Apsis-Pericenter (minimum distance)

The Apsis-Pericenter Minimum Distance calculator computes the minimum distance from the center of gravity in an orbit at perigee based on the semi-major axis (a) and eccentricity (e).

INSTRUCTION: Choose units and enter the following:

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

Minimum Distance (r_per): The calculator returns the distance in meters.  However this can be automatically converted to compatible units via the pull-down menu.

Related Calculators

• Force of Gravity computes the force of gravity between two bodies.
• Apsis-Apocenter (minimum speed) computes the minimum velocity at the maximum distance of an orbit.
• Apsis-Apocenter (maximum distance) computes the greatest distance from the center of gravity in an orbit.
• Apsis-Pericenter (maximum speed) computes maximum velocity at the minimum distance of an orbit.
  The apsides indicate the nearest
  and furthest points of an
  orbiting body around its host.
  (1) farthest - apocenter
  (2) nearest - pericenter
  (3) focus - primary
• Apsis-Pericenter (minimum distance) computes the minimum distance from the center of mass in an orbit.
• Standard Gravitational Parameter

The Math / Science

The Apsis-Pericenter (minimum distance) is an extreme point in an object's orbit. For elliptical orbits about a larger body, there are two apsides. The pericenter is the point closest to the object being orbited. 

The formula for the Apsis-Pericenter minimum distance is:

`r_(per)=(1-e)a`

where:

• r_per is distance at perigee
• e = eccentricity
• a = semi-major axis

References

Wikipedia (https://en.wikipedia.org/wiki/Apsis)