Fig. 148.
Let V, in Fig. 148, represent the position of Venus at its greatest elongation from the sun, S the position of the sun, and E that of the earth. The line EV will evidently be tangent to a circle described about the sun with a radius equal to the distance of Venus from the sun at the time of this greatest elongation. Draw the radius SV and the line SE. Since SV is a radius, the angle at V is a right angle. The angle at E is known by measurement, and the angle at S is equal to 90°- the angle E. In the right-angled triangle EVS, we then know the three angles, and we wish to find the ratio of the side SV to the side SE.
The ratio of these lines may be found by trigonometrical computation as follows:—
VS : ES = sin SEV : 1.
Substitute the value of the sine of SEV, and we have
VS : ES = .723 : 1.
Hence the relative distances of Venus and of the earth from the sun are .723 and 1.
Superior Planets.
131. The Superior Planets.—The superior planets are those which lie beyond the earth. They are Mars, the Asteroids, Jupiter, Saturn, Uranus, and Neptune.