🪐Exoplanet Detection Simulator - Transit Light Curves, Radial Velocity, Habitable Zone

How to use Exoplanet Detection Simulator

1. 1On the transit tab, pick a preset (Earth, hot Jupiter HD 209458 b, TRAPPIST-1e, Kepler-186f) or set the star and planet
2. 2Press Play to watch the planet cross the star with a cursor on the light curve; change the noise, cadence and number of transits to see if SNR passes 7.1
3. 3On the radial velocity tab, change mass, period, eccentricity and inclination to see K, the RV curve and the exaggerated line shift
4. 4On the habitable zone tab, choose a star or set its temperature and luminosity to see the zone edges and planet temperatures

FAQ

What does the transit method measure?

The depth is roughly (Rp/R*)², so a known stellar radius gives the planet's radius: Earth dims the Sun by only about 84 ppm, a hot Jupiter by 1–2%. The time between transits is the period, and Kepler's third law then gives the orbital distance; the duration and ingress shape give the inclination and impact parameter. The orbit must be almost edge-on for a transit, which happens with probability about R*/a: only 0.47% for an Earth–Sun system.

What is limb darkening, and why is the bottom of the dip curved?

A star's disc is brighter at the centre than at the edge, because near the limb we see cooler, higher layers. A common description is the quadratic law I(μ) = 1 − u₁(1 − μ) − u₂(1 − μ)², where μ is the cosine of the angle between the line of sight and the surface normal. At mid-transit the planet blocks the brightest part, so the dip is a little deeper than (Rp/R*)² and gets shallower towards the limb, giving a rounded bottom. The tool integrates numerically over every stellar annulus the planet covers.

Why does radial velocity only give m sin i?

Doppler shifts only reveal the star's velocity along our line of sight. In the semi-amplitude K = (2πG/P)^⅓ · m sin i / (M* + m)^⅔ / √(1 − e²), the planet mass and inclination always appear together as m sin i, so the same curve could come from an ordinary planet at i = 90° or a much heavier body seen nearly face-on. Jupiter moves the Sun at about 12.5 m/s, Earth only about 0.09 m/s, which is why Earth twins are so hard to find this way.

How is the habitable zone defined?

It is the range of orbital distances where a planet could keep liquid water on its surface. Kopparapu et al. (2013) used 1-D climate models: the inner edge is the runaway greenhouse (oceans boil away) and the outer edge the maximum greenhouse (more CO₂ no longer helps). The effective stellar flux at each edge, S_eff, is a polynomial in stellar temperature, and the distance is d = √(L/S_eff). For the Sun the conservative zone is about 0.98–1.69 AU, the optimistic one (recent Venus to early Mars) about 0.75–1.77 AU.

Why is the equilibrium temperature different from the real surface temperature?

Equilibrium temperature balances absorbed starlight against thermal emission, T_eq = [L(1 − A)/(16πσa²)]^¼, with no greenhouse effect. Earth's is about 255 K (−18 °C) while its mean surface temperature is about 15 °C; the 33 °C difference is the atmosphere's greenhouse effect, and on Venus the gap is over 400 °C. So it is a way to compare how much energy planets receive, not a verdict on habitability.