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1

I can partially answer this from a pulsar perspective. Across the board, parallax measurements are a fairly new development in radio astronomy. Interferometers are required to attain any reasonable degree in accuracy, and so parallax measurements have come into play mainly in the last two decades, with instruments like the Very Long Baseline Array taking ...

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The derivation Carefully observe the following triangle: We (the observers) are moving between the points $A$ and $B$, our object is in $C$. By the definition of the sine: $$\sin\frac{\alpha}{2}=\frac{L}{2D}$$ and with expressing $D$: $$D=\frac{L}{2\sin(\alpha/2)}$$ but for small angles in radians: $$\sin x = x$$ so $$D=\frac{L}{2\alpha/2}=\frac{L}{\alpha}$$...

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Using user38308's approach: First, find the distance between you and your friend, knowing lat/long of your positions. You need to solve a spherical triangle with vertices at the north pole and the locations of you and your friend. Piece of cake. You have 2 sides And their included angle. The (included) angle at the pole is the difference in your longitudes. ...

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To measure the distance $D$ of moon observe it from two different positions on the Earth (observatories in India and in the US) $A$ and $B$, separated by distance $AB = b$ at the same time. As the moon is very far away, $\frac{b}{D}<<1$ and therefore, $θ$ is very small. Then we approximately take $AB$ as an arc of length $b$ of a ...

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Yes, your argument is right. In astronomy, we use the term 'Secular parallax', associated with the motion of the sun or the solar system relative to the fixed star which provides a longer baseline. It gives more accuracy of parallax measurements compared to the Stellar parallax. References: https://en.wikipedia.org/wiki/Stellar_parallax#Statistical_parallax ...

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For stars, no. It is quite actively used to determine the distance of objects within the solar system though. For example, a NEO asteroid will show a marked deflection in position between observations from the north and southern hemispheres (or even between Mainland USA and Hawaii). What helps is that the two observations can be synchronized to any arbitrary ...

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In actual fact its a bit more complicated, because the Earth's orbit is not perfectly circular, The star does not lie exactly on the Earth's orbital plane, so the observation is not a line of movement but an ellipse both the Sun and the Star are moving relative to everything, so the ellipse is not an ellipse but a helix Observational errors from various ...

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You measure it on the photographs. If you take multiple images of the same star over the year you will find that it moves in a loop (compared to the very distant background stars) You measure the size of the loop. A larger loop is a larger angle. Because the angles are small, the size of the loop is in direct proportion to the angle. If you know the scale ...

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