Conversion from 3 Astronomical units to Centimeters

Information about the Astronomical unit (au)

The astronomical unit is a length equal to exactly 149,597,870,700 metres, or very nearly 150 million kilometres. The symbol is au. It approximates the mean distance between the Earth and the Sun and is the standard measure for distances within the solar system.

The unit was originally defined by that orbital relationship rather than by a fixed number. Earlier definitions tied it to the properties of a hypothetical body orbiting the Sun, which meant its value depended on the gravitational constant and was subject to revision as measurements improved. The International Astronomical Union ended that dependence in 2012 by fixing the astronomical unit as an exact number of metres. The change simplified calculations and removed an inconvenience: a unit whose length shifted whenever a physical constant was refined.

Determining its value was one of the great problems of observational astronomy. Transits of Venus across the Sun's disc, observed from widely separated points on Earth, allowed the distance to be triangulated. Expeditions were mounted for the transits of 1761, 1769, 1874 and 1882, and James Cook's first Pacific voyage was organised around the 1769 event. Radar ranging to Venus in the 1960s eventually settled the figure far more precisely than any optical method.

The unit makes solar system distances legible. Mercury orbits at 0.39 au, Mars at 1.52 au, Jupiter at 5.2 au and Neptune at 30.1 au. The Kuiper Belt extends to roughly 50 au. Voyager 1, the most distant human-made object, has passed 165 au. Light takes about 499 seconds to cover one astronomical unit, so the Sun is a little over eight light minutes away.

Beyond the solar system the unit becomes unwieldy, and astronomers switch to light years and parsecs. One parsec is 206,265 au.

Spacecraft navigation depends on the unit being exact rather than approximate. Trajectories to the outer planets are computed over distances of tens of astronomical units, and an error in the length of the unit itself would propagate into every position calculation. Fixing the value in 2012 removed that source of drift from the ephemerides used for mission planning.

One astronomical unit equals 149,597,870.7 kilometres, or about 92.956 million miles.

Information about the Centimeter (cm)

The centimetre is one hundredth of a metre, written cm. Among the metric subdivisions it is the one people reach for most readily in daily life, occupying the range where objects are small enough to hold but too large to measure comfortably in millimetres.

Body measurement is its most common application. Height, waist, chest and inside leg are recorded in centimetres across most of the world, and clothing is sized accordingly. Paediatric growth charts plot height and head circumference in centimetres against age. Rainfall over long periods, snow depth and the dimensions of furniture and luggage are all reported the same way.

The unit had a formal role in science for nearly a century. The centimetre-gram-second system, adopted by the British Association for the Advancement of Science in 1874, took the centimetre as its base unit of length. CGS units such as the erg, the dyne and the gauss were standard in physics until the metre-kilogram-second system displaced them, and SI formally superseded CGS in 1960. Some CGS units persist in astronomy and in parts of electromagnetism.

Volume follows naturally. A cubic centimetre, written cm³ or cc, equals exactly one millilitre. Engine displacement is often quoted in cubic centimetres, particularly for motorcycles, and medical syringes are marked the same way.

Despite its usefulness, the centimetre sits awkwardly in engineering practice. Technical drawings prefer millimetres precisely to avoid mixing units that differ by a factor of ten, since a misplaced decimal point between the two is a plausible and expensive error.

Map scales often make the unit explicit. A 1:25,000 map means one centimetre on the paper represents 25,000 centimetres on the ground, or 250 metres, so four centimetres cover a kilometre. Walkers and orienteers use this relationship constantly, and it is one of the clearer illustrations of why a decimal system is convenient: converting between the two scales requires only moving a decimal point.

Two well-known wavelengths fall in this range and are named by it. Neutral hydrogen radiates at 21 centimetres, a line predicted in 1944 and detected seven years later, and because hydrogen fills the galaxy that single wavelength has mapped the spiral arms of the Milky Way and the rotation curves that first indicated dark matter. Domestic microwave ovens work at 12.2 centimetres, chosen from a band set aside for industrial and medical use rather than for any special resonance with water. In both cases the centimetre is the natural unit because the wave is the size of a hand.

One centimetre equals 10 millimetres or 0.01 metres, and is very close to 0.3937 inches.