Question

What is the angular diameter ( in arcseconds) of an object that has a linear diameter of 23 meter and a distance of 1.5 km

Answer 1

It is given that,

`\begin{gathered} D\text{ = 23 m} \\ d\text{ = 1.5 km = 1500 m} \end{gathered}`

The relation between angular diameter to linear diameter and the distance is given as,

`\theta\text{ = 206265}*\text{ \lparen}(D)/(d)\text{ \rparen}`

Substituting the value in the formula,

`\begin{gathered} \theta\text{ = 206265}*\text{ }(23)/(1500) \\ \theta\text{ = 206265 }*\text{ 0.0153} \\ \theta\text{ = 3155.9 arc second} \end{gathered}`

Thus the angular diameter is 3155.9 arc second.