Canonical units

A canonical unit is a unit of measurement agreed upon as default in a certain context.

In astrodynamics

In astrodynamics, canonical units are defined in terms of an object's reference orbit. In this system, a reference mass, for example the sun, is assumed to be 1 "mass unit" and the mean distance from the orbiting object to the reference object is considered the "distance unit".

Canonical units are useful when the precise distances and masses of objects in space are not available. However, by setting the mass of a given object to be 1 mass unit and the mean distance of the reference object to another object in question, many calculations can be simplified.

Overview

The Distance Unit $DU\$ is defined to be the mean radius of the reference orbit.

The Time Unit $TU\$ is defined by the gravitational parameter $\mu \$:

$\mu =G*M\,\!$

• $G\$ is the gravitational constant
• $M\$ is the mass of the central reference body

For canonical units, the gravitational parameter is defined as:

$\mu =1*{\frac {DU^{3}}{TU^{2}}}$

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The quantity of the time unit (TU) can be solved in another unit system (e.g. the metric system) if the mass and radius of the central body has been determined. Using the above equation and applying dimensional analysis, set the two equations expressing $\mu$ equal to each other:

$\mu =G*M=1*{\frac {DU^{3}}{TU^{2}}}$

The time unit (TU) can be converted to another unit system for a more useful qualitative solution using the following equation:

$TU={\sqrt {\frac {DU^{3}}{G*M}}}$

For Earth satellites, approximate unit conversions are as follows:

• 1 DU = 6378.1 km = 20,925,524.97 ft
• 1 DU/TU = 7.90538 km/s = 25,936.29 ft/sec
• 1 TU = 806.80415 s

Astronomical Unit

The astronomical unit is a canonical unit based on the orbit of the Earth around the Sun

See also

• Astronomical unit
• Conversion of units

References

Roger R. Bate, Donald D. Mueller, Jerry E. White. Fundamentals of Astrodynamics.