Historically, the first known person to use geometry to estimate the Earth-Sun distance was Aristarchus (c. (However, Mars and the outer planets are more complicated.) Similar observations and calculations yield the relative distance between the Sun and Mercury. The greatest elongation of Venus is about 46 degrees, so by this reasoning, the Sun-Venus distance is about 72% of the Sun-Earth distance. (distance between Venus and the Sun) = a × sin(e) Similarly, with a little more trigonometry: (distance between Earth and Venus) = a × cos(e) Now, using trigonometry, one can determine the distance between Earth and Venus in terms of the Earth-Sun distance: In the diagram, this angle will be the Sun-Earth-Venus angle marked as "e" in the right angled triangle. One can also measure the angle between the Sun and Venus in the sky at the point of greatest elongation.
Now, by making a series of observations of Venus in the sky, one can determine the point of greatest elongation. This, by the way, is the reason why Venus is never visible in the evening sky for more than about three hours after sunset or in the morning sky more than three hours before sunrise. (More formally, these are the two points at which the angular separation between Venus and the Sun, as seen from Earth, reaches its maximum possible value.)Īnother way to understand this is to look at the motion of Venus in the sky relative to the Sun: as Venus orbits the Sun, it gets further away from the Sun in the sky, reaches a maximum apparent separation from the Sun (corresponding to the greatest elongation), and then starts going towards the Sun again. These two points indicate the greatest elongation of Venus and are the farthest from the Sun that Venus can appear in the sky. At these points, the line joining Earth and Venus will be a tangent to the orbit of Venus. From the representation of the orbit of Venus, it is clear that there are two places where the Sun-Venus-Earth angle is 90 degrees.
Take a look at the diagram below (not to scale). To a first approximation, the orbits of Earth and Venus are perfect circles around the Sun, and the orbits are in the same plane. (For instance, what is the ratio of the Jupiter-Sun distance to the Earth-Sun distance?) So, let us say that the distance between Earth and the Sun is "a". The first step in measuring the distance between the Earth and the Sun is to find the relative distances between Earth and other planets. Before radar, astronomers had to rely on other (less direct) geometric methods. Since 1961, we have been able to use radar to measure interplanetary distances - we transmit a radar signal at another planet (or moon or asteroid) and measure how long it takes for the radar echo to return. Then we use what we know about the relations between interplanetary distances to scale that to the Earth-Sun distance. Short version: What we actually measure is the distance from the Earth to some other body, such as Venus. How do astronomers calculate the distance of the Sun from the Earth, or the actual size of the Sun, or the speed of travel of Earth in its orbit around the Sun? Clearly, from an answer to one of these questions one can find out the answers to the others.