But the fixed stars are so distant, that if a line, _eA_, were drawn to a fixed star at the first observation, and a line, _EB_, drawn from the earth to the same fixed star at the second observation, these two lines would be sensibly parallel; that is, the fixed star would be seen in the direction of the line _eA_ at the first observation, and in the direction of the line _EB_, parallel to _eA_, at the second observation. But if Mars were seen in the direction of the fixed star at the first observation, it would appear back, or west, of that star at the second observation by the angular distance _BEA_; that is, the planet would have retrograded that angular distance. Now, this retrogression of Mars during one day, at the time of opposition, can be measured directly by observation. This measurement gives us the value of the angle _BEA_; but we know the rate at which both the earth and Mars are moving in their orbits, and from this we can easily find the angular distance passed over by each in one day. This gives us the angles _ESA_ and _MSA_. We can now find the relative length of the lines _MS_ and _ES_ (which represent the distances of Mars and of the earth from the sun), both by construction and by trigonometrical computation. Since _EB_ and _eA_ are parallel, the angle _EAS_ is equal to _BEA_. _SEA = 180° - (ESA + EAS)_ _ESM = ESA - MSA_ _EMS = 180° - (SEA + ESM)_. We have then _MS : ES = sin SEA : sin EMS._ Substituting the values of the sines, and reducing the ratio to its lowest terms, we have _MS : ES = 1.524 : 1._ Thus we find that the relative distances of Mars and the earth from the sun are 1.524 and 1. By the simple observation of its greatest elongation, we are able to determine the relative distances of an inferior planet and the earth from the sun; and, by the equally simple observation of the daily retrogression of a superior planet, we can find the relative distances of such a planet and the earth from the sun. IV. THE SUN. I. MAGNITUDE AND DISTANCE OF THE SUN. [Illustration: Fig. 154.] 138. _The Volume of the Sun._--The apparent diameter of the sun is about 32', being a little greater than that of the moon. The real diameter of the sun is 866,400 miles, or about a hundred and nine times that of the earth. As the diameter of the moon's orbit is only about 480,000 miles, or some sixty times the diameter of the earth, it follows that the diameter of the sun is nearly double that of the moon's orbit: hence, were the centre of the sun placed at the centre of the earth, the sun would completely fill the moon's orbit, and reach nearly as far beyond it in every direction as it is from the earth to the moon. The circumference of the sun as compared with the moon's orbit is shown in Fig. 154.