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Radial Velocity & Transit Methods Revision Notes | A Level AQA Physics

The transit method detects periodic dips in a star's brightness as a planet passes in front of it and blocks some of its light. Notes and 13 questions answered.

Updated 12 Sept 2026 · Revise Right Team

Radial Velocity & Transit Methods is part of Cosmology (A-level only) in A Level AQA Physics.

9 min

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23

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A Level AQA

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What this lesson covers

The transit method detects periodic dips in a star's brightness as a planet passes in front of it and blocks some of its light. Notes and 13 questions answered.

  • Explain how the radial velocity method uses Doppler shift to detect exoplanets
  • Describe how the transit method detects exoplanets through changes in stellar brightness
  • Interpret a typical light curve produced during a planetary transit
  • Compare the radial velocity and transit methods, including their limitations

Key ideas to keep in view

Use this lesson to stay inside Cosmology (A-level only) while connecting the detail back to the wider Astrophysics (A-level only) topic.

  • Radial velocity method: A detection technique that identifies exoplanets by measuring periodic Doppler shifts in a star's spectral lines, caused by the gravitational pull of an orbiting planet on the star.
  • Transit method: A detection technique that identifies exoplanets by monitoring the periodic dip in a star's apparent brightness as a planet passes across the star's disc from the observer's line of sight.
  • Light curve: A graph of a star's apparent brightness (flux) against time, used in the transit method to reveal the characteristic dip caused by a transiting planet.
  • Doppler shift: The change in observed wavelength of electromagnetic radiation caused by relative motion between the source and the observer; a blueshift indicates approach and a redshift indicates recession.

Revision notes

Read the core explanations from Radial Velocity & Transit Methods before testing yourself from memory.

1. The Hunt for Exoplanets

Stars are so overwhelmingly bright that a planet orbiting one is essentially invisible from Earth — like trying to spot a firefly next to a lighthouse from several kilometres away. So astronomers had to get clever. Rather than looking for the planet directly, they look for what the planet does to its host star.

The AQA specification focuses on two detection techniques: the radial velocity method (which exploits the Doppler shift of starlight) and the transit method (which monitors changes in stellar brightness). Both are indirect — they detect the planet's influence, not the planet itself. That distinction matters enormously when you are asked to evaluate either method in an exam.

2. The Radial Velocity Method

Here is the key insight: a planet does not orbit a stationary star. Both the planet and the star orbit their common centre of mass. Because the star is vastly more massive, its orbit is tiny — but it is real, and it produces a measurable wobble.

As the star wobbles, part of that motion is directed towards or away from Earth. This component — the motion along the line of sight — is called the radial velocity. When the star moves towards us, its light is blueshifted; when it moves away, its light is redshifted. By measuring these periodic Doppler shifts in the star's spectral lines, astronomers can infer the presence of an orbiting planet.

The Doppler shift equation links the observed change in wavelength to the radial velocity of the source. For speeds much less than the speed of light — which is always the case for stellar wobbles — the relationship is:

In practice, astronomers observe a known spectral line — for example the hydrogen-alpha line at 656.3 nm — and measure how its wavelength shifts over time. A periodic oscillation in that shift, repeating with the same period as the planet's orbit, is the signature of an exoplanet.

Worked example: Calculating Radial Velocity from a Doppler Shift

A star's hydrogen-alpha spectral line has a rest wavelength of $\lambda_0 = 656.3 \text{ nm}$. During observation, the line is measured at $\lambda = 656.5 \text{ nm}$. Calculate the radial velocity of the star and state whether it is moving towards or away from Earth.

  1. $\Delta \lambda = \lambda - \lambda_0 = 656.5 \text{ nm} - 656.3 \text{ nm} = 0.2 \text{ nm}$ — A positive $\Delta\lambda$ means the observed wavelength is longer than the rest wavelength — this is a redshift. [M1]
  2. $\lambda_0 = 656.3 \times 10^{-9} \text{ m}$, $\Delta\lambda = 0.2 \times 10^{-9} \text{ m}$ — Keep units consistent throughout. Both values must be in the same unit before dividing.
  3. $v = \frac{\Delta\lambda}{\lambda_0} \times c = \frac{0.2 \times 10^{-9}}{656.3 \times 10^{-9}} \times 3.0 \times 10^8$ — Rearrange $\frac{\Delta\lambda}{\lambda_0} = \frac{v}{c}$ to give $v = \frac{\Delta\lambda}{\lambda_0} \times c$. [M1]
  4. $\frac{0.2}{656.3} = 3.048 \times 10^{-4}$ — Carry enough significant figures here to avoid rounding errors in the final step.
  5. $v = 3.048 \times 10^{-4} \times 3.0 \times 10^8 = 9.1 \times 10^4 \text{ m/s}$ — $3.048 \times 10^{-4} \times 3.0 \times 10^8 = 9.144 \times 10^4 \approx 9.1 \times 10^4 \text{ m/s}$ (2 s.f.). [A1]
  6. Redshift ($\Delta\lambda > 0$) $\Rightarrow$ star is moving away from Earth. — A redshift always means recession. This is the half of the wobble where the star moves away from us — the other half will show a blueshift of equal magnitude. [B1]

Answer: $v \approx 9.1 \times 10^4 \text{ m/s}$ (approximately 91 km/s); the star is moving away from Earth (redshift).

Notice that the radial velocity oscillates: as the planet completes one orbit, the star first moves away from us (redshift), then towards us (blueshift), then away again. The period of this oscillation equals the orbital period of the planet. This is the core of what the radial velocity method measures.

The radial velocity method is most sensitive to massive planets in close, short-period orbits — because a more massive planet produces a larger stellar wobble, and a closer planet completes orbits quickly, making the periodic signal easier to detect. This is an important limitation to keep in mind when evaluating the method.

3. The Transit Method

Now for the second technique. Picture a planet passing directly between its star and Earth — a transit. During the transit, the planet blocks a small fraction of the star's light, causing a measurable dip in the star's apparent brightness. The transit method detects exoplanets by monitoring this periodic dimming.

The fractional drop in brightness depends on the ratio of the planet's cross-sectional area to the star's cross-sectional area. For a spherical planet of radius $r_p$ orbiting a star of radius $r_s$, the fractional decrease in flux is:

A Jupiter-sized planet transiting a Sun-like star produces a dip of roughly 1%, which is detectable from ground-based telescopes. An Earth-sized planet produces a dip of only about 0.01% — far harder to detect, which is why space-based observatories such as Kepler and TESS were designed for this purpose.

3a. The Light Curve

The data product of the transit method is the light curve: a graph of the star's flux (or normalised brightness) plotted against time. Understanding the shape of a typical light curve is a direct AQA specification requirement, so let us work through each feature carefully.

The light curve has a characteristic flat-bottomed shape. Before and after the transit, the flux is constant at its baseline value (normalised to 1.0). As the planet begins to cross the stellar disc, the flux drops — this is called ingress. Once the planet is fully in front of the star, the flux reaches a constant minimum value — the flat bottom. As the planet exits, the flux rises again during egress, returning to baseline.

  • Baseline flux: constant before and after the transit — no planet in front of the star.
  • Ingress: flux drops as the planet moves onto the stellar disc.
  • Flat bottom: flux is at its minimum and constant — planet fully in front of the star.
  • Egress: flux rises as the planet moves off the stellar disc.
  • Depth of dip: proportional to $(r_p / r_s)^2$ — tells us the planet's size relative to the star.
  • Duration of transit: depends on the planet's orbital speed and the size of the stellar disc.
  • Period between successive dips: equals the orbital period of the planet.

Each of these features carries physical information. The depth gives the planet-to-star radius ratio. The duration, combined with knowledge of the star's radius, constrains the orbital speed. The period between successive transits gives the orbital period directly, and Kepler's third law then allows the orbital radius to be calculated.

One subtlety worth noting: the ingress and egress slopes are not perfectly vertical. They are slightly curved because the planet takes a finite time to move fully onto and off the stellar disc. A perfectly sharp-edged dip would require the planet to appear and disappear instantaneously — physically impossible. Examiners sometimes ask you to describe this feature, so be precise: the flux decreases gradually during ingress and increases gradually during egress.

Worked example: Estimating Planet Radius from a Light Curve

A light curve shows a fractional flux dip of $\Delta F / F = 0.0064$. The host star has a radius of $7.0 \times 10^8$ m. Estimate the radius of the transiting planet.

  1. $\frac{\Delta F}{F} = \left(\frac{r_p}{r_s}\right)^2$ — This is the starting relationship. The dip depth equals the square of the radius ratio. [M1]
  2. $\frac{r_p}{r_s} = \sqrt{\frac{\Delta F}{F}} = \sqrt{0.0064}$ — Take the square root of both sides to isolate $r_p / r_s$. [M1]
  3. $\sqrt{0.0064} = 0.08$ — Check: $0.08 \times 0.08 = 0.0064$. Confirmed.
  4. $r_p = 0.08 \times r_s = 0.08 \times 7.0 \times 10^8 \text{ m}$ — Multiply the ratio by the known stellar radius. [M1]
  5. $r_p = 0.08 \times 7.0 \times 10^8 = 5.6 \times 10^7 \text{ m}$ — $0.08 \times 7.0 = 0.56$, so $r_p = 0.56 \times 10^8 = 5.6 \times 10^7$ m. Always include units. [A1]

Answer: $r_p = 5.6 \times 10^7 \text{ m}$

4. Comparing the Two Methods

Now that both methods are clear, it is worth comparing them directly — this is exactly the kind of analysis AQA expects at A-level. The two techniques are complementary: each reveals different physical properties of the exoplanet system, and each has distinct observational requirements and limitations.

FeatureRadial Velocity MethodTransit Method
Physical principleDoppler shift of stellar spectral lines due to stellar wobblePeriodic dip in stellar flux as planet crosses the disc
What it measures directlyRadial velocity amplitude of the starFractional decrease in stellar flux
What it tells us about the planetMinimum mass (lower bound, due to orbital inclination uncertainty)Radius (relative to star's radius)
Orbital inclination requiredWorks for any inclination (but gives only minimum mass)Requires near edge-on orbit (transit must be visible from Earth)
Best suited to detectMassive planets in close orbits (large wobble, short period)Large planets transiting small stars (deeper dip)
Key limitationCannot determine true mass without knowing orbital inclinationRequires precise alignment — most planetary systems will not transit as seen from Earth

A crucial point for evaluation questions: the radial velocity method gives only a lower bound on the planet's mass. This is because only the component of the star's velocity directed towards or away from Earth is measured. If the orbital plane is tilted relative to the line of sight, the true orbital speed is larger than the measured radial velocity component, so the true mass is larger than the calculated minimum mass.

When both methods are applied to the same system — which is possible when a planet both transits and produces a detectable wobble — astronomers can determine both the planet's radius and its true mass, and therefore calculate its mean density. This works because the transit geometry constrains the orbital inclination, which when combined with the radial velocity amplitude, allows the true (not minimum) mass to be calculated. That density then constrains whether the planet is rocky, icy, or gaseous. This is a powerful example of how the two methods work together.

5. Exam Technique and Common Pitfalls

Both detection methods appear regularly in AQA exam questions, and the marks are often lost not through lack of knowledge but through imprecise language. The following guidance targets the most common errors seen in mark schemes.

When asked to describe the radial velocity method, examiners expect you to mention: the star and planet orbiting a common centre of mass; the resulting periodic change in the star's radial velocity; and the consequent periodic Doppler shift in the star's spectral lines. Saying only "the star wobbles" without linking it to the Doppler shift will not score full marks.

When asked to describe a light curve, work through the features in sequence: constant baseline flux, gradual ingress, flat-bottomed minimum, gradual egress, return to baseline. State explicitly that the depth of the dip is related to the ratio of the planet's area to the star's area — not the ratio of radii. The ratio of areas equals the square of the ratio of radii, and conflating these two is a mark-losing error.

For extended-response questions asking you to evaluate both methods, structure your answer as: what each method measures, the physical principle behind it, what it can tell us about the planet, and a clear limitation of each. End with a conclusion — for example, noting that combining both methods yields the most complete picture of an exoplanet's properties.

Together, the radial velocity and transit methods represent the two core indirect detection techniques required by the AQA specification — each grounded in a distinct physical principle (Doppler shift and flux measurement respectively), each revealing different properties of the exoplanet, and each subject to specific observational constraints that must be stated precisely in exam answers.

Frequently asked questions

How does the transit method detect exoplanets?

The transit method monitors a star's brightness for periodic dips caused by a planet passing directly between the star and Earth and blocking a small fraction of its light. The fractional drop in flux equals the square of the planet-to-star radius ratio, so a Jupiter-sized planet dims a Sun-like star by about 1% and an Earth-sized planet by about 0.01%.

What is radial velocity?

Radial velocity is the component of a star's velocity along the line of sight between the star and the observer. A positive radial velocity means recession and a redshift, a negative one means approach and a blueshift, and it is measured in m/s or km/s.

How does the radial velocity method detect exoplanets?

In the radial velocity method, a star and its planet orbit their common centre of mass, so the star wobbles. As it moves towards Earth its light is blueshifted, and as it moves away it is redshifted. A periodic Doppler shift in its spectral lines, repeating with the planet's orbital period, reveals the planet. It works best for massive planets in close orbits.

What does a transit light curve look like?

A transit light curve shows constant baseline flux, a gradual drop during ingress as the planet moves onto the stellar disc, a flat-bottomed minimum while it is fully in front of the star, a gradual rise during egress, then a return to baseline. The depth gives the planet's size relative to the star, and the time between dips gives the orbital period.

Why does the radial velocity method only give a minimum mass?

The radial velocity method measures only the component of the star's velocity along the line of sight. If the orbital plane is tilted, the true orbital speed is larger than the measured radial velocity, so the true planet mass is larger than the calculated value. Combining it with the transit method, which constrains the inclination, gives the true mass and the mean density.

How do you estimate a planet's radius from a transit?

A planet's radius is estimated from a transit by taking the square root of the fractional dip, which gives the planet-to-star radius ratio, then multiplying by the star's radius. A dip of 0.0064 gives a ratio of √0.0064 = 0.08, so for a host star of radius 7.0 × 10⁸ m, the planet's radius is 0.08 × 7.0 × 10⁸ = 5.6 × 10⁷ m.

How do you calculate radial velocity from a Doppler shift?

Radial velocity comes from v = (Δλ/λ₀) × c. A hydrogen-alpha line with a rest wavelength of 656.3 nm observed at 656.5 nm has Δλ = 0.2 nm, so v = (0.2 ÷ 656.3) × 3.0 × 10⁸ ≈ 9.1 × 10⁴ m/s; the redshift shows the star is moving away from Earth.

What are ingress and egress in a transit?

Ingress is the part of a transit when the planet moves onto the stellar disc and the flux drops; egress is when it moves off and the flux rises again. Both slopes are gradual rather than vertical, because the planet takes a finite time to move fully onto and off the stellar disc.

How do you find the density of an exoplanet?

An exoplanet's density is found by combining both methods: the transit gives its radius and constrains the orbital inclination, which turns the radial velocity method's minimum mass into a true mass. Mass and radius together give the mean density, showing whether the planet is rocky, icy or gaseous.

Which planets are easiest to detect with the radial velocity method?

The radial velocity method is most sensitive to massive planets in close, short-period orbits. A more massive planet produces a larger stellar wobble, and a closer planet completes its orbit quickly, making the periodic Doppler signal easier to detect.

Why were Kepler and TESS put in space?

Space observatories such as Kepler and TESS were designed for the transit method because an Earth-sized planet dims a Sun-like star by only about 0.01%, far harder to detect than the roughly 1% dip from a Jupiter-sized planet, which ground-based telescopes can detect.

Why does a star wobble?

A star wobbles because it and its planet both orbit their common centre of mass. The star is vastly more massive, so its orbit is tiny, but part of that motion is towards or away from Earth, producing a periodic Doppler shift with the same period as the planet's orbit.

What does the time between transits show?

The time between successive dips in a transit light curve equals the planet's orbital period. Using Kepler's third law, that period then allows the orbital radius to be calculated, while the duration of each transit constrains the planet's orbital speed.

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