Near Resonance Ttv Scale

Evaluate a supplied near-resonance TTV scaling coefficient P·mass-ratio/(π·|Δ|); free eccentricity, exact resonance and mass inference are not modeled.

Description

Near-resonance transit timing variation models can scale with orbital period, a perturber/star mass ratio and inverse resonance offset.

Near-resonance transit timing variation models can scale with orbital period, a perturber/star mass ratio and inverse resonance offset. Such an approximation becomes singular at exact resonance.^[1]

Evaluate a supplied near-resonance TTV scaling coefficient P·mass-ratio/(π·|Δ|); free eccentricity, exact resonance and mass inference are not modeled.

When to use Near Resonance Ttv Scale

Use this tool to evaluate a supplied near-resonance TTV scaling coefficient P·mass-ratio/(π·|Δ|); free eccentricity, exact resonance and mass inference are not modeled.

Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.

How to use Near Resonance Ttv Scale and understand its results

Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
Enter innerPeriodDays, perturberStarMassRatio, resonanceOffset, modelCoefficient using the field table and calculation rules, then run the tool.
Read amplitudeDays, amplitudeMinutes. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
innerPeriodDays	Inner period days	number	Required
perturberStarMassRatio	Perturber star mass ratio	number	Required
resonanceOffset	Resonance offset	number	Required
modelCoefficient	Model coefficient	number	Required

Supply positive inner period in days, perturber/star mass ratio and model coefficient, plus a finite nonzero signed offset. The tool uses its absolute value and returns the positive amplitude in days and minutes, multiplying by 1,440 for conversion.

amplitudeDays = coefficient × innerPeriodDays × massRatio /(π|offset|)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
amplitudeDays	Amplitude days	number
amplitudeMinutes	Amplitude minutes	number

json

{
  "input": {
    "innerPeriodDays": 10,
    "perturberStarMassRatio": 0.00001,
    "resonanceOffset": 0.01,
    "modelCoefficient": 1
  },
  "output": {
    "amplitudeDays": 0.0031830988618379067,
    "amplitudeMinutes": 4.583662361046586
  }
}

Limitations and assumptions

It does not infer masses, fit a transit series or include free eccentricity. Zero offset is an input error, and arbitrarily close resonance need not remain within the approximation's physical validity.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Reduced Resonance Detuning: Reduce a candidate period-ratio resonance to coprime integers and report relative detuning; proximity alone does not show resonant angle libration. For a complementary task, use Quadrupole Kozai Timescale: Estimate a quadrupole Kozai–Lidov timescale with the 8/(15π) convention in the same units as supplied periods; not a cycle-existence test.

References

Near Resonance Ttv Scale — tool.io

Similar or alternative tools

Reduced Resonance Detuning
Reduce a candidate period-ratio resonance to coprime integers and report relative detuning; proximity alone does not show resonant angle libration.
Quadrupole Kozai Timescale
Estimate a quadrupole Kozai–Lidov timescale with the 8/(15π) convention in the same units as supplied periods; not a cycle-existence test.