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I am doing a project on "how astronomers measure distance" where i came about with stellar parallax.

i realized how it works with trigonometry but i am having a slight doubt tan p=distance between sun and earth/distance between sun and star where i can find out distance between two star.

but why do we have to wait for six months?

we can measure the distance simply staying in june

why do we need to go to december again??

we can only work with triangle ACD

enter image description here

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There is obviously the practical problem that we cannot observe from the Sun! But of course there would be a time of year when the Earth was on the projection of the line CD.

The cartoon is just that. In practice, measurements are taken at different points in the orbit on multiple occasions over several years. Two measurements would not be enough to separate the apparent motion of the star from parallax from its proper motion on the sky. The cartoon is shown in that way because making observations at those points for that star, will give the largest measurable difference in position and therefore the most precise estimate of the parallax.

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