Question

As observed from Earth, the Sun has an angular size of about 0.53o. From the observation, estimate the diameter of the Sun. How large in volume is the Sun when compared to Earth?

Answer 1

Formula
Angular Diameter = 206265 * (Actual
diameter / Distance)
Angular Dia * Distance = 206265 X Actual
dia
(Angular Dia * Dist.) / 206265 = Actual
diameter.
Given Data Angular diameter = 0.5 degrees
we know that sun is approximately 1AU
away
Distance = 93,000,000 miles
Angular size = 0.5 degrees X (60 min / deg)
X (60 sec / min)
Angular size = 1800 seconds of arc
Act. Diameter = (1800 X 93,000,000) /
206265
Act.diameter = 810,000 miles = 1,300,000
km
Assume sun as sphere
Volume of sun = 1.15*10 ^18 km?
We know that Volume of earth = 1.08 *
10 ^12 km3
Dividing vol. Of sun by earth
Volume difference is sun is 1.3 million times
bigger than earth. That's 1.3 million earth
could fit inside sun