Apoapsis From Orbit Calculator

Find apoapsis radius from simple orbit values. Convert altitude, check eccentricity, and compare methods fast. Download clean CSV and PDF summaries after every calculation.

Calculator

Formula Used

From semi-major axis and eccentricity: apoapsis radius = a × (1 + e).

From periapsis radius and eccentricity: apoapsis radius = rp × (1 + e) ÷ (1 - e).

From semi-major axis and periapsis radius: apoapsis radius = 2a - rp.

Apoapsis altitude: apoapsis altitude = apoapsis radius - body radius.

The calculator treats the orbit as a closed ellipse. Eccentricity must stay below one. Distances are converted to kilometers internally, then shown in your selected output unit.

How To Use This Calculator

  1. Select the calculation method that matches your known orbit values.
  2. Choose the central body or select a custom body.
  3. Enter semi-major axis, periapsis, eccentricity, or custom values.
  4. Select input and output units.
  5. Press the calculate button to show results below the header.
  6. Use CSV or PDF buttons to save the result.

Example Data Table

Scenario Body Known Values Formula Path Expected Apoapsis Radius
Low Earth study orbit Earth a = 10000 km, e = 0.2 a × (1 + e) 12000 km
Lunar transfer example Earth rp = 6678.137 km, e = 0.7 rp × (1 + e) ÷ (1 - e) 37842.776 km
Mars planning example Mars a = 6000 km, periapsis altitude = 250 km 2a - rp 8360.5 km

Understanding Apoapsis From Orbit

Apoapsis is the farthest point of an elliptical orbit. It is measured from the center of the main body. Many users also need apoapsis altitude. That value subtracts the body radius from the apoapsis radius. This calculator supports both views. It can work from semi-major axis and eccentricity. It can also work from periapsis and eccentricity. A third path uses semi-major axis with periapsis data.

Why It Matters

Apoapsis helps describe orbit size and mission reach. A satellite with a high apoapsis spends more time far from the body. That changes speed, lighting, communication range, and observation windows. In games, classroom tasks, and planning notes, the same geometry applies. The calculator keeps the main values together, so the orbit can be checked quickly.

Inputs And Units

The body radius is important when altitude is used. Earth, Moon, Mars, Jupiter, and Sun presets fill common values. A custom option lets you enter another radius. Distances may be entered in kilometers, meters, or miles. The tool converts them internally. The output unit can also be changed. This helps compare results without rewriting the inputs.

Reading The Results

Apoapsis radius is the distance from the center of the body. Apoapsis altitude is the height above the surface. Periapsis radius shows the nearest orbital distance. The semi-major axis is the average of apoapsis and periapsis radii. Eccentricity shows the orbit shape. Values near zero are almost circular. Values close to one are very stretched.

Advanced Notes

When a gravitational parameter is available, the calculator also estimates orbital period and speeds. These numbers come from standard two-body equations. They ignore drag, thrust, uneven gravity, and third-body forces. Therefore they are best for ideal orbit study. Real mission design should add safety margins and detailed simulation. Use exported CSV or PDF files to save results.

Good Practice

Check that eccentricity is below one for a closed ellipse. Use positive distances only. Confirm whether your periapsis value is a radius or an altitude. Mixing those two ideas creates large errors. If the apoapsis altitude is negative, the path intersects the body. That means the orbit is not physically clear. Record every unit choice, because later reviews depend on consistent distance labels and notes.

FAQs

What is apoapsis?

Apoapsis is the farthest point in an elliptical orbit. It is measured from the center of the body being orbited.

What is apoapsis altitude?

Apoapsis altitude is the height above the body surface. It equals apoapsis radius minus body radius.

Which input method should I choose?

Choose the method that matches your known values. Use semi-major axis and eccentricity when both are known.

Can eccentricity be one or greater?

No. This calculator is for closed elliptical orbits. Eccentricity must be lower than one.

Why does the body radius matter?

Body radius is needed when converting radius to altitude. Altitude is measured above the surface.

Are the speed values exact?

They are ideal two-body estimates. They do not include drag, thrust, uneven gravity, or other bodies.

Can I use miles or meters?

Yes. Select the input unit and output unit. The calculator handles conversion internally.

What does a negative altitude mean?

It means that part of the orbit is inside the body. The path is not physically clear.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.