# Mercury is .387 times Earth's distance from the Sun, Pluto is 39.53 times the Earth's distance from the Sun. If the Sun has an angular diameter of .5 degrees as seen from the Earth, what is the...

Mercury is .387 times Earth's distance from the Sun, Pluto is 39.53 times the Earth's distance from the Sun.

If the Sun has an angular diameter of .5 degrees as seen from the Earth, what is the Sun's angular diameter as seen from Mercury? From Pluto?

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### 1 Answer

The angular diameter of an object is the size of the object expressed as an angular measurement when it is viewed from a particular spot.

If an object is at a distance D from the point it is being viewed from and the diameter of the object as a length is L, the angular diameter A is given by the formula:

`A = 2*tan^-1(L/(2D))`

From the Earth, the Sun's angular diameter is 0.5. Let the distance of the sun from the Earth be represented by D. The diameter of the Sun as a length is:

`L = 2*D*tan(0.5/2) = 2*D*tan 0.25`

Now, Mercury is closer to the Sun and its distance from the Sun is equal to 0.387*D. The angular diameter of the Sun from Mercury is:

`2*tan^-1((2*D*tan 0.25)/(2*0.387*D))`

= `2*tan^-1((tan 0.25)/0.387)`

= 1.2919 degrees

As Pluto is at a distance equal to 39.53*D, the angular diameter of the Sun from Pluto is:

`2*tan^-1((2*D*tan 0.25)/(2*39.53*D))`

= `2*tan^-1((tan 0.25)/(39.53))`

= 0.1264 degrees

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