Question

The Sun has an angular diameter of about 0.5∘ and an average distance of about 150 million km. What is the Sun's approximate physical diameter in km?

Answer 1

To find the physical diameter of the Sun, we can use the formula for angular size:

d = D * tan(Θ/2),

where d is the physical diameter, D is the distance from the observer to the object, and Θ is the angular size.

Given that the angular diameter of the Sun is about 0.5 degrees and its average distance is about 150 million km, we have:

d = 150 million km * tan(0.5∘/2) = 150 million km * tan(0.25∘)

Since the tangent function is a continuous function, we can use an approximation to find its value:

tan(0.25∘) ≈ 0.0043

Therefore:

d ≈ 150 million km * 0.0043 = 645,000 km

So, the Sun's approximate physical diameter is 645,000 km