### Measuring distance by parallax/triangulation

The basic method has been used in mapping for centuries. Suppose we have a remote island some distance off shore. If we first draw out a baseline on the shore and measure itʼs length. We then stand at one end of the baseline, look at a point on the island and measure the angle between our line of sight and the baseline. We do the same thing from the other end of the baseline. We then have a triangle from which we can calculate distances. (It helps to make the calculation easier if one of the angles is 90 degrees).

so Tan 70 = opp/150 metres

so opp = 150 Tan 70 = 412 metres

If we tried to use a baseline on earth then the angle to a very distant star would be very hard to measure accurately. To get a large baseline we take a measurement and then wait six months to take a second measurement. During that time the Earth completes half of its orbit around the Sun and we use that as the baseline.The change of angle is measured against the background shift of very distant stars behind the one which we are measuring.

We measure the change of angle and then half it to get α.

sin α=opp/hyp = 1AU/d

so distance d = 1AU/sin α

The astronomical distance “The Parsec” is based on this method.

The distance to the star is one parsec if the angle alpha (α) is one second, of one minute of one degree (that is 1/3600 of one degree). A parsec is equivalent to a little over 3 light years