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Relation between angular diameters and actual diameters of celestial objects

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The problem is:

An object is 50000 parsecs from Earth and has an angular diameter of
30 arcseconds. What is the physical width of the object to the nearest tenth of a parsec?

Can you explain, in detail, how to do his problem and what the correct answer is?

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Solution Summary

Detailed explanations are given about how to relate visible angular and actual linear sizes of objects observed
on the sky. The difficulty is in using small angles, such as arcseconds, common in
astronomical observations.

Solution Preview

A parsec is a unit of length commongly used in astronomy. It is like any other unit, for example,
a mile or a kilometre. Just a lot longer. In this problem, angular diameter of the object has nothing
to do with the definition of a parsec. 30 arcseconds is an angle subtended by the object on
the sky ...

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