Lesson 1 of 6 · Transit signals
Transit signals
10 minute lesson · 3 checks along the way
Your goal for this lessonInfer a radius ratio and a repeating interval from a light curve while keeping the geometric and stellar assumptions visible.
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A changing point of light
For most distant planetary systems, a telescope cannot separate the planet from its star in an ordinary image. It can still measure their combined brightness repeatedly. A plots that measurement against time. If an orbit carries an opaque planet across the visible face of its star, the planet blocks some starlight and produces a . The system does not have to disappear for the event to be measurable.
Kepler and the Transiting Exoplanet Survey Satellite use this approach. The relevant observation is a timed series, not one dark spot in a photograph. Scientists correct detector and pointing effects, compare the signal with stellar variability, and retain information about measurement uncertainty. A repeated depression is a candidate orbital signal. Dust, another star, or an instrumental effect can also dim a measured source, so repetition alone does not establish a planet.
Kepler recorded this 60-second first-light exposure across its full focal plane before science operations. The dark rectangular gaps belong to the detector layout; the image is one exposure, not a transit light curve.
Look closely
What additional evidence would turn one of these stellar points into a transit candidate?
See what to notice
Repeated calibrated measurements of the same source are needed to establish a timed brightness change. A dark detector gap or one faint star in this exposure does not show a planet passing in front of a star.
A depth measures an area ratio
Start with an ideal model: a uniformly bright stellar disk, an opaque planet entirely inside that disk at mid-transit, negligible planet light, and no contaminating neighboring light. The fractional depth is δ = (Rp/Rstar)². The squared radius appears because blocked area and stellar area both scale with radius squared. A one-percent loss therefore corresponds to a of 0.10, rather than 0.01.
Real stars have : the disk edge is generally dimmer than its center in the relevant optical bands. A grazing passage blocks only part of the planet’s projected disk, and nearby unresolved stars can dilute the signal. A fitted transit model accounts for such effects. Even an excellent radius ratio does not supply an absolute planetary radius unless the stellar radius is constrained independently. The star is part of the measuring ruler.
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Work through a decision
Read a fictional observing log
Suppose a controlled example has an out-of-transit signal of 10,000 counts per exposure and a full-transit signal of 9,900 counts with the same exposure time. Ignore noise and background for this exercise. The missing fraction is (10,000 − 9,900)/10,000 = 0.01. Under the ideal assumptions, Rp/Rstar = √0.01 = 0.10. For an adopted stellar radius of 700,000 kilometers, the inferred planetary radius is 70,000 kilometers.
Transit centers occur on days 2, 12, and 22. If they are consecutive passages of the same object, the is 10 days. A two-hour would describe the crossing, not the full orbit. If the stellar radius were revised upward by ten percent while the fitted radius ratio stayed fixed, the planetary radius would also rise ten percent, to 77,000 kilometers. A better light curve cannot remove uncertainty in a separately supplied stellar size.
Depth and radius
Original instructional diagram. The vertical flux scale is quantitative; the crossing shape and horizontal time scale are schematic. A 1% depth gives a 10% radius ratio only for the uniform, uncontaminated, full-transit model.
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Use the whole shape and observing window
The entry, bottom, and exit of a transit provide more information than its deepest point. Their shapes help constrain the path across the star, although several parameters can remain correlated. Timing several transits improves predictions of future events. Missing observations matter: two observed dips need not be consecutive if the telescope was not watching when intervening passages could have occurred.
A careful report separates directly measured flux and timestamps from fitted geometry and inferred physical size. It also states what the data leave unresolved. This lesson’s model establishes a radius ratio, not a planetary mass, surface temperature, or inhabited environment. Later lessons will add velocity measurements and tests of alternative explanations. That sequence turns a small brightness change into a defensible physical interpretation rather than a label attached to a dip.
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Put it together
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