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THE FEUTEX TOOLKIT

Elliptic Orbit Apsides

Find eccentricity, semimajor axis and speed at the near and far points of an orbit.

Astronomy workspace● Runs in your browser
01 Your input
02 Your result
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FormulaSemimajor axis = (rp+ra)/2; Eccentricity = (ra-rp)/(ra+rp); Periapsis speed = sqrt(mu*(2/rp-2/(rp+ra))); Apoapsis speed = sqrt(mu*(2/ra-2/(rp+ra)))
Sources and model references

Worked example

Inputs

Periapsis radius
7000 km
Apoapsis radius
14000 km
Gravitational parameter
398600.4418 km³/s²

Expected results

Semimajor axis
10500 km
Eccentricity
0.3333333333
Periapsis speed
8.713431797 km/s
Apoapsis speed
4.356715898 km/s

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Find eccentricity, semimajor axis and speed at the near and far points of an orbit.
  2. Set periapsis radius, apoapsis radius, gravitational parameter in the indicated units.
  3. Calculate and compare semimajor axis, eccentricity, periapsis speed, apoapsis speed.

Try this example

{
  "rp": 7000,
  "ra": 14000,
  "mu": 398600.4418
}

Accuracy and scope

Idealized educational model. Enter measured values in the displayed units; real systems may require additional corrections.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.