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# How do you find the diameter of the sun given angular diameter and distance ?

Last updated date: 09th Sep 2024
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Hint: The angular diameter of a spherical object determines its size to view from a particular distance. This angular diameter determines how small or big the object is from the viewer’s point. So we can say that the angular diameter changes from the viewer’s distance from the object.

(i) Imagine we people are seeing the sun from the earth’s surface. It appears in particular size. We think that the sun is in that size. But it is not. Our earth is $1.5 \times {10^{11}}m$ away from the size. This distance affects our view on its size.We can imagine the triangle for this picture.

(ii) This picture gives us a right angled triangle. The angle$\alpha$is the angular diameter. The D is the diameter of the sun and d is the distance between the observer and the object.
(iii) On considering the right angled triangle here,
$\tan \alpha = \dfrac{D}{d}$
$\therefore D = d.\tan \alpha$
Hence we can find the diameter of the sun by just knowing the distance between the observer from the sun and the angular diameter.

(i) The angular diameter is said to be$0.54^\circ$. We know that the earth is $1.5 \times {10^{11}}m$. This is taken as d. The diameter of the sun is estimated as $1.4 \times {10^9}m$.
$\alpha = {\tan ^{ - 1}}\left[ {\dfrac{{1.4 \times {{10}^9}}}{{1.5 \times {{10}^{11}}}}} \right]$
$\Rightarrow \alpha = 0.54^\circ$