Although the methods used differ greatly it amazing that measurements, of the distances of the Earth from the sun and the moon, made thousands of years ago are very similar to modern days.
Eratosthene was a Greek mathematician that lived in the 3rd century BC (276-195 BC). He was the first person; to record the circumference of the Earth, to prove the Earth was round, calculated the tilt of the Earth’s axis and quite accurately measured the distance of the Earth from the sun. He calculated the circumference of the Earth using shadows. He noticed one day that sunlight shone directly down a well and he was able to see the bottom. This meant that the sun was directly above the well at that time and he realised that if he were to place a stick in the ground next to the well it would cast no shadow. However, a stick in a different city father north would cast a shadow and if he knew the distance between the two cities then he could measure the angle of the shadow and use this to calculate the circumference of the Earth.
In fact Erathosthene’s calculation of the Earth’s circumference was incredibly close to our modern day measurement. He calculated the Earth’s circumference as 39,690km compared to modern day measurement of 40,0009km. Knowing the size of the Earth is important for understanding size and distances of other planets.
Aristarchus was another Greek astronomer and mathematician that calculated the distance of earth from the sun and the moon. He used shadows and trigonometry to work out the distances. He hypothesised that the moon received its light from the sun and that moon’s movements indicated that it was a sphere, hence when there is a half moon the angle E-M-C (Earth- Moon- Sun) is 90°, he could then measure the angle M-E-C (Moon- Earth- Sun) and using that information he would be able to calculate the distance of the sun from the earth. He measured the angle MEC as 87° which is infact 89°. It is impressive he was so close, as it is difficult to determine the centre of the moon and also to determine when the moon is exactly half full. Although his answer was not correct his method indicated that the sun is larger than the moon.
The understanding of how far away planets are was affected by the models of the universe. Aristarchus’s theory of a sun-centred universe was rejected at the time and was not a popular theory until Copernicus’s time, 17 centuries later. Later, when telescopes were invented, Copernius was able to make rather accurate measurements of the distances of the planets from the earth.
Today the distances between planets is measured in a more scientific and technological approach. The main method used to calculate the distance between planets in the 21st century is the use of spaces probes orbiting a planet. These space probes can transmit radio waves, which have a definite speed, so we know how far they travel a set time (usually recorded in seconds). With this we can work out how far planets are, as we know when the radio wave was transmitted and when we receive the wave transmission back on the surface of Earth, we can work out how long the wave took to travel, and therefore the distance.
Distance = speed of the radio wave times the time taken to receive the wave (after transmission).
d = s x t
Distance is measured in metres (m).
Speed is measured in metres per second (ms-1).
Time is measured in seconds (s).
The radio wave transmitted by the space probe travels at 300,000 metres per second. It takes 23 seconds for the wave to reach Earth. Therefore the distance between the Earth and Planet X is = 300,000 metres times 23 seconds which equals 6,900,000 metres. The distance between the space probe and Planet “X” also has to be taken into account, as well as the radius of the Earth (r).
The unit used as the standard distance between planets is called the Astronomical Unit (AU). This is the average distance between the Earth and the Sun which is around 149,597,870.7 kilometers. So therefore 1 AU = 149,597,870.691 kilometres.
The accuracy of this system is much greater than that of measurements done by the ancient Greek Copernicus. This is because we know very precise details about the speed of waves and we have extremely accurate timing systems (often going into lots of decimal points!). This therefore allows us to calculate very exact distances between planets.
Having said that, the general measurements that were observed thousands of years ago are surprising close to modern day equivalents, even though with the measurements of further out planets are not completely accurate, they are very close, remember these measurements were taken over 2200 years ago!
A limitation to this system of measuring is the amount of time taken for such probes to be constructed and launched, let alone the vast amount of time for the probe to get in position around a planet. Other limitations include the delay between the command from Earth to the probe to transmit the radio wave (think of the diagram above, but in reverse!).
References:
Kitty Ferguson, (2000), Measuring the Universe, London, headline book publishing
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