How can you determine the diameter of the sun?

Answer 1

If #\theta# is the angular diameter of the sun as measured from earth and #D# is the distance to the sun, then the diameter of the sun #d_{sun}# is
#d_{sun}=2*D*tan (\theta/2) #.
Using the small angle approximation (#tan\theta~=\theta# in radians)
# d_{sun}= D*\theta # in #\theta# radians or
# d_{sun}= D*\pi/180*\theta # in #\theta# degrees.

Draw the sun, given the sun some size, draw a point to represent the location of the earth (this does NOT need to be to scale).
Draw a line from the location of the earth to the center of the sun.
Draw the diameter of the sun at right angles to this like.
Make an isosceles triangle by connecting the ends of the diameter to the loctaion of the earth. Should look something like this.

#\theta# the angular size of the sun is the angle bound by the diameter.

#\theta/2# is the little angle in the two right angle triangles.

#tan(\theta/2)=r_{sun}/D#

rearranging we have

#r_{sun}=D tan(\theta/2)#.

since #d_{sun}=2* r_{sun}#

#d_{sun}=2*D *tan(\theta/2)#.
Using the small angle approximation (which only works in radians) we have,
# d_{sun}=2*D* \theta/2=D *\theta_{radians} #.
If we have #\theta# in degrees we can convert using #\theta_{radians}=pi/180 \theta_{degrees}#
giving
# d_{sun}=pi/180 D *\theta_{degrees} #

note that #\theta_{degrees}# is around half a degree.

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Answer 2

The diameter of the sun can be determined using various methods, including geometric calculations, solar observations, and astronomical measurements. One common method involves using the angular size of the sun as observed from Earth and its known distance from Earth to calculate its diameter. This can be done using trigonometry and the formula: Diameter = 2 * Distance * tan(Angle), where the angle is the angular size of the sun as observed from Earth and the distance is the average distance from Earth to the sun, approximately 149.6 million kilometers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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