Planetary Phase Triangle Angle
Solve the Sun–planet–observer phase angle from simultaneous triangle side lengths in any common distance unit.
Description
A planet's phase angle is the angle at the planet between the Sun and observer.
A planet's phase angle is the angle at the planet between the Sun and observer. Simultaneous triangle distances determine that angle without supplying a planetary ephemeris.1
Solve the Sun–planet–observer phase angle from simultaneous triangle side lengths in any common distance unit.
When to use Planetary Phase Triangle Angle
Use this tool to solve the Sun–planet–observer phase angle from simultaneous triangle side lengths in any common distance unit.
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 Planetary Phase Triangle Angle 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 sunPlanetDistance, planetObserverDistance, sunObserverDistance using the field table and calculation rules, then run the tool.
- Read phaseAngleDegrees. 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 |
|---|---|---|---|
| sunPlanetDistance | Sun planet distance | number | Required |
| planetObserverDistance | Planet observer distance | number | Required |
| sunObserverDistance | Sun observer distance | number | Required |
Enter three positive distances in a common unit. They must satisfy triangle inequalities; degenerate equality is allowed. The tool applies the cosine law, clips its cosine into [−1,1] against roundoff and returns degrees.
phase = acos[(SunPlanet²+PlanetObserver²−SunObserver²)/(2 SunPlanet PlanetObserver)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| phaseAngleDegrees | Phase angle degrees | number |
{
"input": {
"sunPlanetDistance": 1,
"planetObserverDistance": 1,
"sunObserverDistance": 1.4142135623730951
},
"output": {
"phaseAngleDegrees": 90.00000000000001
}
}Limitations and assumptions
It does not retrieve positions, apply light-time corrections or calculate illuminated brightness. Distances from different observation times do not define the intended simultaneous triangle.
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 Mutual Event Inclination Band: Screen circular mutual-event geometry against the sum-of-radii projected inclination band; orbital phase is not inferred. For a complementary task, use Spherical Pair Separation Angle: Compute robust great-circle separation and first-to-second position angle east of north, rejecting directionally undefined coincident/antipodal pairs.
References
-
Planetary Phase Triangle Angle — tool.io
Similar or alternative tools
- Mutual Event Inclination Band
Screen circular mutual-event geometry against the sum-of-radii projected inclination band; orbital phase is not inferred.
- Spherical Pair Separation Angle
Compute robust great-circle separation and first-to-second position angle east of north, rejecting directionally undefined coincident/antipodal pairs.