Mutual Event Inclination Band
Screen circular mutual-event geometry against the sum-of-radii projected inclination band; orbital phase is not inferred.
Description
A circular mutual event requires projected inclination close enough to edge-on for the bodies' apparent disks to overlap.
A circular mutual event requires projected inclination close enough to edge-on for the bodies' apparent disks to overlap. This geometric band depends on their summed radii relative to separation.1
Screen circular mutual-event geometry against the sum-of-radii projected inclination band; orbital phase is not inferred.
When to use Mutual Event Inclination Band
Use this tool to screen circular mutual-event geometry against the sum-of-radii projected inclination band; orbital phase is not inferred.
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 Mutual Event Inclination Band 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 firstRadius, secondRadius, separation, viewingOffsetDegrees using the field table and calculation rules, then run the tool.
- Read maximumOffsetDegrees, eventGeometryPossible. 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 |
|---|---|---|---|
| firstRadius | First radius | number | Required |
| secondRadius | Second radius | number | Required |
| separation | Separation | number | Required |
| viewingOffsetDegrees | Viewing offset degrees | number | Required |
Enter nonnegative radii, positive separation at least their sum, and a signed viewing offset within ±90 degrees. The tool returns the maximum offset and tests absolute viewing offset inclusively against it. Zero total radius gives a zero-width band.
maximumOffset = asin[(radius1+radius2)/separation] in degrees Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| maximumOffsetDegrees | Maximum offset degrees | number |
| eventGeometryPossible | Event geometry possible | boolean |
{
"input": {
"firstRadius": 1,
"secondRadius": 1,
"separation": 10,
"viewingOffsetDegrees": 10
},
"output": {
"maximumOffsetDegrees": 11.536959032815489,
"eventGeometryPossible": true
}
}Limitations and assumptions
This does not determine orbital phase, event timing, brightness or actual visibility. Spherical bodies and the supplied circular geometry are assumptions, and all lengths must share a unit.
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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Planetary Phase Triangle Angle: Solve the Sun–planet–observer phase angle from simultaneous triangle side lengths in any common distance unit. For a complementary task, use Ellipse From Apsis Radii: Recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes.
References
-
Mutual Event Inclination Band — tool.io
Similar or alternative tools
- Planetary Phase Triangle Angle
Solve the Sun–planet–observer phase angle from simultaneous triangle side lengths in any common distance unit.
- Ellipse From Apsis Radii
Recover ellipse shape parameters from ordered center-referenced periapsis and apoapsis radii, not surface altitudes.