PSLE Science Reality Lab Vol No.311 | “Transit Depth = 1%” — Is the Planet 1% as Wide as Its Star?

Series ID: PSLE-SCI-REALITY-0311

Wait, What? The Star Dims by 1% — So Is the Planet 1% as Wide?

A discovery graphic shows a star’s brightness falling from 100% to 99% while a planet passes in front of it. The caption says transit depth: 1%. A learner looks at the number and makes a neat-sounding conclusion: “The planet must be 1% as wide as the star.”

The observation is real. The conclusion is not. A transit-depth percentage describes how much of the measured starlight disappeared during the transit. Under a simple geometric model, the blocked fraction is linked mainly to the area of the planet compared with the visible area of the star. Width and area do not scale in the same way. A planet that blocks about 1% of a uniformly bright stellar disk has a radius roughly one-tenth of the star’s radius, not one-hundredth.

Reality Lab habit: when a percentage is produced by an area, do not silently turn it into the same percentage of a length.

Quick Answer

Transit depth is the fractional decrease in measured starlight during a transit.
It is not directly the percentage of the star’s diameter occupied by the planet.
In a simplified case, transit depth is approximately the planet-to-star area ratio, so the radius ratio is related to the square root of the depth.
A 1% depth therefore suggests a planet radius near 10% of the stellar radius under the simple model.
The real inference can be affected by the star’s brightness pattern, a grazing transit, extra light from another star, starspots, instrument effects and the accuracy of the stellar radius.
Repeated transits and an appropriate light-curve model strengthen the inference.
The transit can support a size estimate without proving the planet’s mass, composition, atmosphere, habitability or surface appearance.

The Exact Learner Job This Volume Owns

This volume owns one narrow real-world evidence-transfer job: how to evaluate an exoplanet light curve, catalogue entry or science-news graphic that reports transit depth as a percentage without mistaking that percentage for the planet’s diameter as a percentage of the star’s diameter.

It does not take over graph reading, ratio mathematics, models, measurement uncertainty, astronomy, stellar physics or the broader transit method. Those jobs remain with their existing owners. Here we apply them to one communication object: the small dip in starlight from which a surprisingly large amount of information can be inferred.

Rebuild the Evidence Object: A 1% Dip

Imagine an original composite observation. A telescope measures the same star repeatedly before, during and after a predicted transit.

Stage	Relative brightness	What it means
Before transit	100.0%	Reference brightness for this observation
Middle of transit	99.0%	About 1% less measured light
After transit	100.0%	Brightness returns near the reference

The direct evidence is a brightness change. The planet-size estimate comes later, through a model connecting the blocked light to the fraction of the stellar disk hidden by the planet.

Observed, Calculated, Inferred and Claimed

Observed: detector measurements show a repeatable decrease in light at the expected time.
Calculated: the light curve gives a transit depth near 1% relative to the chosen out-of-transit baseline.
Inferred: under a suitable transit model, the planet-to-star radius ratio can be estimated.
Combined inference: if the star’s radius is known, an absolute planetary radius can be estimated.
Unsupported leap: “1% depth means the planet is 1% as wide as the star.”
Unsupported leap: “The 1% dip proves the planet is Earth-like.”
Unsupported leap: “The artist’s illustration shows what the planet really looks like.”

Why Area Changes Faster Than Width

Draw a square that is 10 cm by 10 cm. Its area is 100 cm². Now place a 1 cm by 1 cm square on top. The small square is only one-tenth as wide, but it covers one-hundredth of the large square’s area: 1%.

A circular planet crossing a circular star is not literally two squares, but the same geometry is useful. Area depends on the square of a radius. That is why a 1% blocked-area fraction corresponds, in the simple case, to a radius ratio near 0.1 rather than 0.01.

The Primary Science lesson is not “memorise a square-root formula”. It is more valuable: identify what the percentage belongs to before transferring it to another dimension.

The Star Matters Too

A transit does not give the planet’s kilometres directly. First it helps estimate the planet’s size relative to its star. If the star is larger than scientists first thought, the planet can also be larger than first estimated. If the stellar radius is revised, the planetary radius may be revised even though the transit depth itself has not changed.

This is a powerful evidence-chain lesson. One measured object can depend on a second measured or modelled object. A neat planet-size number therefore carries provenance from both the transit and the star.

Representation Check: A Light Curve Is Not a Photograph of the Planet

NASA explains that transiting planets are often detected because they cause tiny dips in a star’s measured brightness. The familiar U-shaped graph is a representation of brightness through time. It is not a silhouette photograph with the planet’s diameter drawn to scale.

A science-news page may place an artist’s concept beside the light curve. Keep the two evidence objects separate. The graph can be observational evidence. The illustration can be a useful visual model. The illustration does not add oceans, clouds or colours to the measurements.

Baseline Check: What Does “1% Less” Mean?

A percentage decrease needs a reference. Transit depth normally compares in-transit brightness with an out-of-transit baseline after the data have been processed appropriately. A learner should ask whether the baseline is stable and whether changing stellar brightness or instrument behaviour has been accounted for.

If a star naturally varies by a similar amount, one isolated dip is weaker evidence than a dip that repeats at a consistent interval with the expected shape. Repetition does not make every alternative impossible, but it strengthens a patterned explanation.

Method Check: Why a Perfect Little Circle Is an Approximation

The simplest classroom model imagines a dark circular planet crossing a uniformly bright circular star. Real transit analysis is more complicated. Stars are not perfectly uniform disks. Their edges can appear dimmer than their centres. A planet may cross near the edge rather than straight through the middle. Another unresolved star may add extra light. Spots on the star can change brightness locally.

These details do not make the transit method unreliable. They explain why scientists fit models to the full light curve instead of treating one percentage as a ruler pressed directly against the planet.

Worked Case 1: 1% Light Lost, 1% Width?

A student reads “transit depth = 1%” and writes: “The planet’s diameter is 1% of the star’s diameter.”

Repair: the 1% refers to the brightness decrease and, in the simple model, roughly the blocked area fraction. Because area depends on radius squared, the corresponding radius ratio is about 10%, not 1%.

Worked Case 2: Two Planets With the Same 1% Transit Depth

Planet P transits a smaller star. Planet Q transits a larger star. Both produce a depth near 1%. A learner claims they must have the same radius.

Repair: the similar depth supports a similar planet-to-star size ratio under comparable geometry. If the stars differ in radius, the planets’ absolute radii can differ too.

Worked Case 3: Hidden Extra Starlight

A telescope cannot separate two close stars. Only one is being transited, but both contribute light to the measurement. The combined system dims by 1%.

Repair: extra light can dilute the observed dip. NASA has highlighted this problem in real exoplanet work: if an unresolved companion contributes light, the planet can be larger than a simple single-star interpretation suggests. The correct response is not to guess a correction but to include the additional star in the model.

Worked Case 4: One Dip Versus Repeated Dips

Signal A shows one 1% dip. Signal B shows four similar 1% dips separated by the same time interval.

Repair: repeated, regularly timed dips generally provide stronger evidence for a periodic transit interpretation than one isolated dip. Yet alternative explanations and instrumental checks still matter. The evidence status comes from the whole pattern and validation process, not the size of the percentage alone.

Worked Case 5: A Deeper Transit Means a Bigger Planet — Always?

Two planets orbit different stars. Planet A gives a 2% transit depth and Planet B gives 1%. A post declares A must be physically larger.

Repair: not from depth alone. The host stars may have different radii, and the transit geometry or dilution may differ. Compare the full model and stellar sizes before ranking absolute planet radius.

Worked Case 6: The Dip Is Deeper in One Colour

Webb measures slightly different transit depths at different wavelengths. A learner says, “The solid planet changes size with colour.”

Repair: an atmosphere can absorb particular wavelengths, making the planet-plus-atmosphere block a slightly different effective fraction of starlight at different wavelengths. The evidence can reveal atmospheric information without the solid body physically expanding and shrinking during the same transit.

What Evidence Strengthens the Size Inference?

Several consistent transits rather than one unexplained dip.
A stable and well-characterised out-of-transit baseline.
A well-measured stellar radius.
Checks for nearby or unresolved stars that add light.
A light-curve model that accounts for transit geometry and the star’s brightness profile.
Independent observations with another instrument or observing season.
A reported uncertainty rather than an unrealistically exact size.

What Would Weaken an Overconfident Claim?

The percentage is treated as a diameter percentage with no geometric reasoning.
The stellar radius is poorly known.
Only one event was observed.
A nearby star contributes unknown extra light.
The transit is grazing and the geometry is uncertain.
The star itself is variable at a similar scale.
A colourful illustration is used as though it were additional measured evidence.

Tempting Reasoning That Fails

Tempting thought	Why it fails
1% light = 1% width	The simple relationship is with blocked area, not directly with length.
Same depth = same planet size	The host-star sizes can differ.
Deeper dip = definitely larger planet	Star size, dilution and geometry also matter.
One dip = confirmed planet	Repeated evidence and alternative explanations must be checked.
Artist image = observed surface	An illustration is a representation, not direct surface imagery.

How Far Can the Conclusion Travel?

Suppose repeated observations show a clean transit depth near 1%, the host star is well characterised, and a suitable model supports a planet-to-star radius ratio near 0.1. A bounded conclusion is:

The transit blocks about 1% of the measured starlight, and the fitted transit model supports a planetary radius near one-tenth of the stellar radius under the stated assumptions and uncertainty.

The same evidence does not by itself establish the planet’s mass, density, surface, atmospheric composition, habitability or presence of life.

PSLE-Style Transfer Case: The Two Circular Cards

This is an original transfer problem, not an examination question. A large circular card has radius 10 cm. A smaller circular card has radius 1 cm. The small card is placed over the centre of the large one. A pupil says, “The small card is 10% as wide, so it covers 10% of the large circle.”

A strong response explains that area depends on radius squared. The small circle has 1/100 of the large circle’s area, so it covers about 1%, not 10%. The same geometry helps explain why a 1% transit depth can correspond to a planet radius around 10% of its star’s radius in the simple model.

Delayed Independent Return: Percent of What Dimension?

Length: a one-dimensional comparison.
Area: a two-dimensional comparison.
Volume: a three-dimensional comparison.
Brightness: a measured signal that may be linked to geometry through a model.

Return later to any percentage involving size and ask which dimension produced it. This single question prevents many confident mistakes.

Explained Practice

A transit depth is 4%. Is the planet 4% as wide as the star? No. Under the simple area model, a 4% blocked fraction corresponds to a radius ratio near 20%, before other effects are considered.
Two systems have equal transit depth. Are the planets equal in kilometres? Not necessarily. The host stars may differ in size.
Why can a hidden companion star matter? Its extra light can dilute the observed dip and change the inferred radius.
Why repeat a transit? Repetition tests whether the signal occurs consistently with a periodic orbit and helps separate the proposed pattern from noise or alternatives.
What does the transit most directly measure? A change in received starlight through time; planetary size is inferred by fitting the measurement with an appropriate model.

Routes to Existing Canonical PSLE Science Owners

For the core distinction between evidence and interpretation, use How to Tell Observation, Inference, Prediction and Explanation Apart in PSLE Science. For checking whether data sets really measure comparable outcomes, use How to Tell Whether Two PSLE Science Data Sets Measured the Same Outcome in Comparable Ways. For the separate headline problem of turning one planetary property into many, use Reality Lab Vol No.219 — “Earth-Sized Exoplanet”.

Parent and Tutor Teaching Guide: Cover the Board, Then Change the Shape

Start with two square cards because the geometry is visible. Use a 10 cm square and a 1 cm square. Ask for width ratio first, then area ratio. Do not introduce astronomy until the learner can explain why 10% of the width becomes 1% of the area.

Next draw a simple light curve with a 1% dip. Ask four questions in order: What was directly measured? What percentage was calculated? What model connects the percentage to size? What extra information is needed for kilometres? Reward the learner for preserving those stages instead of jumping straight to the planet.

Finally change the problem. Give two stars of different sizes with identical 1% dips. If the learner now refuses to declare the two planets equal in kilometres without the star radii, the reasoning has transferred.

Why This Belongs in PSLE Science Reasoning

The current 2026 PSLE Science assessment objectives include interpreting and analysing information, evaluating observations, information and methods, and communicating explanations and reasoning. The 2023 Primary Science syllabus also develops healthy scepticism, attention to assumptions and uncertainty, and evidence-based model building. A transit light curve makes those habits concrete: the graph is real evidence, the size is a model-supported inference, and the final claim must stay within what the evidence chain can carry.

Authoritative Sources

The Quiet Return

The star dimmed by 1%. That is already remarkable evidence.

Do not make it less scientific by forcing the same 1% onto a different dimension. Ask what the percentage measured, follow the geometry, keep the model visible, and let the conclusion grow only as far as the evidence allows.

Small Group Tutorials