Radius Of Apogee

vCalc Reviewed
Equation / Last modified by KurtHeckman on 2018/07/27 18:32
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vCalc.Radius Of Apogee
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8e7aa04b-e613-11e3-b7aa-bc764e2038f2

The Radius of Apogee calculator computes is the distance between an object (often a planet) and orbiting body when the orbiting body is at apogee based on the semi-minor axis (a) and the eccentricity (e) of the orbit.

INSTRUCTIONS: Choose the preferred distance units and enter the following:

  • (a)  This is the semi-major axis of the orbital ellipse.
  • (e)  This is the eccentricity of the orbit (ellipse)

Radius of Apogee (ra): The calculator returns the radius of apogee in kilometers.  However this can be automatically converted to other distance units including a full suite of astronomical distance units (e.g. light years, parsecs, astronomical units) RadiusOfApogee-illustration.png diagram illustrating various orbital characteristics,
including radius of apogee ra

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The Math / Science

The formula for the radius of apogee is:

        ra = a•(1+e)

where:

Apogee is the point in an orbit at which the orbiting body is furthest to the object it orbits.  Thus, the Radius of Apogee represents the maximum distance between an orbiting body and the object it orbits.  Radius of Apogee may be contrasted to  Radius of Perigee, which is the minimum distance between orbiting and orbited bodies.

This equation produces the Radius of Apogee ra, based on length of semi-minor axis (a) and eccentricity (e) of an elliptical orbit.  Distances are measured from the centers of bodies.

Example Parameters

 Orbit  Semi major axis  Eccentricity
Earth (about Sun)1149.60 x 106 km 0.0167
Moon (about Earth)20.3844  x 106 km 0.0549
Saturn (about Sun)31,433.53  x 106 km 0.0565

Remembering the Difference between Perigee and Apogee

Since apogee and perigee are not commonly used terms, they are often confused.  A simple memory convention to remember the difference is this, count the number of letters.  Apo and far, have three letters.  Peri and near have four letters.  Therefore perigee is the nearest point in the orbit, and apogee is the farthest point in the orbit. 

History

The understanding of orbital perigee arose directly from Kepler's laws of planetary motion published in 16094.

References