# Units/Astronomy

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This chart shows the increasing accuracy of NIST (formerly NBS) atomic clocks. Credit: National Institutes of Standards and Technology (NIST), USA.

A unit, especially in radiation astronomy, is often a quantity chosen as a standard in terms of which quantities may be expressed.

## Notations

Each unit so chosen is likely to have a sign, symbol, or notation to represent the quantity.

Notation: let m represent a metre.

Notation: let km represent a kilometre.

Notation: let the symbol ${\displaystyle R_{\oplus }}$ indicate the Earth's radius.

Notation: let the symbol ${\displaystyle R_{J}}$ indicate the radius of Jupiter.

Notation: let the symbol ${\displaystyle R_{\odot }}$ indicate the solar radius.

Notation: an astronomical unit is usually represented by au, or AU.

## Astronomical units

"The International Astronomical Union (IAU) is responsible for maintaining and approving a special set of units in astronomy, formally defined in 1976."[1]

"One of the most important of these is the astronomical unit. It is a unit of length approximating the Sun-Earth distance (of about 150 million kilometres) which is of convenient use in astronomy. According to its definition adopted by the XXVIIIth General Asssembly of the IAU (IAU 2012 Resolution B2), the astronomical unit is a conventional unit of length equal to 149 597 870 700 m exactly. This definition is valid irrespective of the used time scale. The unique symbol for the astronomical unit is au."[1]

Def. "a conventional unit of length equal to 149 597 870 700 m exactly"[1] is called an astronomical unit (au).

"Beyond the Solar System the distances in astronomy are so great that using the au becomes too cumbersome."[1]

## Days

"The IAU also defines other astronomical units: the astronomical unit of time is 1 day (d) of 86,400 SI seconds (s) (SI is the International System of Units)."[1]

## Masses

"The astronomical unit of mass is equal to the mass of the Sun, [${\displaystyle M_{\odot }}$], 1.9891 × 1030 kg."[1]

${\displaystyle M_{J}=1.8986\times 10^{27}kg}$

${\displaystyle M_{S}=5.6846\times 10^{24}kg}$

${\displaystyle M_{U}=5.6846\times 10^{24}kg}$ and

${\displaystyle M_{N}=1.0243\times 10^{26}kg}$

## Parsecs

This sketch illustrates the definition of the parsec unit. Credit: jd.

The IAU recognises several other distance units to be used on different scales. For studies of the structure of the Milky Way, our local galaxy, the parsec (pc) is the usual choice. This is equivalent to about 30.857 × 1012 km, or about 206,000 aus, and is itself defined in terms of the au – as the distance at which one Astronomical Unit subtends an angle of one arcsecond.

Def. a unit of length, used in astronomy, defined as the distance from the Earth [T in the second image down on the right] of an object that exhibits a parallax of 1 arcsecond is called a parsec, or a parallax second.

## Light-years

"Alternatively the light-year (ly) is sometimes used in scientific papers as a distance unit, although its use is mostly confined to popular publications and similar media. The light-year is roughly equivalent to 0.3 parsecs, and is equal to the distance traveled by light in one Julian year in a vacuum, according to the IAU. To think of it in easily accessible terms, the light-year is 9,460,730,472,580.8 km or 63,241 au. While smaller than the parsec, it is still an incredibly large distance."[1]

Def. "9,460,730,472,580.8 km" is called the light-year (ly).[1]

1 Parsec = 3.08568025 × 1016 meters = 3.2616 light-years.

## Years

"Defining a unit is often more complex than first appears. For instance, to define a light-year it is necessary to understand exactly what a year is. When referring to a year in the precisely defined astronomical sense, it should be written with the indefinite article “a” as “a year”. Although there are several different kinds of year, the IAU regards a year as a Julian year of 365.25 days (31.5576 million seconds) unless otherwise specified. The IAU also recognises a Julian century of 36,525 days in the fundamental formulas for precession (more info). Other measurements of time such as sidereal, solar and universal time are not suitable for measuring precise intervals of time, since the rate of rotation of Earth, on which they ultimately depend, is variable with respect to the second."[1]

## Theoretical astronomical units

Def. a standard measure of a quantity is called a unit.

## Lengths

This is a foldable, or pliant, wood, double meter, or double-meter stick. Credit: Isabelle Grosjean ZA.
This is a scanning electron micrograph of a gold nanowire 30 nm x 21.57 µm. Credit: Goldnanoparticles.
This is an integrated circuit die image. Credit: ZeptoBars.
HRTEM lattice images and electron diffraction patterns (top-right insets) are taken along the [0001] direction. Credit: Materialscientist.
Image size is 1,750 x 810 pm. Credit: Boris J. Albers, Todd C. Schwendemann, Mehmet Z. Baykara, Nicolas Pilet, Marcus Liebmann, Eric I. Altman and Udo D. Schwarz.
The symmetry of the protrusions in this image can only be explained by identifying them with the locations of the atoms in the lattice. Credit: Boris J. Albers, Todd C. Schwendemann, Mehmet Z. Baykara, Nicolas Pilet, Marcus Liebmann, Eric I. Altman and Udo D. Schwarz.

Def. a basic unit of length in the International System of Units (SI: Système International d'Unités) is called a metre, or meter.

Def. a unit of length; the thousandth part of one millimeter; the millionth part of a meter is called a micron.

"As one spacecraft lurches and drags through the Earth's uneven gravity field, the second follows 210 km behind, measuring changes in their separation to the nearest micron (a thousandth of a millimetre)."[2]

Def. an SI subunit of length equal to 10-9 metres is called a nanometre.

The second image down on the right is an integrated circuit die image of a STM32F103VGT6 ARM Cortex-M3 MCU (microcontroller) with 1 Mbyte Flash, 72 MHz CPU, motor control, USB and CAN. Die size is 5339x5188 µm. View is from a Scanning Electron Microscope looking at the 180 nanometre SRAM cells on the die.

The third image down on the right is a high-resolution, transmission electron micrograph (HRTEM) lattice image with an electron diffraction pattern (top-right inset) taken along the [0001] direction; i.e., looking down the [0001] axis. An image simulation is added in the bottom-left inset, and a model fragment of the crystal structure is on the right of the bottom-left inset. On the lower right of the composite image is a 1 nanometre (nm) marker.

Def. 10-12 of a metre is called a picometre.

The fourth lower image down on the right has an image of 1,750 x 810 pm.[3]

It is an atomic force microscope image of stacked graphene sheets in graphite.[3]

This compares with the image on the left which was taken at a height of ~97 pm above the surface.[3]

The image on the lowest right was at ~12 pm.[3]

For most heights above the surface the features display a three-fold symmetry as on the right.[3]

## Distances

Public meter standard by Chalgrin is from 18th century. Credit: Airair.

The public meter standard by Chalgrin in the image on the right is from the 18th century (36, rue de Vaugirard, 6th arrondissement of Paris, near the Luxembourg Palace). The public could bring meter rulers and check if they were accurate. A bar that just fit between the end stops was exactly one meter.

Def.

1. a "series of interconnected rings or links usually made of metal",[4]
2. a "series of interconnected links of known length, used as a measuring device",[4]
3. a "long measuring tape",[4]
4. a "unit of length equal to 22 yards. The length of a Gunter's surveying chain. The length of a cricket pitch. Equal to 20.12 metres. Equal to 4 rods. Equal to 100 links.",[4]
5. a "totally ordered set, especially a totally ordered subset of a poset",[4]
6. iron "links bolted to the side of a vessel to bold the dead-eyes connected with the shrouds; also, the channels",[4] or
7. the "warp threads of a web"[4]

is called a chain.

Def. a unit of length equal to 220 yards or exactly 201.168 meters, now only used in measuring distances in horse racing is called a furlong.

Def.

1. a trench cut in the soil, as when plowed in order to plant a crop or
2. any "trench, channel, or groove, as in wood or metal

is called a furrow.

Def. the distance that a person can walk in one hour, commonly taken to be approximately three English miles (about five kilometers) is called a league.

Def. an SI unit of length equal to 103 metres is called a kilometre, or kilometer.

## Times

Def. a period of fourteen nights; two weeks is called a fortnight.

Def. a period of seven nights; a week is called a sennight.

Def.

1. any period of seven consecutive days,
2. a period of seven days beginning with Sunday or Monday,
3. a subdivision of the month into longer periods of work days punctuated by shorter weekend periods of days for markets, rest, or religious observation such as a sabbath, or
4. seven days after (sometimes before) a specified date

is called a week.

## Physical units

Both physics and astronomy use units and dimensions to describe observations.

Units of Physics and Astronomy
Dimension Astronomy Symbol Physics Symbol Conversion
time 1 day d 1 second s 1 d = 86,400 s[5]
time 1 "Julian year"[6] J 1 second s 1 J = 31,557,600 s
distance 1 astronomical unit AU 1 meter m 1 AU = 149,597,870.691 km[5]
angular distance 1 parsec pc 1 meter m 1 pc ~ 30.857 x 1012 km[5]

## Hypotheses

1. Units have changed over time.