E.5.6—Stellar parallax

Use the Earth’s orbit

Observe a nearby star from opposite sides of Earth’s orbit at different times of year. Its apparent position shifts against distant background stars; half of the total angular shift is the parallax angle $p$ .

d(\mathrm{pc})=\frac{1}{p(\mathrm{arcsec})}

Calculate distance

When $p$ is measured in arcseconds, distance in parsecs is $d=1/p$ . For $p=0.25$ arcsec, $d=4$ pc, which can then be converted to light-years.

Distance unit	Conversion
1 astronomical unit (AU)	$1.50\times10^{11}\,\mathrm{m}$
1 light-year (ly)	$9.46\times10^{15}\,\mathrm{m}$
1 parsec (pc)	$3.09\times10^{16}\,\mathrm{m}=3.26\,\mathrm{ly}=2.06\times10^5\,\mathrm{AU}$

Know the range

Parallax is a geometric distance method and is most useful for relatively nearby stars. It does not use a star’s spectrum or brightness directly.

Common trap

Do not use the full annual position shift as p if the diagram shows the total displacement from one side of Earth’s orbit to the other.

How it is assessed

Questions calculate distance from a parallax angle or identify what is measured in the method.

Command terms

Calculate / Identify

What earns marks

Identify the positional shift, use p in arcseconds, calculate parsecs, then convert units if requested.

Watch for

Choosing spectral wavelength or intensity as the measured quantity, or forgetting the inverse relation.

E.5.6—Stellar parallax

Measure Stellar Parallax

E.5.6 Exam Analysis

Assessment in practice