Radius Of Apogee

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)  Semi-major Axis of orbital ellipse.
• (e)  Eccentricity of orbit (ellipse)

Radius of Apogee (r_a): 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) diagram illustrating various orbital characteristics,
including radius of apogee r_a

The Math / Science

The formula for the radius of apogee is:

        r_a = a•(1+e)

where:

• r_a is the radius of apogee
• a is the semi-major axis
• e the eccentricity of the orbital ellipse

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 r_a, 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

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.

1. ^ http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
2. ^ http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
3. ^ http://nssdc.gsfc.nasa.gov/planetary/factsheet/saturnfact.html
4. ^ http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

Related Calculators

• Radius of Apogee
• Radius of Perigee
• Kepler's 3rd Law
• Astronomy Calculator