Edexcel A-Level Physics Trigonometric Parallax

Review trigonometric parallax in Edexcel A-Level Physics through nearby-star distance calculations, six-month observations and parallax limits.

Exam points

describe six-month parallax observations against distant stars and the required Earth-Sun distance
calculate star distance or parallax angle using trigonometry or the small-angle approximation
explain why parallax only works for nearby stars when angular shifts become too small

[Maximum number: 3]

The astronomer Hertzsprung used parallax to determine the distances to some of the variable stars known as Cepheids.

Using parallax measurements, astronomers can determine distances to all stars with a parallax angle larger than $2.4 \times 10^{-7} \mathrm{rad}$ .

The variable star Alpha Cephei is $4.6 \times 10^{17} \mathrm{~m}$ from the Earth.
Deduce whether the distance to Alpha Cephei could be determined from parallax measurements.
distance from Earth to Sun $=1.5 \times 10^{11} \mathrm{~m}$

Use $\alpha\approx R/d$ for the small parallax angle. $\alpha=(1.5\times10^{11})/(4.6\times10^{17})=3.26\times10^{-7}\,\mathrm{rad}$ . This is larger than $2.4\times10^{-7}\,\mathrm{rad}$ , so the distance can be determined by parallax.

Figure for Answer to Question 5.6.165 - Distance by trigonometric parallax question 1 — Edexcel A-Level Physics A2

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5.6.165 - Distance by trigonometric parallax question 1