Question

Examplo 4 The distance of the sun from
earth is 1.496 * 1011 m. If the angular diameter
of the sun is 2000”, find the diameter of the sun.​

Answer 1

Answer :

Given -

• The distance of sun from earth is 1.496 * 10¹¹ m
• Angular diameter = 2000"

To Find -

• Diameter of the sun

Solution -

We know that, Angular diameter = basis/Distance

Hence, ∅ = b/D

Converting the angular Distance into radians.

➸ 2000"

➸ (2000 * 1/60)'

➸ (2000 * 1/60 * 1/60)°

➸ (2000 * 1/60 * 1/60 * π/180) rad

➸ 2π/(6*6*18) rad

➸ π/36*9 rad

➸ π/324 rad

Now, Using the formula :

⇒ (0.55 * 1/60 * 1/60 * π/180) = basis/1.496 * 10¹¹

⇒ π/324 = basis/1.496 * 10¹¹

⇒ π/324 * 1.486 * 10¹¹ = basis

⇒ basis = 0.0045π * 10¹¹

⇒ basis = 4.5π * 10⁸

⇒ basis = 4.5 * 22/7 * 10⁸

⇒ basis = 14.142 * 10⁸ m

Hence, Diameter of sun = 14.142 * 10⁸ m