Transit timing variations, or TTVs, are departures of measured transit midpoints from a constant-period schedule. Gravitational interactions between planets can produce them, allowing astronomers to constrain planetary masses and sometimes infer a companion that does not transit. A late transit alone is not a planet discovery.
Build the reference clock first
For transit number E, a linear ephemeris predicts Tcalc = T0 + E P. Subtract that value from each observed midpoint. Positive O − C means late relative to the chosen schedule; negative means early.
For an illustrative ten-day period, transit E = 3 is expected 30 days after T0. An observed midpoint 30.002 days after T0 is late by 0.002 day, or 2.88 minutes. The significance depends on the timing uncertainty, not on the number of digits written down.
A constant offset adjusts T0. A straight residual slope usually adjusts P. Structure remaining after those corrections is more informative. Reference-period uncertainty is shared between predictions and should not be treated as independent random noise at every event.
Why neighboring planets shift the schedule
Each planet perturbs the others’ motion. Near a mean-motion resonance, the configuration changes slowly enough to produce a long timing cycle. For planets near a 2:1 commensurability, a useful approximate super-period is 1/|2/Pouter − 1/Pinner|.
With illustrative periods of 10 and 20.5 days, that scale is about 410 days. Observing a few transits over one month would sample only a small portion. The formula is an orientation tool near the relevant resonance, not a full dynamical fit or proof of resonant libration.
What can actually be inferred?
A numerical dynamical model predicts transit times for candidate masses and orbital elements. Several parameter combinations may reproduce a limited record. Mass and eccentricity can be degenerate, as discussed in the study of extracting mass and eccentricity from TTVs. Additional timing structure, radial velocities or a longer baseline can reduce that ambiguity.
The Kepler-19 discovery analysis is a concrete example of inferring a non-transiting companion from perturbations while recognizing that its orbit was not uniquely determined by the initial signal.
Rule out shifted measurements
Spots can deform a transit and move a fitted midpoint. Incomplete events, aggressive detrending, wrong exposure timestamps and mixed time conventions can also generate apparent timing changes. Model correlated noise and exposure integration, and inspect individual events.
Evidence is stronger when multiple planets show a consistent interaction pattern and one stable model predicts later timings. An anticorrelation is useful evidence in appropriate systems, not a substitute for all validation. Nor does a TTV non-detection exclude every companion.
Compare duration variations, which change the crossing time, and spot-related timing bias. They help separate orbital dynamics from a shifting light-curve shape.
Revised October 26, 2026. Timing and super-period calculations are illustrative.