Questions: Transit Timing Variations and Exoplanet System Detection

Question 1

A planet orbiting a star shows transits that arrive 8 minutes earlier or later than a strict periodic schedule. Which interpretation is best supported by transit timing variation (TTV) theory?

• A. The star's rotation is influencing the apparent transit period
• B. A second planet—possibly one that never transits—is gravitationally perturbing the first
• C. The transiting planet's atmosphere is absorbing some of the stellar light, altering timing precision
• D. The transiting planet is accelerating due to tidal forces from its host star

Answer: (B)

TTVs are caused by gravitational interactions with other bodies in the system. The perturbing companion does not need to transit—its gravitational fingerprint is encoded in the timing deviations of the planet that does transit. This is one of TTV's key strengths: it can reveal non-transiting planets that would be invisible to other methods.

Question 2

Why are TTV signals especially large near mean-motion resonances?

• A. Mean-motion resonances cause planets to merge, releasing gravitational energy
• B. Gravitational kicks arrive at nearly the same orbital phase each time, so perturbations accumulate constructively over many orbits
• C. Resonant planets orbit at higher speeds, producing shorter transit durations that are easier to time
• D. Near resonance, planets pass through the stellar disk simultaneously, amplifying the photometric signal

Answer: (B)

When two planets' orbital periods form a near-integer ratio, they encounter each other at approximately the same orbital geometry on each cycle. The gravitational kick from each close approach adds coherently, building up TTV amplitudes from minutes to hours over many orbits. Far from resonance, kicks arrive at random orbital phases and partially cancel, producing much smaller net timing deviations.

Question 3

Transit timing variations can be used to constrain the mass of a non-transiting planet in a multi-planet system.

• T. True
• F. False

Answer: True

This is one of TTV's most powerful applications. The amplitude and pattern of timing deviations encode information about the perturbing planet's mass and orbital parameters through N-body dynamics. Kepler measured masses of hundreds of planets this way—often to 10–20% precision—without any radial velocity data, making TTV indispensable for small planets around faint stars.

Question 4

A planet whose transits are perfectly periodic is proof that it has no planetary companions in the system.

• T. True
• F. False

Answer: False

Perfectly periodic transits indicate only that there are no significant gravitational perturbations detectable at current precision, not the absence of companions. A companion in a very different orbit (far from mean-motion resonance, or far from the transiting planet) may produce TTVs too small to detect given photometric noise. TTV non-detection sets an upper limit on perturber mass and orbital configuration, not a definitive absence.

Question 5

Explain why TTVs are most sensitive to planets near mean-motion resonances, and what makes TTVs valuable compared to radial velocity follow-up.

Model answer: Near mean-motion resonances, gravitational kicks accumulate coherently—planets encounter each other at approximately the same orbital phase each cycle, so small perturbations build up over many orbits into large, measurable timing deviations. Far from resonance, kicks come at random phases and tend to cancel. TTVs are valuable compared to RV because they can detect and characterize non-transiting planets, constrain masses without spectroscopy, and work for small planets around faint stars where RV signals are too weak to measure.

The accumulation principle (coherent vs. incoherent perturbations) is the physical reason resonances dominate TTV science. The practical advantage of TTVs—mass measurements for RV-inaccessible targets—is why Kepler's statistical characterization of exoplanet populations relies heavily on TTV data.