How can we find a planet around another star?

A planet can reveal itself without appearing as a separate dot in a photograph. If its orbit carries it across the face of its star from our viewpoint, it blocks a little starlight. Astronomers measure that temporary dimming, test whether it repeats, and ask whether a planet is the best explanation. The key evidence is a changing measurement, not an artist’s picture of a distant world.

Predict first. Two dark planets cross the same star along the same central path. One has twice the other’s radius. Will its deepest dip be twice as large or four times as large?

A transit changes the measured light

A transit happens when one object passes in front of another from the observer’s direction. For an exoplanet—a planet outside our Solar System—the background object is its host star. A telescope usually measures the combined, unresolved light of the system. The planet can be far too faint to photograph separately while its effect on the total light is measurable.

Plot the received light against time and you have a light curve. Before a transit, the star sets a baseline. During the crossing, less light reaches us. After the planet leaves the stellar disk, the measurement returns toward the baseline. Repeated, similarly spaced dips can reveal an orbital period. NASA n.d., “How We Find and Characterize,” § Transits: Planets Found in Dips in Light

Part of a transit	Geometry	Expected light in a simple model
Before entry	Planet misses the visible stellar disk	Baseline
Ingress	More of the planet overlaps the disk	Decreasing
Fully inside the disk	Its full silhouette blocks the star	Below baseline
Egress	The overlapping area becomes smaller	Increasing
After exit	No overlap	Baseline again

Explore the linked transit laboratory. It puts the model geometry beside the changing light curve and distinguishes simulated predictions from measured data. Change one quantity at a time; predict the result before moving a control.

The blocked area gives a size clue

Start with a deliberately simple star: a flat-looking disk with uniform brightness. Give the planet an opaque circular silhouette. When the entire silhouette is inside the star’s disk, the fraction of starlight blocked is the ratio of their projected areas.

Doubling the planet’s radius multiplies its area by four. So the answer to the opening prediction is four times the depth, under these assumptions. It is a size measurement relative to the star. To infer kilometres, we also need an estimate of the star’s radius.

Planet radius divided by star radius	Full-overlap depth for a uniform star	Remaining relative light
0.1	1%	0.99
0.2	4%	0.96

Show the math: from depth to radius ratio

Let $R_p$ and $R_\star$ be the planet’s and star’s radii. Normalize the unobscured stellar flux to 1. For a fully overlapping, opaque planet smaller than a uniformly bright star, the transit depth is

$$\delta=\frac{\pi R_p^2}{\pi R_\star^2} =\left(\frac{R_p}{R_\star}\right)^2.$$

A radius ratio of 0.1 gives a depth of 0.01: a 1% drop to relative flux 0.99. A ratio of 0.2 gives a 4% drop to 0.96. Conversely, $R_p/R_\star=\sqrt{\delta}$.

This simple result is the full-overlap part of the uniform-source transit model. During partial overlap, use the actual overlapping area of two disks. A grazing crossing never reaches the full area assumed above. Mandel and Agol 2002, § 2, “Uniform Source”

Real stars usually look dimmer near their edges, an effect called limb darkening. The path across the star, light from neighbouring stars, measurement noise, and the duration of each exposure all affect the observed curve. A real analysis fits an appropriate model and reports uncertainties; the simple area rule explains the main size dependence.

A dip is a candidate, not the whole case

An eclipsing pair of stars can produce dips too. If its light blends with a brighter nearby star, the eclipse can look deceptively shallow. Instrument effects and stellar variability can also complicate a light curve. Comparing alternating dips, checking where the changing light originates, and obtaining further observations help distinguish these possibilities. The Kepler tables explicitly track several such false-positive diagnostics. NASA Exoplanet Archive 2012, table definitions, §§ 1, 5–6: disposition and vetting statistics

Another method measures a star’s motion toward and away from us using shifts in its spectral lines. A star and its planet orbit their shared centre of mass, so the star can show a repeating radial-velocity signal. Transits primarily constrain relative size; radial velocities constrain mass through an orbital model, with the orbit’s tilt also relevant. Combining methods can give stronger information than either alone. NASA n.d., “How We Find and Characterize,” § Radial Velocity: Reading the Wobble See how several shifted spectral lines measure a speed, then explore shared-centre motion in the binary-star laboratory.

Neither a transit nor a mass estimate, by itself, shows that a planet has life.

Try an orbit we see from above

A star’s light curve shows no transits. Can we conclude that it has no planets?

Answer

No. A planet whose orbital plane is viewed nearly face-on circles around the star in our view without crossing its disk. A small planet’s signal could also fall below the measurement sensitivity, or its transit could happen outside the observing window. A nondetection becomes useful only when we say which sizes, orbits, alignments, and observing times the search could have tested.

For classrooms and clubs

Preparation: ratios and the table above; familiarity with circle areas helps with the optional calculation. Objective: connect a light-curve feature to geometry and state one alternative explanation. In 20 minutes, compare radius ratios 0.1 and 0.2, then central and grazing crossings. The full-overlap depths are 1% and 4%; a grazing crossing blocks less area than the same planet fully inside the disk. The numerical table and written answers support an activity without interaction.

For a longer extension, compare equal 1% dips around stars of radius $R$ and $2R$, keeping the uniform-star, full-overlap assumptions. The inferred planets have radii $0.1R$ and $0.2R$: a depth gives a relative size, not kilometres by itself. Then name an alternative to a planet, such as a blended eclipsing binary, and a useful follow-up observation. The common misconception is that every repeating dip proves a planet; agreement with one feature is insufficient to eliminate competing explanations.

Next, learn how to read a star’s spectrum, then ask what would count as evidence of life.

References

• Mandel, Kaisey, and Eric Agol. “Analytic Light Curves for Planetary Transit Searches.” The Astrophysical Journal Letters 580 (2002), L171–L175. DOI: 10.1086/345520. Open PDF.
• NASA Exoplanet Archive. “Threshold-Crossing-Event and Kepler-Object-of-Interest Table Definitions.” Version 1.0, delivered by the Kepler Project December 7, 2012. Caltech/IPAC. Column definitions and vetting statistics.
• NASA Science. “How We Find and Characterize.” NASA, n.d. Exoplanet detection methods. Accessed September 27, 2026.