A globular cluster of stars is measured to have an angular diameter of 20.6 arcseconds, and its distance from Earth is measured to be 200,000 light-years. What is its approximate physical diameter in light-years?
A)200,000
B)1/20
C)20
D)2

Question

Quizplus · Accepted Answer

We can use the small angle formula to find the physical diameter of the globular cluster:
θ = d/D
where θ is the angular diameter in radians, d is the physical diameter, and D is the distance. Converting 20.6 arcseconds to radians gives:
θ = (20.6/3600) degrees x (pi/180) = 0.0009596 radians
So, we can solve for d:
d = θ x D = 0.0009596 radians x 200,000 light-years = 191.92 light-years 
Therefore, the approximate physical diameter is 191.92 light-years, which is closest to Choice C, 20.

A Globular Cluster of Stars Is Measured to Have an Angular