To find parsec, why do we need to divide AU by (1/3600)× (pi/180)

Answer 1

By the definition of parsec,

a point is 1 parsec away from us, provided anybody looking at us from that point

will see the Earth and the Sun separated by 1 arcsecond.

It will help to draw a picture of an isosceles triangle whose vertices are the Earth,

the Sun and that distant point 1 parsec away.

Imagine a circle whose center is that distance point and whose radius

r = 1 parsec.

So both the Earth and the Sun lie on that circle.

Let α = 1" be the angle at that distant point.

Since the angle α is so small we can approximate the distance (of 1 AU)

between the Earth and the Sun by the length of the arc along that circle.

So we can write

1AU = rα,

provided α is given in radians, not degrees.

The angle of 1 arcsecond is (1/3600)×π/180 radians.

Thus

r = 1AU/α = 1AU/(1/3600)×π/180 radians.