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The sun has an apparent angular diameter of about 0.5
degrees of arc. Given that the sun is 1 AU (approximately 93
million miles) away, compute the approximate true diameter
of the Sun.
STEP 1
The problem tells us that the angular diameter of the Sun
is 0.5 degrees, and that the distance of the Sun is 93
million miles. So we write out the data:
- Angular diameter = 0.5 degrees
- Distance = 93,000,000 miles
STEP 2
There is only one equation needed in this problem, but we
have to use it in a slightly different way. Start with the
angular size formula, and rearrange it so that the factor we
want, actual size, is isolated:
Angular Diameter = 206265 X
(Actual diameter / Distance)
Angular Diameter X Distance = 206265 X
Actual diameter
(Angular Diameter X Distance) / 206265
= Actual diameter
STEP 3
The third step is unit conversion. The units of angular
size are in degrees, which are not right for this equation.
This is a smple conversion:
Angular size = 0.5 degrees X (60 min / deg) X (60
sec / min)
Angular size = 1800 seconds of arc
STEP 4
The final step is to plug and chug!
Actual diameter = (angular size X
distance) / 206265
Actual diameter = (1800 X 93,000,000) /
206265
Actual diameter = 810,000 miles =
1,300,000 km
We compute the actual diameter of the Sun to be 810,000
miles, or 1,300,000 kilometers, fairly close to the current
best value.
Back to Angular
Size
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Updated 7/7/06
By James
E. Heath