Astronomical distances

Astronomers use special equations and measuring methods to determine distances in the universe and our solar system. Calculations in meters or kilometers will always result in very large figures, for example the nearest galaxy is the Andromeda galaxy, which is located at a distance of 21 quintillion km (21.000.000.000.000.000.000 km) away. Such a large figure is difficult to comprehend, when expressed in lightyears, the distance is 2.2 million lightyears, which is much easier to read.

A Lightyear.
The speed of light is the universal maximum velocity, approximately 300,000 km/second.

To comprehend how fast this is, just image that ifyou were to travel around the Earth at the speed of light, you would make 7.5 complete rotations in only one second.

Distances in the universe are incredibly large, to make calculations easier distances are measured in lightyears. This is the distance traveled at the speed of light in one year, approximately 9.5 trillion kilometers (9,500,000,000,000 km).

Parallax.
In astronomy the apparent shift in position of (nearby) stars against the background of more distant stars is used to determine the distance of a star. As a result of the motion of Earth in its orbit around the Sun, a star, observed from Earth, will shift against its background. This is called a parallax, which is the angle of shift and is measured in distance.

By measuring twice, with an interval of six months (exactly half an orbit around the Sun) the distance can be measured in arc seconds.

A full circle is 360 degrees, one degree is subdivided in 60 minutes, and one minute is subdivided in 60 arc seconds, so a circle is divided into 1,296,000 arc seconds.

This is a standard measure, which is often used is the parsec, which is the distance were a star's parallax is equal to 1 arc second. This distance equals 3.26 lightyears, so approximately 31 trillion kilometer (31,000,000,000,000 km). A parsec also equals approximately 206,000 Astronomical Units.

Astronomical Unit.
Making calculations in lightyears within our own solar system is not that handy. These distances are too small, for examle the Sun is positioned only 8 lightminutes away from Earth. For easy calculations within our solar system a much smaller unit is used: the Astronomical Unit or AU. This is the average distance between the Earth and the Sun, about 150 million km (150,000,000 km). Pluto for instance is placed at 40 AE from the Sun.

On the image below the position of a comet is indicated against the Sun and Earth. By means of the Astronomical Unit we can determine the length of its tail.

The distance between Earth and Sun (SE) is by definition 1 AU. The orbit of a comet is generally known, we also know the distance between the comet and the Sun (SC). Furthermore, it is not too difficult to measure the angles between the Sun and the comet (SEC) and between the Sun and the tip of the tail of the comet (SET).

Suppose one certain day SC = 0.68 AU and the following angles are being measured:
SEC = 33º and SET = 48º. Then we may determine the length of the comet's tail:

SE / sin(SCE) = SC / sin(SEC)
so: 1 AU / sin(SCE) = 0.68 AU / sin(33º) » SCE = 52º

now we know : CSE = 180º - SCE - SEC = 95º
and so STE = 180º - CSE - SET = 37º

SE / sin(STE) = ST / sin(SET)
so: 1 AU / sin(37º) = ST / sin(48º) » ST = 1.2 AU

The length of the tail is: CT = ST - SC = 0,52 AU = 78 million km.

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