Transit Probability Calculator

Not every planet transits its star from Earth’s perspective. Whether a transit happens at all is pure geometry. The orbital plane has to be close to edge-on from where we are standing, and for most systems it simply is not.

Transit probability formula:

p ≈ R_star / a

More precisely, including the planet’s radius:

p = (R_star + R_planet) / a

Where a is the orbital semi-major axis, all in the same units.

Why this formula? For a randomly oriented orbit, the probability that the inclination brings the planet across the star’s disk is proportional to the ratio of the star’s (and planet’s) apparent size to the orbit size.

Real-world transit probabilities:

Why close-in planets are detected more:

• Higher transit probability (shorter orbit = more likely to transit)
• More transits per year = more opportunities to detect and confirm
• Deeper transit signal (hot Jupiters block more light)

Survey strategy: TESS focuses on nearby stars because they are brighter, making small transits (from Earth-sized planets) easier to detect. Kepler stared at one patch of sky to detect long-period planets with low transit probability.

The detection bias: Most known exoplanets are hot Jupiters (large, close-in) not because they are common, but because they are the easiest to detect by transit. Surveys must apply careful statistical corrections.