Lesson 1 of 6 · estimating size and mass
Turn signals into a planet’s size and mass
10 minute lesson · 3 checks along the way
Your goal for this lessonCombine transit and dynamical measurements while keeping stellar properties, inclination and model assumptions visible.
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A discovery signal is not every physical property
A confirmed planet can still have a poorly measured size or mass. A transit records a change in the combined light reaching a detector. Radial-velocity observations track the star’s motion along our line of sight. Converting either signal into a planetary property requires a model and information about the host star. The result is not a scale reading taken beside the distant world.
Kepler measured repeated brightness changes, while follow-up observations helped characterize its target stars. Gaia’s distances can improve stellar luminosity estimates; together with temperatures and stellar models, these constrain stellar radii. An improved star measurement can therefore revise a planet’s inferred radius even when the transit itself has not changed. The archive should preserve both the numerical result and the analysis from which it came.
Kepler’s April 8, 2009 first-light exposure records its full focal plane over 60 seconds. The display assigns red to fainter stars and white to brighter ones; those colors do not measure planetary composition. Repeated measurements of selected stars, rather than one frame, supplied transit light curves.
Look closely
Find a bright stellar point and the detector gaps. Why is neither its displayed dot size nor one exposure enough to measure a transiting planet’s physical radius?
See what to notice
A point’s recorded shape reflects optics, sampling and signal strength, rather than a resolved planetary disk. Repeated photometry supplies a transit depth, and a model plus the host-star radius converts its fitted radius ratio into a physical scale.
Check 1 of 3
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Work through a decision
A transit compares projected areas
For an opaque planet completely crossing a uniformly bright stellar disk, with no and negligible light from the planet, the fractional depth is approximately the squared ratio of planet radius to star radius. A one-percent dip corresponds to a of one tenth, not one hundredth. Real fitting accounts for the star’s darker limb, the path across its disk, exposure timing, and light blended from nearby objects.
Consider an invented host star with radius 100 Earth radii and a clean, non- depth of 0.0025, or 0.25 percent. Taking the square root gives a radius ratio of 0.05. The inferred planet radius is therefore five Earth radii. If revised stellar analysis changes the host radius to 110 Earth radii while the fitted ratio stays fixed, the planet becomes 5.5 Earth radii.
Motion constrains mass through gravity
A star and planet move around their shared center of mass. An orbital fit uses the stellar velocity variation, period, , and stellar mass to constrain the companion. In the usual approximation that the planet is much lighter than its star, alone generally supplies planet mass multiplied by the sine of orbital inclination. Inclination here is zero for a face-on orbit and ninety degrees for an edge-on orbit.
If that fitted product is eight Earth masses, an independently established sine of inclination of 0.5 gives sixteen Earth masses. An edge-on orbit would instead give eight. A transiting system constrains inclination close to edge-on, but its geometry should still be fitted. Interactions between multiple planets can also perturb transit times, supplying information rather than another direct measurement of blocked area.
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Keep the inference attached to its evidence
Uncertainty in stellar properties can affect several planets in the same system together. Treating those radius errors as entirely independent may exaggerate how different two planets appear. Stellar activity can also shift spectral lines or change brightness. Agreement among repeated transits, velocities, and a consistent stellar analysis is more informative than one small formal error bar from a model with an untested assumption.
Before comparing catalog entries, check whether a mass is measured dynamically, reported as a minimum, or estimated from a population relation. Check whether radii share the same host-star solution and whether uncertainties are limits or symmetric errors. These distinctions determine which later calculations are justified. A compelling planet portrait starts with measured signals, followed by explicit geometry and assumptions, and ends with properties whose limitations remain traceable.
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Put it together
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