Why are measurements taken six months apart?

The Earth is then on opposite sides of its orbit, giving the largest baseline and the largest measurable shift.

Define the parallax angle.

Half the angular shift in position over six months: the angle subtended at the star by 1 AU.

The distance at which a star has a parallax angle of one arcsecond.

Why does parallax only work for nearby stars?

For distant stars the parallax angle is too small to measure.

What is a standard candle?

An object of known luminosity, whose distance can be found from the intensity received.

Give an example of a standard candle.

A Type Ia supernova, which reaches the same peak luminosity each time.

State two limitations of standard candles.

The luminosity must be known reliably (calibrated), and absorption by dust or gas must be negligible.

Measuring astronomical distancesEdexcel A-Level Physics: Flashcards

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What is trigonometric parallax?

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What is trigonometric parallax?: The apparent shift of a nearby star against distant background stars as the Earth orbits the Sun, used to find its distance.
Why are measurements taken six months apart?: The Earth is then on opposite sides of its orbit, giving the largest baseline and the largest measurable shift.
Define the parallax angle.: Half the angular shift in position over six months: the angle subtended at the star by 1 AU.
Define a parsec.: The distance at which a star has a parallax angle of one arcsecond.
State the relationship between distance in parsecs and parallax angle.: $d\,(\text{pc}) = 1/p\,(\text{arcseconds})$
What is 1 parsec in metres?: $3.09 \times 10^{16}$ m
What is an arcsecond?: 1/3600 of a degree.
Why does parallax only work for nearby stars?: For distant stars the parallax angle is too small to measure.
What is a standard candle?: An object of known luminosity, whose distance can be found from the intensity received.
Give an example of a standard candle.: A Type Ia supernova, which reaches the same peak luminosity each time.
Write the equation for the distance to a standard candle.: $d = \sqrt{\dfrac{L}{4\pi I}}$
State two limitations of standard candles.: The luminosity must be known reliably (calibrated), and absorption by dust or gas must be negligible.

Exam questions on Measuring astronomical distances

An astronomer measures the position of a nearby star against the background of very distant stars. She repeats the measurement six months later and finds that the position of the nearby star appears to have shifted. The parallax angle of the star is 0.25 arcseconds.
Explain why the astronomer repeats the measurement six months later.2 marks
A Type Ia supernova is observed in a distant galaxy. All Type Ia supernovae reach the same peak luminosity, 2.0 × 10³⁶ W. At its peak the intensity received at the Earth from this supernova is 1.0 × 10⁻¹⁴ W m⁻².
Suggest why the distance to this supernova cannot be found using trigonometric parallax, and why a standard candle can be used instead.2 marks
A star, X, has a parallax angle of 0.050 arcseconds. The intensity of the light received from it at the Earth is 2.4 × 10⁻¹⁰ W m⁻². One parsec is 3.09 × 10¹⁶ m, and the luminosity of the Sun is 3.85 × 10²⁶ W.
Calculate the distance to star X in parsecs and in metres.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).