Exoplanet transit duration calculator

Non-positive semi-major axis values fail with invalid_input because they cannot define a physical closed orbit for this formula.

What central transit duration means and what the response contains

Transit duration is the time a planet spends in front of its star as seen by a distant observer, measured from first to fourth contact when the full stellar chord is considered under the simple geometric model. For a circular orbit with a perfectly central transit the impact parameter is zero, the planet path goes through the centre of the stellar disk, and when the planet radius is neglected relative to the star the half-chord angle reduces to arcsin of R-star over a. Multiplying that angle by the orbital period over pi recovers the full duration in the same time unit as the period. This capability takes the period in days—the unit used by most exoplanet catalogues—and multiplies the day-scale duration by twenty-four so the primary field duration_hours matches how observers quote hot-Jupiter and super-Earth events. The response echoes the cleaned inputs period, stellar_radius, and semi_major_axis, reports radius_over_a for quick sanity checks, and includes duration_days and duration_minutes for worksheets that prefer those units. A small_angle_hours field shows the linear approximation obtained by replacing arcsin of x with x itself, which is accurate when the star is much smaller than the orbital separation. Method and formula strings document that the path is central_transit with circular_orbit_b0_rp_neglected so clients do not confuse this estimate with a full Mandel–Agol light-curve fit. There is no network lookup of stellar catalogues and no Monte Carlo draw of impact parameters: either the three numbers define a valid central transit and the engine returns deterministic floats, or the request fails with invalid_input naming the geometric or positivity rule that failed.

Input contract, units, and error behaviour

Solar radii for both R-star and a are common when you convert a from astronomical units using the solar radius in AU; metres work equally well if both fields are SI. POST a JSON body with three required finite numbers: period, the orbital period in days and strictly greater than zero; stellar_radius, the host-star radius in any length unit you choose; and semi_major_axis, the orbital semi-major axis in that same length unit. Each field may arrive as a JSON number or as a numeric string; missing fields, empty strings, NaN, and Infinity fail with invalid_input. The product rule that callers must remember is that semi_major_axis must be positive: zero and negative values are rejected with a clear message that a non-positive semi-major axis is non-physical for a closed transit geometry, and those failures are not billed. Period and stellar_radius must also be positive. Example: period equals three point five days, stellar_radius equals one, and semi_major_axis equals ten yields radius_over_a equals zero point one and a duration of roughly two point six eight hours, with the small-angle reference slightly shorter as expected. Pair the response with your own inclination or planet-radius corrections if your science case needs them; this endpoint answers only the central, circular, Rp-neglected rewrite.