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The Structure of our Universe

Basic Measures in Astronomy

Astronomy has it own units of measure. They are the natural units for conducting scientific research from Earth-based observatories, and they persist despite technological developments that make them superfluous. The values of the standard units of measure are given in the table below in terms of cgs units (centimeters, grams, and seconds). The values are from the compilation of constants by Yoder (1995).[1] Go to table.

Astronomical Measures

Astronomical Unit (AU)

1.495978706×1013 cm

Parsec

3.085677580×1018 cm

206,264.81 AU

3.262 ly (Julian)

Mean Solar Day (d)

86400 s

Mean Sidereal Day

86164.09054 s

Tropical Year

365.2421897 d

Sidereal Year

365.25636 d

The Astronomical Unit (AU) is the mean radius of Earth's orbit around the Sun. The AU is a natural unit because the relative distances between the planets is easily derived by applying Euclidean geometry to the observations of planetary motions. The expression of the AU in metric units, however, requires additional physics, such as knowledge of the speed of light. The value of the AU in metric units is therefore a modern result.

The parsec is the standard unit of length for expressing the distance to a star. This word is derived from “parallax arc-second”, which shows the unit's origin. The distances to the closest stars are determined by measuring how they move relative to very distant stars over the course of a year. As Earth orbits the Sun, the nearby stars appear to move relative to the distant stars. By measuring the angle that a star moves for a baseline of 1 AU, one can derive a distance by taking the inverse of the angle. If the angle is measured in units of arc second, then the distance derived from this inverse is in units of parsec. A star at one parsec distance would move 1 arc second in angle on the sky when Earth moves 1 AU perpendicular to the line of sight to the star. Over the course of a year, a 1 parsec star moves by 2 arc seconds across the sky, because the baseline is the diameter of Earth's orbit, which is 2 AU. That said, understand that no star is this close to the Solar System.

The second value for the length of the parsec is expressed in Julian light years (the distance light travels in a Julian year of 365.25 days). Astronomers never use light years in their research—the light year is simply a tool for grasping the immense distances between the stars.

Time is a complicated topic in astronomy because some of the primary time standards are defined in ways that make them vary. Earth's wobble, the precession of Earth's rotation axis, and the slowing of Earth's rotation from tidal interactions with the Sun and Moon make the day and the year vary. There is also the issue of how one determines the starting point of a day or a year: relative to a fixed point in the sky, or relative to a point that moves over time.

The physicist's measure of time is the second, which is defined in terms of the transition between two atomic states of cesium 133. The mean solar day, which is approximately the time for a complete rotation of Earth relative to the Sun, is defined by fiat as 24 hours, with hours and minutes defined in the standard way. The standard that is broadcast by time stations differs slightly from the mean solar day; this standard is Coordinated Universal Time (UTC), or more commonly Greenwich Mean Time (GMT). UTC is kept by atomic clocks. Usually the UTC day is the mean solar day, but occasionally a leap second is added to correct for the drift caused by the slowing of Earth's rotation. UTC midnight is always within 0.9 seconds of true midnight. The time of a complete rotation of Earth relative to a point on the sky is called a sidereal day; this is measured relative to the first point of Aries (the vernal equinox),[ 2] which is a point on the sky that slowly moves as the Earth's rotation axis precesses. The mean value of the sidereal day is shorter than the Julian day by 3 minutes 55.9 seconds. The tropical year, which is the year that the Gregorian calendar is based on, is measured relative to the first point of Aries. The sidereal year is measured relative to a fixed point in space; quasars are used as the reference points.

Positions on the sky are measured in terms of right ascension (RA or α) and declination (dec. or δ). These correspond to longitude and latitude on Earth. The declination is measured in degrees relative to the celestial equator, which is the projection of Earth's equator onto the sky. The declination of the equator is 0°, the declination of the north pole is 90°, and the declination of the south pole is −90°. The right ascension is defined in units of time, with 0 hour at the first point of Aries, and the value of the right ascension at the zenith increasing as time passes. A full circle of the equator corresponds to 24 hours. Right ascension was defined to make finding objects with a telescope easier: the right ascension at the zenith changes by one hour in one hour of sidereal time.

Because the precession of Earth's rotation axis causes the first point of Aries to moves along the equator over time, the right ascension and declination of the stars change with time. To counteract this, astronomers traditionally express the positions of stars for the coordinate system of a particular date. Currently current standard is Epoch 2000, or the coordinate system for January 1, 2000. Epoch 1950 was used previously.

[1] Yoder, Charles F. “Astrometric and Geodetic Properties of Earth and the Solar System.” In Global Earth Physics: A Handbook of Physical Constants edited by T.J. Ahrens, 1–31. AGU Reference Shelf, No. 1. Washington: American Geophysical Union, 1995.

[2] The equinoxes are the two points in the sky where the celestial equator and the ecliptic (the path in the sky that the Sun appears to travel along) cross. The Sun crosses the first point of Aries, or the vernal equinox, at the end of spring, and it crosses the first point of Libra, or the autumnal equinox, at the end of fall. While at one time long ago the equinoxes were in the constellations Aries and Libra, they are now in the constellations of Pisces and Virgo because of the precession of Earth's rotation axis.

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