Figure 2: Stellar parallax formed by earth’s orbit. The angular displacement that the line represents is known Point C is the sun, Point S is star of interest, Points B and A are different points in Earth’s orbit
The distance to the star (the length of CS) can be calculated with simple trigonometry if the parallax (ϑ) of said star and the distance between Earth at two dates are known. Throughout the course of a year, astronomers use telescopes to observe the parallax shift of the star in comparison to the fixed position of background stars. When the images of the background stars are oriented and imposed on each other, the line between the two stars in question is the parallax
Figure 3: Parallax shift of star
shift.
Measurements are taken until the largest possible parallax is found 8 . Theoretically, the maximum parallax shift would be between two observations made six months apart, when the Earth is the furthest away from another point in orbit. As an example, the observed parallax shift of Proxima Centauri, the closest star to our solar system, is 1.52’’(arcseconds), making ∠ ϑ 0.72’’. This completes the right angled triangle CAS. Because the radius of the Earth’s orbit (line CA) is 1 AU 9 , the length of CS, in parsecs, can be given as so:
Which works out to 1.388 parsecs, only 7% off from the literature value of 1.301 parsecs. Here is another example: the observed parallax shift of Polaris is 0.015’’, making ∠ ϑ 0.0075’’, using the equation, we find:
The distance from the Sun to Polaris is 133.3 parsecs, which is exactly equal to the literature value of 133 parsecs. What exactly is a parsec, though?
8 Minimizes error and creates the isosceles in Fig. 2 which makes calculations more convenient by ensuring ∠ BCS is 90 o 9 Convenient unit used in astronomy (≈ 150 million kilometres)
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