How do we measure Earth-Sun distance?

How is the distance between Earth and any planet, measured?

Take for example the planet nearest to the Sun, namely, Venus. This distance to Venus can be obtained at any time during its travel by radar measurements.

For this, a pulse of radio wave is transmitted from Earth and is received when it bounces off Venus and comes back to Earth. Since radio waves travel at the speed of light, by measuring the total time taken for the pulse to come back, the distance can be calculated as: Distance = 0.5 X (time taken by radar pulse to travel both ways)X (speed of light)

Now we come to the other question, namely, the measurement of distance between earth and sun. Obviously we cannot use the earlier radar measurements since the sun itself is a source of intense electromagnetic waves and in addition it is too far away from the earth.

But our measurement of distance between planet and earth will become useful for this important measurement. Let us assume that the distance between Earth and the Sun is 'R.' To first approximation, the orbits of Earth and Venus are perfect circles around the Sun. Now, let us consider the orbit of Venus. There are two places where the Sun-Venus-Earth angle is 90 degrees.

At these points, the line joining Earth and Venus will be a tangent to the orbit of Venus. These two points indicate the greatest elongation of Venus and is the farthest that Venus will get away from the Sun in the sky with respect to an earth observer. Now, by making observations of Venus in the sky, one can determine the point of greatest elongation. One can also measure the angle between the Sun and Venus in the sky at the point of greatest elongation. In the diagram, this angle will be the Sun-Earth-Venus angle marked as in the right angled triangle. Now, using the trigonometry, one can determine the distance between Earth and Sun R, in terms of the Earth-Venus distance at this time: R= (Earth–Venus distance at point of greatest elongation)/ Cos . We get the distance between the Sun and Earth to be 1.496x10{+1}{+1}metres (nearly 150million kilometers or 93 million miles!).