Orbital eccentricity from apsides calculator

Calculate orbital eccentricity and semimajor axis with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use orbital eccentricity and semimajor axis to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Periapsis distance
1
Apoapsis distance
3
Orbital eccentricity
0.5
Semimajor axis (same units)
2

Try another scenario

Periapsis distance
1.1
Apoapsis distance
3
Orbital eccentricity
0.463415
Semimajor axis (same units)
2.05
Calculation method

Calculation method

Orbital eccentricity

e=(ra-rp)/(ra+rp); a=(ra+rp)/2.

Semimajor axis (same units)

e=(ra-rp)/(ra+rp); a=(ra+rp)/2.

Symbols and units
a
Periapsis distance
b
Apoapsis distance

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Calculation uses the entered values and stated mathematical model; quantities must use the labelled units. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. e=(ra-rp)/(ra+rp); a=(ra+rp)/2.
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