Calculator Inputs
Example Data Table
| Case | Mode | Central body | Key inputs | Use case |
|---|---|---|---|---|
| Low orbit sweep | Circular | Earth | Radius 7000 km, 90 degrees | Coverage timing |
| Elliptic arc | Elliptical | Earth | a 10000 km, e 0.2, 10 to 140 degrees | Anomaly arc review |
| Orbit raise | Hohmann | Earth | 6678 km to 42164 km | Transfer planning |
| Flyby segment | Hyperbolic | Mars | |a| 12000 km, e 1.5 | Escape or flyby study |
Formula Used
Circular Orbit
The period is T = 2 pi sqrt(r^3 / mu). The time is T multiplied by the selected angular fraction.
Elliptical Orbit
The mean motion is n = sqrt(mu / a^3). True anomaly is converted to eccentric anomaly. Then M = E - e sin(E). Time is delta M divided by n.
Hohmann Transfer
The transfer semi-major axis is at = (r1 + r2) / 2. The time of flight is pi sqrt(at^3 / mu).
Hyperbolic Segment
The calculator uses F = 2 atanh(sqrt((e - 1) / (e + 1)) tan(nu / 2)). Then M = e sinh(F) - F. Time is absolute delta M divided by n.
How to Use This Calculator
- Select the calculation mode that matches your orbit problem.
- Choose the central body, or enter a custom gravitational parameter.
- Select the distance unit before entering distances.
- Enter radius, semi-major axis, eccentricity, or transfer radii as needed.
- Add start and end true anomalies for arc calculations.
- Choose the output time unit.
- Press Calculate to show the result above the form.
- Use CSV or PDF buttons to save the result.
Time of Flight Calculator for Orbits
Why Orbital Time Matters
Orbital time matters in every early mission study. A small timing error can shift coverage, burns, or tracking windows. This calculator gives fast estimates for common two body cases. It is built for study, concept design, and quick checks.
Supported Orbit Modes
The tool covers four useful modes. Circular mode estimates time for an angular sweep. Elliptical mode estimates time between two true anomalies. Transfer mode estimates a Hohmann half orbit. Hyperbolic mode estimates time during escape or flyby motion.
Each mode uses the selected gravitational parameter. You can choose Earth, Moon, Mars, or Sun. You can also enter a custom value. This helps with asteroids, planets, and teaching examples.
Circular and Elliptical Use
Circular motion is the simplest case. The radius gives the orbit period. The selected angle gives the fraction of that period. Use this when the orbit is nearly circular.
Elliptical motion changes speed along the path. The calculator converts true anomaly to eccentric anomaly. It then finds mean anomaly. Mean anomaly difference gives elapsed time after division by mean motion. This follows Keplerian two body motion.
Transfer and Hyperbolic Use
Hohmann transfer mode uses two circular orbit radii. The transfer semi major axis is their average. The time of flight is half the transfer period. This gives a clean estimate for orbit raising or lowering.
Hyperbolic mode uses hyperbolic anomaly. It works for valid true anomalies only. Values must stay inside the asymptote limit. This mode can help with flyby and escape studies.
Output and Review
Distance units can be kilometers or meters. The calculator converts them before solving. Output can be seconds, minutes, hours, or days. This keeps the same form useful for many scales.
The CSV download stores a compact row of results. The PDF download creates a readable report. Both are useful for records and review.
These outputs are planning estimates. Real missions include thrust, drag, oblateness, and third body gravity. Navigation updates also change timing. Use this calculator for early analysis before detailed simulation.
Good inputs improve every estimate. Use radius from the central body center. Do not enter altitude alone. Add body radius first. Check eccentricity limits before running. Compare prograde and short path choices. Save one result. Then adjust one value at a time. Review units twice carefully.
FAQs
1. What is orbital time of flight?
It is the elapsed time needed to move between two points on an orbit or complete a selected transfer segment.
2. Should I enter altitude or radius?
Enter radius from the central body center. If you have altitude, add the body radius first.
3. What does mu mean?
Mu is the standard gravitational parameter. It equals gravitational constant times central body mass.
4. Which mode should I use for orbit raising?
Use Hohmann transfer mode for a simple two impulse transfer between circular orbits.
5. Can this calculator handle eccentric orbits?
Yes. Use elliptical mode when eccentricity is at least zero and below one.
6. Why does hyperbolic mode reject some angles?
Hyperbolic trajectories have asymptote limits. True anomalies outside those limits are not valid for that path.
7. Are perturbations included?
No. The calculator uses two body equations. Drag, thrust, oblateness, and third body effects are not included.
8. What can I export?
You can export the calculated result as a CSV file or a simple PDF report.