Apsis-Apocenter (minimum speed)

The Apsis-Apocenter Minimum Speed calculator computes the minimum speed in an orbit at apogee based on the semi-major axis (a), eccentricity (e), the mass of the primary body (M), and the Universal Gravitational Constant (G).

INSTRUCTION: Choose units and enter the following:

• (M) This is the mass of the primary body.
• (a) This is the semi-major axis of the orbit
• (e) This is the eccentricity of the the orbit

Maximum Orbital Speed(V_ap): The calculator returns the velocity in meters per second.  However this can be automatically converted to compatible units via the pull-down menu.
The apsides indicate the nearest
and furthest points of an
orbiting body around its host.
(1) farthest - apocenter
(2) nearest - pericenter
(3) focus - primary

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.
• Apsis-Pericenter (minimum distance) computes the minimum distance from the center of mass in an orbit.
• Standard Gravitational Parameter

The Math / Science

The Apsis-Apocenter is an extreme point in an object's orbit. For elliptical orbits about a larger body, there are two apsides. This is commonly known as the apogee. The apocenter is the point furthest away from the object being orbited.

The formula for the Apsis-Apocenter minimum speed is:

`v_(ap) = sqrt ( ((1-e)mu)/((1+e)a) )`

where:

• v_ap is velocity at apogee
• e = eccentricity
• a = semi-major axis
• μ = standard gravitational parameter  (μ = M•G)  

References

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