The sun subtends an angle of about 0.5∘ to us on earth, 150 million km away.

Asked by maham237 @ 27/12/2020 in Geography viewed by 327 People

The Sun subtends an angle if about 0.5° to us on Earth,150 million km away. Estimate the radius of the Sun.

Answered by maham237 @ 27/12/2020

Answer: 654498.469 km

We can use the figure attached as a guide to estimate the radius of the Sun.

How?

Well, if we consider the angle $aeb=\theta=0.5\º$ , this is the angle subtended.

By definition "the angle subtended (in radians) $\theta$ is given by an arc whose length $l$ is equal to the radius $d$ ":

$\theta=\frac{l}{d}$ (1)

In this case the red arc in the figure is the arc length $l$ , $d$ the distance between the Earth and the Sun and we need to convert the $0.5\º$ to radians, as follows:

If: $360\º=2\pi rad$ (2)

Then: $0.5\º\frac{2\pi rad}{360\º}=0.0087rad$ (3)

Now we can substitute (3) in (1):

$0.0087rad=\frac{l}{150000000km}$ (4)

and find the arc length $l$ :

$l=1308996.93km$ (5)

Approximating this arc length to the diameter $D$ of the Sun, we can say that $D=1308996.93km$

But, we are asked to estimate the radius of the Sun, and we can find it knowing the radius is one half of the diameter:

$r=\frac{D}{2}$ (6)

$r=\frac{1308996.93km}{2}$

Finally we get the estimation of the radius of the Sun:

$r=654498.469km$

The sun subtends an angle of about 0.5∘ to us on earth, 150 million km away.

Answer: 654498.469 km

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