Cosmology: (b) stellar parallax

The idea

Stellar parallax is the apparent shift in a nearby star's position against more distant background stars as the Earth moves from one side of its orbit to the other. The parallax angle p is half the total angular shift measured over six months, with the baseline equal to 1 astronomical unit. The effect is tiny: even the nearest stars have parallaxes below one second of arc, which is why space missions are needed for accurate measurement. In multiple-choice questions you may be asked to identify the baseline, the definition of the parallax angle, why the measurement is taken six months apart, or why the method fails for very distant stars.

What earns the marks

• Defines stellar parallax as the apparent change in a star's position against background stars due to the Earth's orbital motion.
• Identifies the baseline as 1 au, the Earth–Sun distance, with observations six months apart.
• States that the parallax angle p is half the maximum angular shift observed over the year.
• Explains that parallax angles are very small, so distant stars cannot be measured accurately from the ground.
• Links the measured parallax to distance through d = 1/p with p in seconds of arc.

Common mistakes and how to put them right

• Using the diameter of the Earth's orbit as the baseline instead of 1 au.

  Put it right: The parallax angle is defined with the Earth–Sun distance as baseline, so the full orbital diameter would double the angle.

• Taking the total angular shift over six months as p rather than half of it.

  Put it right: p is half the maximum shift between the two extreme positions.

• Believing parallax can measure any distance.

  Put it right: The angle becomes too small to resolve for distant stars, so the method is limited to relatively nearby stars.

• Confusing parallax with aberration or with the star's proper motion.

  Put it right: Parallax is the annual shift caused by the observer's changing viewpoint.

Exam tips

• Sketch the Earth at two positions six months apart with the nearby star and a background star, and mark the baseline as 1 au and the angle p at the star.
• Remember the factor of one half: if a question gives the total shift between January and July, divide by two before using d = 1/p.
• Check the units of the angle; parallax must be in seconds of arc for d = 1/p to give parsecs.
• Use the inverse relationship to reason about options: a smaller parallax means a greater distance, so the most distant star has the smallest p.