spherical HII region which rests at a distance of 500 pc that subtends an angle of 20' at the observer. [1'=3x10-4 radians]

Homework Equations



L=D(theta)

Where D is the distance, L is the angular size and theta is the angle.


The Attempt at a Solution



L= 500*20*3*10^-4 = 3pc

L=3pc

Radius = 1.5 pc
 
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Yes, as given, and to the likely limits of precision of the inputs. The 500pc distance in particular probably has ±50pc or more. So my instinct to quibble about how many radians in 1' isn't worthwhile :-).
 
Thank you! :-)
 

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