Astronomical unit

The gray line indicates the distance between the Earth and the Sun that is, on average, an astronomical unit (AU).

The astronomical unit (abbreviated ua, au, AU or AU) is a unit of length equal, by definition, to 149,597,870,700 m, which is approximately equivalent to the average distance between the Earth and the Sun. This definition has been in force since the general assembly of the International Astronomical Union (IAU) of August 31, 2012, in which the «Gaussian» definition used since 1976, which was «the radius of a Newtonian circular orbit free of disturbances around the Sun described by a particle of infinitesimal mass that moves averaging 0.01720209895 radians per day."

The symbol UA is the one recommended by the International Bureau of Weights and Measures and by the international standard ISO 80000, while au is the only one considered valid by the UAI, and the most common in English-speaking countries. It is also common to see the symbol written in capital letters, UA or AU, despite the fact that the International System of Units uses capital letters only for the symbols of the units that carry the name of a person

The name comes from the 16th and 17th centuries, when the absolute distances between the bodies of the solar system were not yet accurately calculated, and only the relative distances were known taking as a standard the average distance between the Earth and the Sun, which was called astronomical unit. It was even stated that the day this value was measured, "the size of the universe would be known."

History

A direct antecedent of the astronomical unit can be found directly in the demonstrations of Nicholas Copernicus (also known as “Copernicus”) for his heliocentric system in the 16th century. In volume V of his book De Revolutionibus Orbium Coelestium (1543) he calculated, using trigonometry, the relative distances between the then known planets and the Sun, based on the distance between the Earth and the Sun. By measuring the angles between the Earth, the planet and the Sun at the moments in which they form a right angle, it is possible to obtain the Sun-planet distance in astronomical units. This was one of his demonstrations to prove that the planets, including the Earth, revolved around the Sun (heliocentrism), ruling out Claudius Ptolemy's model which postulated that the Earth was the center around which the planets and the Sun revolved (geocentrism).. He thus established the first relative scale of the solar system using the distance between the Earth and the Sun as a standard.

Later, Johannes Kepler, based on the careful observations of Tycho Brahe, established the laws of planetary motion, which are justly known as “Kepler's laws”. The third of these laws relates the distance of each planet from the Sun to the time it takes to travel its orbit (that is, the orbital period) and, as a consequence, establishes an improved relative scale for the solar system: for example, it is enough to measure how many years does it take Saturn to orbit the Sun to know what is the distance of Saturn from the Sun in astronomical units. Kepler estimated the sizes of the planetary orbits with very good precision; for example, he fixed the distance between Mercury and the Sun at 0.387 astronomical units (the correct value being 0.389), and the distance from Saturn to the Sun at 9.510 astronomical units (the correct value being 9.539). However, neither Kepler nor any of his contemporaries knew how much this astronomical unit was worth, and therefore were completely ignorant of the actual scale of the known planetary system, which at the time extended as far as Saturn.

Based on Kepler's laws, it was enough to measure the distance of any planet from the Sun, or from the Earth, to know the astronomical unit. In 1659 Christian Huygens measured the angle that Mars subtends in the sky and, attributing a value to the diameter of this planet, estimated that the astronomical unit should be 160 million kilometers, that is, seven times greater than that estimated by Kepler, but of made less than 10% above the actual value. However, this measurement was not accepted, since, as Huygens himself recognized, everything depended on the value that one attributed to the size of Mars. Curiously, Huygens guessed with remarkable accuracy the size of Mars.

Another more reliable method was known, but it required measurements that were very difficult to perform: the parallax method. If two people located at points far from Earth, say in Paris, France, and Cayenne, French Guiana, simultaneously observe the position of a planet in the sky in relation to the background stars, their measurements give a small difference that It corresponds to the angle that the Paris-Cayenne line would subtend seen from the planet. Knowing this angle, and the Paris-Cayenne distance, the value of the astronomical unit can be deduced. In practice there were three difficulties: first, distances on Earth were not well known; second, the measurement of time was not precise enough to allow simultaneous measurements between points far apart; and third, the measurement of the apparent position of the planet in the sky had to be very precise. More than half a century passed before it was possible to measure the parallax of a planet: in 1672 Jean Richer traveled to Cayenne to measure the position of Mars in the sky at the same instant that his colleagues in Paris were doing the same. Richer and his colleagues estimated the value at 140 million kilometers.

Over time, more accurate and reliable methods were developed to estimate the astronomical unit; in particular, the one proposed by the Scottish mathematician James Gregory and by the British astronomer Edmund Halley (the same as the comet), is based on measurements of the transit of Venus or Mercury on the solar disk and was used until the beginning of the century XX. Contemporary measurements are made with laser or radar techniques and give the value 149,597,870 km, with an apparent error of one or two kilometers.

Difference between the astronomical unit and the actual orbit of the Earth

Newton reformulated Kepler's third law. A planet of mass m, orbiting the sun of mass M, in an ellipse with semi-major axis a and with a sidereal period T, check the equation

k2(m+M)T2=4π π 2a3{displaystyle k^{2}(m+M)T^{2}=4{pi }^{2}a^{3,!}

The German mathematician Carl Friedrich Gauss (1777-1855) used the solar mass as the unit of mass for his calculations of the dynamics of the solar system, the mean solar day as the unit of time, and the semi-major axis of the distance as the unit of distance. earth orbit. Using these units, the above equation is written as

k2(1+M)T2=4π π 2a3,{displaystyle k^{2}(1+M)T^{2}=4{pi }^{2}a^{3},,}

Where k is known as the Gaussian gravitational constant. Gauss used the estimated values in his time

T=365,2563835days{displaystyle T=365,2563835{mbox{ days}},!}

M=365710Earth masses{displaystyle M=365710{mbox{ masses terrestrial}},!}

Gauss recognized that the problem with this definition was that when the sidereal year and the mass of the Sun were determined with better precision, the value of k would change. In 1938, the International Astronomical Union (IAU) adopted the value of the Gaussian gravitational constant (and the astronomical unit derived from it) as a definition in astronomy. However, with the precision of current measurements, it is known that the sidereal year is 56 seconds shorter than the known value in Gaussian times, and that the semimajor axis of Earth's actual orbit is about 17 km smaller than the astronomical unit.

At the August 2012 general assembly of the International Astronomical Union in Beijing, it was decided to cancel the Gaussian definition and give the astronomical unit the current value of 149,597,870,700 meters.

Examples

• La Voyager 1 is currently the object made by man farther from Earth. Being more than 140 ua from this, it is estimated that it moves away at a speed of 3,592 ua per year.

Some conversion factors:

• 1 ua = 149 597 870 700 meters = 149 597 870.7 kilometers.
• 1 ua = 499,00478362 seconds light ≈ 8,317 minutes light.

The following table shows some distances taken in astronomical units. It includes some examples with approximate distances because they are too small or too far apart. Distances change over time. It can also be ordered as the distance increases.