What Is the Hyperbolic Orbit Escape Velocity & C3 Energy Calculator?
A hyperbolic trajectory is an open orbit where an object has enough mechanical energy to escape a central gravitational body completely.
How Does the Hyperbolic Orbit Escape Velocity & C3 Energy Calculator Work?
Uses specific orbital energy conservation to determine asymptotic velocity at infinite separation.
Hyperbolic Orbit Escape Velocity & C3 Energy Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
v_{ ext{esc}} = sqrt{ rac{2mu}{r}}, quad v_infty = sqrt{v^2 - v_{ ext{esc}}^2}, quad C_3 = v_infty^2
Conservation of orbital specific energy for unbound hyperbolic trajectories.
How to Use the Hyperbolic Orbit Escape Velocity & C3 Energy Calculator
- Input burnout radius from planetary center and burnout velocity magnitude.
Step-by-Step Example Calculation
Trans-Mars Injection Burnout
Input Values:
burnBurnoutRadiusKm:6578
burnoutVelocityKmS:11.4
standardGravParamKm3S2:398600.44
Worked Steps: Escape velocity = 11.01 km/s, yielding hyperbolic excess v_∞ = 2.96 km/s and C3 = 8.76 km²/s².
Understanding Your Result
Shows local escape speed, hyperbolic excess velocity (v_inf), and C3 launch energy required by interplanetary launch vehicles.
Factors That Affect the Result
- Lower parking orbit altitudes provide an Oberth effect advantage during departure burns.
When Should You Use This Calculator?
- Interplanetary mission design (Mars, Jupiter missions), solar system escape analysis, and launch vehicle capability sizing.
Assumptions & Limitations
- Patched-conic approximation; ignores third-body solar and lunar gravitational perturbations.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard vis-viva hyperbolic orbital energy relation.