Phasing Loop Catchup Count

Estimate loops to pass a target phase under constant per-loop advance; overshoot is reported rather than claiming exact rendezvous.

Description

A constant phase advance per loop can estimate how many loops are needed to reach or pass a target.

A constant phase advance per loop can estimate how many loops are needed to reach or pass a target. Rounding up may overshoot, which differs from an exact rendezvous.^[1]

Estimate loops to pass a target phase under constant per-loop advance; overshoot is reported rather than claiming exact rendezvous.

When to use Phasing Loop Catchup Count

Use this tool to estimate loops to pass a target phase under constant per-loop advance; overshoot is reported rather than claiming exact rendezvous.

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 Phasing Loop Catchup Count 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 initialPhaseDegrees, phaseAdvanceDegreesPerLoop, loopPeriod using the field table and calculation rules, then run the tool.
Read continuousLoops, wholeLoopsToPassTarget, phaseOvershootDegrees, elapsedToPassTarget. 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
initialPhaseDegrees	Initial phase degrees	number	Required
phaseAdvanceDegreesPerLoop	Phase advance degrees per loop	number	Required
loopPeriod	Loop period	number	Required

Enter initial phase in [0,360), positive advance no greater than 360 degrees per loop and a positive loop period. Return continuous and whole loop counts, whole-loop excess phase and elapsed time. Zero initial phase needs no loops. An unsafe integer count is an input error.

continuousLoops = initialPhase/advance; wholeLoops = ceil(continuousLoops)

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

Output field	Meaning	Value type
continuousLoops	Continuous loops	number
wholeLoopsToPassTarget	Whole loops to pass target	number
phaseOvershootDegrees	Phase overshoot degrees	number
elapsedToPassTarget	Elapsed to pass target	number

json

{
  "input": {
    "initialPhaseDegrees": 90,
    "phaseAdvanceDegreesPerLoop": 30,
    "loopPeriod": 50
  },
  "output": {
    "continuousLoops": 3,
    "wholeLoopsToPassTarget": 3,
    "phaseOvershootDegrees": 0,
    "elapsedToPassTarget": 150
  }
}

Limitations and assumptions

The assumed advance is constant and does not model orbital evolution or maneuver costs. The rounded plan passes the target phase and can have nonzero overshoot.

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 Rendezvous Phasing Period: Choose a phasing-loop period for point rendezvous after supplied target revolutions; no safe pericenter or burn budget is inferred. For a complementary task, 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.

References

Phasing Loop Catchup Count — tool.io

Similar or alternative tools

Rendezvous Phasing Period
Choose a phasing-loop period for point rendezvous after supplied target revolutions; no safe pericenter or burn budget is inferred.
Reduced Resonance Detuning
Reduce a candidate period-ratio resonance to coprime integers and report relative detuning; proximity alone does not show resonant angle libration.