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# Apsis-Apocenter (minimum speed)

EmilyB.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)

**Apsis-Apocenter (minimum speed)**, references 1 equation/constant.

**Equations and Constants **

**Apsis-Apocenter (minimum speed)**, is used in 1 calculator.

**Calculators**