Conic Vis Viva Speed
Evaluate vis-viva for elliptic positive-a or hyperbolic negative-a states with an accessible radius, extending the existing circular-orbit operation.
Description
Vis-viva relates orbital speed to radius and semimajor axis in a two-body conic.
Vis-viva relates orbital speed to radius and semimajor axis in a two-body conic. Positive semimajor axis denotes an ellipse and negative semimajor axis denotes a hyperbola in this convention.1
Evaluate vis-viva for elliptic positive-a or hyperbolic negative-a states with an accessible radius, extending the existing circular-orbit operation.
When to use Conic Vis Viva Speed
Use this tool to evaluate vis-viva for elliptic positive-a or hyperbolic negative-a states with an accessible radius, extending the existing circular-orbit operation.
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 Conic Vis Viva Speed 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 mu, radius, semimajorAxis using the field table and calculation rules, then run the tool.
- Read orbitalSpeed. 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 |
|---|---|---|---|
| mu | Gravitational parameter, using the same distance and time units throughout; km³/s² for km and seconds. | number | Required |
| radius | Radius | number | Required |
| semimajorAxis | Semimajor axis | number | Required |
Enter positive μ and radius plus a finite nonzero semimajor axis in consistent units. The helper rejects a negative speed-squared expression and returns its square root; a zero radicand is accepted. For μ in km³/s² and lengths in km, speed is km/s.
speed = sqrt[μ(2/radius − 1/semimajorAxis)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| orbitalSpeed | Orbital speed | number |
{
"input": {
"mu": 1,
"radius": 1,
"semimajorAxis": 2
},
"output": {
"orbitalSpeed": 1.224744871391589
}
}Limitations and assumptions
It does not validate eccentricity, angular momentum or surface clearance, and no finite semimajor-axis input represents the parabolic limit. A mathematically allowed speed alone is not a full orbit.
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 Hyperbolic Capture Insertion: Calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes. For a complementary task, use Specific Orbital Energy: Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety.
References
-
Conic Vis Viva Speed — tool.io
Similar or alternative tools
- Hyperbolic Capture Insertion
Calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes.
- Specific Orbital Energy
Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety.