Transit Timing Calculator
Free Transit timing Calculator for astronomy. Enter variables to compute results with formulas and detailed steps. Enter your values for instant results.
Formula
T14 = (P/pi) arcsin(sqrt((Rs+Rp)^2 - b^2 Rs^2) / (a sin i))
Where T14 = total transit duration, P = orbital period, Rs = stellar radius, Rp = planet radius, b = impact parameter = a cos(i)/Rs, a = semi-major axis, i = orbital inclination. Transit depth = (Rp/Rs)^2.
Worked Examples
Example 1: Hot Jupiter Transit (HD 209458 b)
Problem: Calculate transit timing for a hot Jupiter with P = 3.524 days, Rs = 1.16 solar radii, Rp = 1.38 Jupiter radii, a = 0.0475 AU, i = 86.71 degrees.
Solution: Rs = 1.16 * 6.957e8 = 8.07e8 m\nRp = 1.38 * 7.149e7 = 9.87e7 m\na = 0.0475 * 1.496e11 = 7.106e9 m\nb = (7.106e9 * cos(86.71)) / 8.07e8 = 0.505\nT14 = (3.524*24/pi) * arcsin(sqrt((8.07e8+9.87e7)^2 - (0.505*8.07e8)^2) / (7.106e9*sin(86.71)))\nT14 = 26.93 * arcsin(0.1089) = 26.93 * 0.1096 = 2.95 hours\nDepth = (9.87e7/8.07e8)^2 = 0.01495 = 1.495%
Result: Transit duration: ~3.0 hours | Depth: ~1.5% (14,950 ppm) | Impact parameter: 0.505
Example 2: Earth-like Planet Transit
Problem: Calculate transit parameters for an Earth-like planet: P = 365.25 days, Rs = 1.0 solar radii, Rp = 0.0892 Jupiter radii (1 Earth radius), a = 1.0 AU, i = 89.99 degrees.
Solution: Rs = 6.957e8 m, Rp = 6.371e6 m, a = 1.496e11 m\nb = (1.496e11 * cos(89.99)) / 6.957e8 = 0.0375\nDepth = (6.371e6/6.957e8)^2 = 8.39e-5 = 0.00839% = 83.9 ppm\nT14 = (365.25*24/pi) * arcsin(sqrt((6.957e8+6.371e6)^2 - (0.0375*6.957e8)^2) / (1.496e11*sin(89.99)))\nT14 approximately 13.1 hours\nTransit probability = Rs/a = 6.957e8/1.496e11 = 0.465%
Result: Transit duration: ~13.1 hours | Depth: ~84 ppm | Transit probability: 0.47%
Frequently Asked Questions
What is an exoplanet transit and how is it detected?
An exoplanet transit occurs when a planet passes directly between its host star and the observer, causing a small, periodic dip in the observed brightness of the star. This is the most prolific method for discovering exoplanets, responsible for the vast majority of confirmed planets found by missions like Kepler and TESS. The depth of the brightness dip reveals the planet size relative to its star, while the period between consecutive transits gives the orbital period. The transit method works best for large planets on short-period orbits around small stars, where the fractional brightness decrease is greatest and transits occur frequently enough to confirm the signal.
How is transit duration calculated?
Transit duration depends on the orbital period, the stellar radius, the planet radius, the semi-major axis, and the orbital inclination. The total transit duration T14 (from first to fourth contact) is given by T14 = (P/pi) * arcsin(sqrt((Rs+Rp)^2 - b^2*Rs^2) / (a*sin(i))), where P is the orbital period, Rs is stellar radius, Rp is planet radius, a is the semi-major axis, i is the inclination, and b is the impact parameter. For eccentric orbits, this is multiplied by sqrt(1-e^2). Typical hot Jupiter transits last 2-3 hours, while Earth-like planets around Sun-like stars transit for about 13 hours.
What is the impact parameter in transit observations?
The impact parameter b describes how centrally the planet crosses the stellar disk, defined as b = (a*cos(i))/Rs, where a is the semi-major axis, i is the orbital inclination, and Rs is the stellar radius. When b = 0, the planet crosses the exact center of the star (an equatorial transit), producing the longest possible transit duration and a symmetric, flat-bottomed light curve. When b approaches 1, the planet grazes the edge of the star, producing a shorter, V-shaped transit. For b greater than 1+Rp/Rs, no transit occurs at all. The impact parameter is a key observable that helps constrain the orbital inclination independently of other measurements.
What is transit depth and what does it reveal?
Transit depth is the fractional decrease in stellar brightness during a transit, equal to the square of the planet-to-star radius ratio: delta = (Rp/Rs)^2. For a Jupiter-sized planet transiting a Sun-sized star, the depth is about 1% (10,000 ppm). For an Earth-sized planet around a Sun-like star, it is only 0.008% (84 ppm), which is extremely challenging to detect from the ground. The transit depth directly measures the planet size relative to the star, making it one of the most fundamental observables in exoplanet science. When combined with radial velocity mass measurements, the planet density and bulk composition can be determined.
What are Transit Timing Variations (TTVs)?
Transit Timing Variations (TTVs) are deviations from strictly periodic transit times, caused by gravitational interactions between planets in a multi-planet system. If a transiting planet has a companion planet, the gravitational tug causes the transiting planet to arrive slightly early or late for its transits, with variations typically ranging from seconds to tens of minutes. TTVs are particularly large near mean motion resonances, where orbital periods are related by small integer ratios like 2:1 or 3:2. This technique has been used to confirm and characterize hundreds of exoplanets, including measuring planet masses without radial velocity data, and even discovering non-transiting planets through their gravitational influence.
What is the geometric probability of observing a transit?
The geometric transit probability is approximately Rs/a, where Rs is the stellar radius and a is the semi-major axis of the planet orbit. This represents the fraction of randomly oriented orbital planes that would produce observable transits from our perspective. For a hot Jupiter at 0.05 AU around a Sun-like star, the probability is about 10%, which is relatively high. For an Earth-like planet at 1 AU, the probability drops to only about 0.5%. This means that for every transiting Earth analog discovered, roughly 200 similar planets exist in non-transiting geometries. Transit surveys must therefore monitor tens of thousands of stars to discover a significant number of planets at various orbital distances.