The Parallax of the annual Orb, or the greatest elongation of the Earth’s orbit seen from any of the superior Planets, being given; the distance of that Planet from the Sun, in respect of the Earth’s distance from him, may be found by the same methods as the distances of the inferior Planets were. Thus, to find the distance of _Mars_ from the Sun, it will be as the Sine of the angle S ♂ A is to the _Radius_, so is the distance AS (the distance of the Earth from the Sun) to S ♂, the distance from the Sun to _Mars_. After the same manner the distances of _Jupiter_ and _Saturn_ are also found. The mean distance of the Earth from the Sun being made 1000, the mean distances of the superior Planets from the Sun are, _viz._ the mean distance from the Sun of
{ ♂ 1524 } { 141 } { ♃ 5201 } and the Excentricity { 250 } { ♄ 9538 } { 547 }
To which, if you add or subtract their mean distances, we shall have the greatest or least distances of those Planets from the Sun.
There are other methods by which the relative distances of the Planets might be found; but that which hath been here illustrated, is sufficient to evince the certainty of that Problem.
[Sidenote: How the absolute distances of the Planets from the Sun are computed.]
[Sidenote: _Parallax_ of the _Earth’s Semidiameter_.]
Hitherto we have only considered the distances of the Planets in relation to one another, without determining them by any known measure; but in order to find their absolute distances in some determinate measure, there must be something given, whose measure is known. Now the circumference of the Earth is divided into 360 degrees, and each of these degrees into 60 Geographical miles, so that the whole circumference contains 21600; and by the known proportion for finding the diameter of a circle from its circumference, the Earth’s diameter will be found to be 6872 miles, and its semidiameter 3436 miles. The Parallax of the Earth’s semidiameter, or the angle under which it is seen from a certain Planet, may be found by comparing the true place of the Planet, as it would be seen from the center of the Earth (which is known by computation) with its apparent place, as it is seen from some point on the Earth’s surface. Let CZA be the Earth, ZC its semidiameter, ♁ some Planet, and BHT arch of a great circle in the Heavens, at an infinite distance. Now the Planet ♁ will appear from the Earth’s center C, in the point of the Heavens H; but a spectator from the point Z upon the Earth’s surface, will see the same object ♁ in the point of the Heavens B; and the arch BH the difference, is equal to the angle B ♁ H = Z ♁ C, the _Parallax_; which being known, the side C ♁ the distance of the Planet from the center of the Earth, at that time, may be easily found. Now if this distance of the Planet from the Earth be determined, when the centers of the Sun, the said Planet, and of the Earth, are in the same right line, we have the absolute distance of the Planet’s orbit from the Earth’s in known measure; then it will be, as the relative distance betwixt the Earth’s orbit and that of the Planet is to the relative distance of the said Planet from the Sun; so is the distance of the Planet’s orbit from the Earth’s in known measure to the distance of the said Planet from the Sun in the same measure: Which being known, the distance of all the other Planets from the Sun may be found. For it will be, as the relative distance of any Planet from the Sun, is to its distance from him in a known measure; so is the relative distance of any other Planet from him to its distance in the same measure. This may be done by finding the distance of the Planet _Mars_, when he is in opposition to the Sun, after the same manner as we find the distance of a tree, or the like, by two stations.