A canonical unit is a

unit of measurement A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multi ...

agreed upon as default in a certain context.

In astrodynamics

astrodynamics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...

, canonical units are defined in terms of some important object’s

orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...

that serves as a reference. In this system, a reference mass, for example the Sun’s, is designated as 1 “canonical mass unit” and the mean distance from the orbiting object to the reference object is considered the “canonical distance unit”. Canonical units are useful when the precise distances and masses of objects in space are not available. Moreover, by designating the mass of some chosen central or primary object to be “1 canonical mass unit” and the mean distance of the reference object to another object in question to be “1 canonical distance unit”, many calculations can be simplified.

Overview

The ''Canonical Distance Unit''

\; \text \;

is defined to be the mean radius of the reference orbit. The ''Canonical Time Unit''

\; \text \;

is defined by the ''

gravitational parameter In celestial mechanics, the standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of the bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM when ...

\; \mu \;

: :

\mu \equiv G \, M ~

where :

\; G \;

is the gravitational constant :

\; M \equiv \text \;

is the mass of the central reference body In canonical units, the gravitational parameter is given by: :

\mu = 1 \, \frac

Any triplet of numbers,

\, M \, ,

\, \text\, ,

and

\, \text\, ,

that satisfy the equation above is a “canonical” set. ---- The quantity of the time unit can be solved in another unit system (e.g. the metric system) if the mass and radius of the central body have been determined. Using the above equation and applying

dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as mi ...

, set the two equations expressing

\; \mu \;

equal to each other:

\mu \equiv G \times M = 1 \, \frac ~

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

\text = \sqrt ~

For Earth-orbiting satellites, approximate unit conversions are as follows: * 1 = 6378.1 km = 20,925,524.97 ft * 1 = 7.90538 km/s = 25,936.29 ft/sec * 1 = 806.80415 s

Astronomical Unit

The

astronomical unit The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits ...

() is the canonical distance unit for the orbit around the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

of the combined

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

system (based on the formerly best-known value). The corresponding time unit is the (sidereal) year)), and the mass is the total mass of the Sun ().

Footnotes

References

* {{cite book , last1=Bate , first1=Roger R. , author-link1=Roger R. Bate , last2=Mueller , first2=Donald D. , last3=White , first3=Jerry E. , year=1971 , title=Fundamentals of Astrodynamics , series=Dover Books on Astronomy and Astrophysics , location=New York , publisher=Dover Publications , isbn=0486600610 , lccn=73157430 , url=https://archive.org/details/fundamentalsofas00bate , url-access=registration Astrodynamics Celestial mechanics

In astrodynamics

Overview

Astronomical Unit

See also

Footnotes

References