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Exoplanet Transit & Habitable Zone Lab

Investigate how astronomers detect exoplanets using the transit method. Observe how a planet crossing its star produces a measurable dip in brightness, apply Kepler's third law to find orbital periods, and calculate habitable zone boundaries for different star types.

Guided Experiment: Transit Depth and Planet Size

How does the planet-to-star radius ratio affect transit depth? Can you predict the depth before measuring it?

Write your hypothesis in the Lab Report panel, then click Next.

Transit Visualization

TimeBrightness8.39e-3%Light CurveStarPlanetOrbit View

Controls

Star Properties
Planet Properties

Transit Results

Transit detected
Transit Depth (ΔF/F)8.39e-5
Transit Depth0.0084%
Transit Duration13.09hours
Orbital Period365.25days
Impact Parameter (b)1.32e-14
Planet Radius (from depth)1R⊕
Key Equation
ΔFF=(RpR) ⁣2\frac{\Delta F}{F} = \left(\frac{R_p}{R_*}\right)^{\!2}

Data Table

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#TrialStar TypePlanet R (R⊕)Distance (AU)Transit Depth (%)Period (days)In HZ?
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Reference Guide

Transit Method

When a planet passes in front of its host star as seen from Earth, it blocks a tiny fraction of the starlight. The fractional brightness drop equals the ratio of the planet's cross-sectional area to the star's cross-sectional area.

ΔFF=(RpR) ⁣2\frac{\Delta F}{F} = \left(\frac{R_p}{R_*}\right)^{\!2}

An Earth-size planet transiting a Sun-like star produces a dip of only 0.0084%, while a Jupiter-size planet produces roughly 1%. This is why large planets orbiting small stars are easiest to detect.

Kepler's Third Law

Kepler's third law relates a planet's orbital period to its distance from the star and the star's mass. For a planet orbiting at distance a (in AU) around a star of mass M (in solar masses), the period P (in years) satisfies this relation.

P2=a3MP^2 = \frac{a^3}{M}

This means a planet at 1 AU around a Sun-mass star orbits in 1 year (365.25 days), while one at 0.05 AU completes an orbit in about 4 days.

Habitable Zone

The habitable zone (HZ) is the range of orbital distances where liquid water could exist on a planet's surface. The boundaries depend primarily on the star's luminosity.

HZinner=L1.1  AU,HZouter=L0.53  AU\mathrm{HZ_{inner}} = \sqrt{\frac{L}{1.1}} \;\text{AU}, \quad \mathrm{HZ_{outer}} = \sqrt{\frac{L}{0.53}} \;\text{AU}

For the Sun (L = 1 L☉), the HZ spans roughly 0.95 to 1.37 AU. A dim M-dwarf at 0.001 L☉ has its HZ at only 0.03 to 0.04 AU, making those planets easier to detect via transit.

Equilibrium Temperature

A planet's equilibrium temperature is the temperature it would reach if heated only by its star, with no atmosphere. It depends on the star's temperature and radius, the orbital distance, and the planet's Bond albedo (fraction of light reflected).

Teq=TR2a(1A)1/4T_{\mathrm{eq}} = T_* \sqrt{\frac{R_*}{2a}} \,(1 - A)^{1/4}

Earth's equilibrium temperature is about 255 K (−18 °C). The actual surface temperature of 288 K (15 °C) is higher because of the greenhouse effect, which this simplified formula does not include.