Radius Of Perigee

vCalc Reviewed
Equation / Last modified by KurtHeckman on 2018/07/27 18:30
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vCalc.Radius Of Perigee
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fe2e1325-e608-11e3-b7aa-bc764e2038f2

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

INSTRUCTIONS: Choose units and enter the following:

Radius of Perigee (rp): The calculator returns the radius of perigee 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) RadiusOfPergiee-illustration.png diagram illustrating various orbital characteristics,
including radius of perigee rp

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The Math / Science

The formula for the radius of perigee is:

        rp = a•(1-e)

where:

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

This equation produces the Radius of Perigee rp, based on length of semi-major axis (a) and eccentricity (e) of 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.

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References