Question

if the angular diameter of an object is 15 arc seconds and it is 1.4 billion kilometers away, how big is its physical size?

Answer 1

the actual diameter of the object is 1.017×10⁵km

actual diameter, d = any line segment that passes through the center of the circle

angular diameter, θ = the angle that an actual diameter of an object makes.

distance, D= the actual path travel

distance of the object ,D= 1.4 billion = 1.4×10⁹km

angular diameter of an object,θ = 15arc

                            θ  = 15 ×π/ (60×60×180) rad

                                                 [ ∵ 1 revolution = 2π = 360°×60×60]

   Using the relation,

     θ = d/D   {angular diameter = actual diameter/ distance}

     d =  θD

      d =  1.4×10⁹×[15×3.14/(60×60×180) ] km

         =  1.017×10⁵km

This shows the actual diameter of the object is  1.017×10⁵km

It is the physical size of object.

To learn more about diameter of an object here

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