Calculator
Formula Used
The calculator uses the circular orbit period relation. It assumes the object follows a near circular path around one central body.
r = ∛( μ × T² / 4π² )
h = r - R
Here, r is orbital radius. h is orbit height. μ is the gravitational parameter. T is the orbital period in seconds. R is the radius of the central body.
Extra values use related circular orbit equations. Speed is v = √(μ / r). Gravity at orbit is g = μ / r².
Example Data Table
These examples use the same circular orbit model.
| Body | Time Period | Orbit Height | Orbit Speed | Revolutions Per Day |
|---|---|---|---|---|
| Earth | 90 minutes | 274.42 km | 7.7406 km/s | 16.0000 |
| Earth | 12 hours | 20,232.09 km | 3.8703 km/s | 2.0000 |
| Earth | 23.9345 hours | 35,786.07 km | 3.0747 km/s | 1.0027 |
| Moon | 2 hours | 122.90 km | 1.6234 km/s | 12.0000 |
| Mars | 2 hours | 435.10 km | 3.3434 km/s | 12.0000 |
How To Use This Calculator
- Enter the full orbital time period.
- Select seconds, minutes, hours, or days.
- Choose the central body.
- Use Custom for special planets, moons, or test bodies.
- Enter custom μ and radius when needed.
- Select the height output unit.
- Choose decimal places for cleaner reporting.
- Press the calculate button.
- Review the result above the form.
- Download CSV or PDF for records.
Why Time Period Matters
Orbit height and orbit time are linked. A short period means a lower orbit. A long period means a wider orbit. This happens because gravity supplies the inward pull. The object keeps falling around the body. It does not fall straight down when speed is high enough.
What This Tool Estimates
This calculator estimates the height above a selected body. It starts with the orbital period. It then finds the orbital radius. After that, it subtracts the body radius. The final value is the orbit height. The tool also shows speed, gravity, angular rate, and daily revolutions.
Main Assumption
The method assumes a circular orbit. Real orbits can be elliptical. In an elliptical orbit, height changes with position. This tool gives the circular orbit that matches the entered period. It is useful for study, quick planning, and comparison work.
Choosing The Body
Each body has a gravitational parameter. It also has a radius. Earth, Moon, Mars, Venus, Jupiter, and Sun values are included. You can enter custom values too. That helps when you work with another moon, asteroid, planet, or classroom example.
Reading The Result
The orbit height is measured above the surface. A negative height means the period is too short for that body. The calculated orbit radius would sit inside the body. That is not a usable circular orbit. Increase the time period or check the selected body.
Speed And Gravity
The speed result is the circular orbital speed. Higher low orbits need faster speeds. Higher wide orbits move slower. Gravity at orbit also falls as radius increases. This helps explain why distant satellites travel slowly while still staying in orbit.
Useful Applications
The calculator can help compare low orbit, medium orbit, and high orbit cases. It can show why a near Earth satellite circles many times each day. It can also show why a daily period creates a much higher orbit. Teachers can use it for demonstrations.
Exporting Results
The CSV option is helpful for spreadsheets. The PDF option is useful for reports. Both exports include the main input and output values. This makes the result easier to save, share, and review later. Always note that the model is idealized.
Accuracy Notes
This tool does not include drag, planet shape, atmosphere, third body effects, or station keeping. It is best for first estimates. Professional mission design needs deeper models. Still, the formula gives a strong starting point for understanding orbital height from time.
FAQs
1. What does orbit height mean?
Orbit height is the distance above the selected body surface. It is found by subtracting the body radius from the full orbital radius.
2. What time value should I enter?
Enter one complete orbital period. That means the time needed for one full revolution around the central body.
3. Does this work for Earth satellites?
Yes. Select Earth and enter the satellite period. The result estimates circular orbit height above Earth.
4. Why can the height be negative?
A negative height means the entered period is too short. The matching circular radius would be inside the selected body.
5. Is the result exact?
No. It is an ideal circular orbit estimate. Real missions may need drag, perturbation, and body shape corrections.
6. What is μ?
μ is the standard gravitational parameter. It combines the gravitational constant and central body mass.
7. Can I use custom planets?
Yes. Select Custom. Then enter the gravitational parameter and body radius in the requested units.
8. What unit is μ using?
This calculator expects μ in cubic kilometers per second squared. The custom radius must be in kilometers.
9. What is orbital radius?
Orbital radius is measured from the body center to the orbit path. Height is measured from the surface.
10. What is orbital speed?
Orbital speed is the circular speed needed at the calculated radius. It is shown in kilometers per second.
11. What are revolutions per day?
It shows how many full orbits occur in one Earth day. It uses 86,400 seconds as the day length.
12. Can this calculate elliptical orbit height?
No. It matches a circular orbit to the entered period. Elliptical orbits need more orbital elements.
13. Why include PDF export?
PDF export helps save the result for lessons, reports, records, or mission comparison notes.
14. Why include CSV export?
CSV export helps move the calculation into spreadsheets. It is useful for tables and repeated analysis.