Angles and their Measurement: The natural way to measure an angle is in Radians. In this case, the distance to the star is given by distance ~ (Astronomical Unit) / (2 x parallax angle)

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Question: What is a Radian?

A Radian is defined by the fact that there are 2 pi Radians per circle. That is, 6.28 Radians = 360^o or that 1 Radian = 57.3o. Radians are the natural unit for angular measurements, however, in most astrophysical situations, the angles with which we deal are tiny. They are in fact << than a Radian and a better unit for angles is needed. There are 360^oper circle. We sub-divide 1^o into 60 parts which we refer to as arc minutes. We then sub-divide 1 arc minute into 60 parts which we refer to as arc seconds. That is, 1 arc second is 1/3,600 of 1^o!!! In most astrophysical situations, the angles we deal with are on the order of arc seconds. The parallax angle for the most nearby star (other than the Sun) is around 1 arc second. If we measure the parallax angle in arc seconds, the distance comes out in a unit known as a parsec. A parsec is the distance of a star whose parallax angle is one arc second. In terms of centimeters, 1 parsec is 3.1x10¹³ kilometers. The smallest parallax angles which we can measure reliably are on the order of 0.01 - 0.02 arc seconds and so, we can reliably get distances of stars in a neighborhood of a hundred or so parsecs in size. This is only a tiny part of galaxy, the Milky Way galaxy, our home, which is at least 10⁵ parsecs in diameter!

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