Parallax And Measurement Of Distance

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An observatory uses the parallax method to measure the distance of a nearby star by recording its angular shift across the diameter of Earth's orbit. This technique primarily relies on which geometric relationship?

RankGuru · Accepted Answer

As explained in NCERT Class 11, Chapter 2 (Units and Measurements), the parallax method determines large distances using the relation between an arc, its radius and the subtended angle. For a small angle θ measured in radians, the relation is θ = b / D, where b is the baseline separation and D is the distance to the object. Rearranging gives D = b / θ, so the distance equals the baseline divided by the parallax angle in radians. The option multiplying angle by baseline is wrong because it inverts the correct dependence on the angle. The option dividing by the square of the angle is wrong as the geometry is linear, not quadratic, for small angles. The option that distance is independent of baseline is wrong since a longer baseline directly increases the measurable shift. A final check confirms that a smaller parallax angle implies a larger distance, which matches D being inversely proportional to θ.

Parallax And Measurement Of Distance

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