Detection techniques will be limited to variation in Doppler shift (radial…

The idea

Exoplanets are detected indirectly because the star and planet orbit a common centre of mass. In the radial velocity method, the star's line-of-sight motion periodically changes the observed wavelength of its spectral lines through the Doppler shift; measuring the shift over time gives the star's orbital speed and period, from which the planet's minimum mass can be inferred. In the transit method, a planet crossing the stellar disc causes a small, regular dip in apparent brightness; the depth, duration and spacing of dips reveal the planet's size and orbital period. Both methods rely on periodic signals, and combining them strengthens the evidence. The specification limits detection techniques to these two, so you should be able to describe each, interpret graphs and compare their strengths and limitations.

What earns the marks

• The radial velocity method detects the periodic Doppler shift of the star's spectral lines as the star moves towards and away from the observer.
• The observed wavelength change Δλ is related to radial speed v by Δλ/λ ≈ v/c for speeds much less than c, so a measured shift gives the star's radial velocity.
• A repeating pattern in the radial velocity curve gives the orbital period, and the amplitude gives information about the planet's mass and orbit.
• The transit method detects a small, regular decrease in the star's apparent brightness when the planet passes across the stellar disc.
• Transit depth relates approximately to the square of the ratio of planet radius to star radius, so a deeper transit indicates a larger planet relative to its star.
• Transit timing gives the orbital period, and the duration and shape of the dip give information about orbital speed and geometry.
• The two methods are complementary: radial velocity gives mass-related information, while transits give radius-related information, and a planet seen by both allows density to be estimated.

Common mistakes and how to put them right

• Thinking the Doppler shift is caused by the planet's light rather than the star's motion.

  Put it right by stating that the star's spectral lines shift as the star orbits the common centre of mass.

• Confusing a transit dip with an eclipse of one star by another or with stellar variability.

  Put it right by requiring a regular, repeating, shallow dip consistent with an orbiting planet.

• Assuming the radial velocity method gives the planet's exact mass directly.

  Put it right by explaining that it gives a minimum mass because the orbital inclination is usually unknown.

• Treating the transit method as measuring mass directly.

  Put it right by stating that transit depth primarily indicates the planet's radius relative to the star's radius.

Exam tips

• Sketch or describe a labelled radial velocity curve and a transit light curve, labelling period, amplitude or depth, and explain what each feature represents.
• Use the approximation Δλ/λ ≈ v/c only when v is much less than c, and state that the shift is measured relative to the star's rest wavelength.
• When comparing methods, refer explicitly to what each measures and to the need for periodic confirmation rather than claiming one method is always better.
• Define symbols clearly in calculations, for example Δλ for wavelength shift, λ for rest wavelength, v for radial speed and c for the speed of light.