Orbit Eccentricity Calculator

Determine orbital shape and parameters from apoapsis and periapsis.

What is an Orbit Eccentricity Calculator?

An orbit eccentricity calculator is a tool used in astronomy and astrodynamics to determine a key parameter of an orbit: its eccentricity. [4] Eccentricity is a dimensionless number that quantifies how much an orbit deviates from being a perfect circle. [2] This calculator is essential for anyone studying celestial mechanics, from students learning about planetary motion to engineers planning satellite trajectories. By inputting the two most extreme points of an orbit—the apoapsis (farthest point) and periapsis (closest point)—the calculator can instantly provide the eccentricity and other vital orbital characteristics.

A common misunderstanding is confusing altitude with orbital radius. This calculator assumes inputs are the distance from the center of the central body, not the altitude above its surface. For accurate results, you must add the body’s radius to the altitude to get the apoapsis and periapsis distances.

Orbit Eccentricity Formula and Explanation

The calculation is based on a straightforward formula that relates the orbit’s farthest and closest points. [1] The formula is:

e = (rₚ – rₚ) / (rₚ + rₚ)

This formula provides the value of ‘e’, which defines the shape of the orbit:

• e = 0: A perfect circular orbit.
• 0 < e < 1: An elliptical orbit. Most planets and moons have orbits in this range.
• e = 1: A parabolic orbit, which is an “escape” orbit that will not return.
• e > 1: A hyperbolic orbit, another type of escape orbit with even more energy.

For more detailed analysis, you might consult a celestial mechanics calculator.

Variables Table

Variable	Meaning	Unit (Auto-Inferred)	Typical Range
e	Eccentricity	Unitless	0 to >1
rₚ	Apoapsis	km, mi, AU	Greater than rₚ
rₚ	Periapsis	km, mi, AU	Positive number

Practical Examples

Example 1: Geostationary Satellite

A geostationary satellite needs to maintain a circular orbit to stay above the same point on Earth. Let’s see how close it is to a perfect circle.

• Inputs:
  • Central Body: Earth
  • Apoapsis: 42,164 km
  • Periapsis: 42,164 km
  • Units: Kilometers
• Results:
  • Eccentricity: 0.0
  • Orbit Type: Perfectly Circular
  • Orbital Period: 23.93 hours (one sidereal day)

Example 2: Halley’s Comet

Halley’s Comet has a famous, highly elongated orbit around the Sun. Its parameters demonstrate a very high eccentricity.

• Inputs:
  • Central Body: Sun
  • Apoapsis: 5.27 billion km (35.2 AU)
  • Periapsis: 87.8 million km (0.587 AU)
  • Units: Astronomical Units (for easier input)
• Results:
  • Eccentricity: ~0.967
  • Orbit Type: Highly Elliptical
  • Orbital Period: ~75.3 years

Understanding these values is crucial, and you can learn more by reading about Kepler’s Laws.

How to Use This Orbit Eccentricity Calculator

Using this calculator is simple and intuitive. Follow these steps for an accurate calculation:

1. Select the Central Body: Choose the primary object being orbited (e.g., Sun, Earth). This is critical for calculating the orbital period.
2. Enter Apoapsis and Periapsis: Input the farthest and closest distances of the orbit. Remember, these values must be the distance from the center of the body, not the altitude above the surface.
3. Choose Your Units: Select the unit of measurement (Kilometers, Miles, or Astronomical Units) that you used for the inputs.
4. Interpret the Results: The calculator will instantly display the eccentricity, classify the orbit type (circular, elliptical, etc.), and provide related values like the semi-major axis and orbital period. The visualization chart will also update to show the shape of the calculated orbit.

Key Factors That Affect Orbit Eccentricity

An orbit’s eccentricity is not always static. Several factors can influence and change it over time:

• Gravitational Perturbations: The gravitational pull from other bodies (like Jupiter affecting Mars’s orbit) can slightly alter an orbit’s shape.
• Initial Launch Conditions: For a satellite, the velocity and angle at which it’s inserted into orbit determine its initial eccentricity.
• Atmospheric Drag: For satellites in low orbit, friction with the upper atmosphere can cause the orbit to decay, often circularizing it before re-entry. An escape velocity calculator can show the energy needed to avoid this.
• Solar Radiation Pressure: Over long periods, the slight push from sunlight can affect the orbits of small objects or satellites with large solar panels.
• Tidal Forces: The gravitational gradient across an orbiting body can create tidal forces that exchange energy and alter the orbit’s eccentricity over millions of years.
• Non-Spherical Central Body: No planet or star is a perfect sphere. These slight bulges create an uneven gravitational field that can perturb an orbit. For more on this, see our article on celestial bodies.

Frequently Asked Questions (FAQ)

What is a good eccentricity for an orbit?

It depends on the mission. A “good” eccentricity for a surveillance satellite might be near zero to maintain a constant altitude, while a “good” eccentricity for a science mission like the Parker Solar Probe is very high to get close to the sun. Planets with low eccentricity (like Earth) have more stable climates.

Can eccentricity be negative?

No, orbital eccentricity is a non-negative value by definition.

Why does the orbital period change?

The orbital period is determined by the semi-major axis of the orbit and the mass of the central body, according to Kepler’s Third Law. A larger orbit means a longer period. This orbit eccentricity calculator computes this automatically. [3]

What’s the difference between apoapsis and apogee?

“Apoapsis” is the general term for the farthest point in any orbit. “Apogee” is specific to an orbit around Earth. Similarly, “Periapsis” is the general term, while “Perigee” is for Earth orbits and “Perihelion” is for Sun orbits.

How does this relate to an orbital parameters calculator?

This tool is a specialized orbital parameters calculator focusing on eccentricity. A full parameters calculator might also solve for inclination, argument of periapsis, and other orbital elements.

What if my apoapsis and periapsis are the same?

If they are identical, the eccentricity is 0, and you have a perfect circle. The calculator will reflect this.

Can I use altitude instead of distance from the center?

No. You must add the radius of the central body to your altitude values before entering them into the calculator for an accurate result.

What does a hyperbolic trajectory (e > 1) mean?

It means the object has enough velocity to escape the gravitational pull of the central body and will never return. This is common for interstellar objects passing through our solar system. A gravitational force calculator can help understand these interactions.