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Part 2 - The Distance to the Sun

From careful observation of the angle between the centres of the Moon and the Sun at the waxing or waning Quarter Moon - i.e. when exactly half of the Moons disk (as seen from the Earth) was in darkness - Aristarchus of Samos (c.310 - 230 BC) arrived at relative distances for the Moon and the Sun (see Figure 3). It is notoriously difficult to gauge exactly when the Moon's shadow - the terminator - is at the half way point: after all the Moon's surface is rough and the shadow does not follow a perfectly straight line. Consequently, the angle measured by Aristarchus was quite inaccurate: 87. Even so, the resulting ratio (1/cos 87), showing that the Sun was about 20 times further away than the Moon, provided the first indication that the Sun was an extraordinarily distant object.

Figure 3: Aristarchus' Method for determining the relative distances of the Sun and Moon

Estimates of the Solar Parallax made in antiquity, by astronomers such as Aristarchus, Hipparchus (c.162 - c.126 BC) and Ptolemy (c.140 AD) were still current in the Seventeenth Century. Even the great observational astronomer, Tycho Brahe (1546 - 1601) accepted the traditional value of 3'. In the years to follow however, estimates of this angle decreased its magnitude drastically. Thus the Sun itself was judged to be further and further from the Earth. The corollary to this was that the Sun was becoming even more immense relative to the Earth. Johannes Kepler (1571- 1630) derived a Parallax of less than 1' from his observations of Mars. Around 1630, Vendelinus used a telescope and Aristarchus' method to obtain a more accurate value for the ratio of the Earth-Sun distance and the Earth-Moon distance. His ratio was about 229 (based on an angle of 89.75 ). This was much closer to the modern value of 390.

The Orbits of the Inferior Planets

Relative distances of the inferior planets - Mercury and Venus - compared with the distance to the Sun could be roughly deduced by measuring the angle between the Sun and these planets at their greatest elongation. Nicholas Copernicus (1473-1543) used this method to determine the relative radii of the orbits of Venus and the Earth (see Figure 4). Observation of the movement of Venus had the potential to yield a much richer harvest of information however than had been imagined by Copernicus. In order to understand how this is so, we need to consider in more detail the orbit of Venus.

Figure 4: Venus at Greatest Elongation

The orbits of Mercury and Venus do not lie in the ecliptic plane - i.e. the orbital planes of these planets are at an angle to that of the Earth's orbit about the Sun.

Inferior Planet

Inclination of Orbit





When at inferior conjunction - i.e. when placed between the Earth and the Sun - these planets do not necessarily lie on a straight line from the Earth to the Sun. Only when the inferior conjunction happens to take place virtually at the point where the planet's orbit crosses the Earth's orbital plane will the planet be on such a straight line. During this kind of conjunction the planet will appear to cross the Sun's disk. This is known as a Transit of the planet.

3. Orbital Details of Venus