junctions with the inner moon in the course of its lunar day. It is likewise evident that the outer satellite will frequently be above the horizon of Mars more than sixty hours, during which period six conjunctions with the inner may occur. Moreover, as the outer moon will go through its cycle of phases in a little more than thirty hours, all of these changes may be accomplished while it is above the horizon of the observer on the surface of Mars.
The apparent diameter of Mars, as seen by an observer on the inner satellite, would be no less than 41·8°, or about seventy-eight and a half times the apparent diameter of the sun as seen from the earth; and from the outer moon the diameter of Mars would subtend an angle of 16·7°, or about 31·3 times the apparent diameter of the sun as seen by us. Of course the apparent areas of the disk of Mars, as seen from his two satellites, would be in the ratio of the squares of these numbers, that is, the apparent area of the disk of Mars, as seen from his inner moon, would be 6,167, and from the outer 980 times the apparent area of the solar disk, as seen from the earth.
From the innermost satellite of Saturn, the diameter of the primary would subtend an angle of 35·8°; from the nearest satellite of Jupiter, the diameter of that planet would subtend an angle of 18·6°; and from our moon the earth's diameter would subtend an angle of less than 2°.
Astronomers are, as yet, ignorant of the real magnitude of the Martial satellites; but, assuming each of them to be one hundred miles in diameter, it is easy to calculate their apparent magnitudes as seen by an observer on Mars.[1] The inner moon being 5,733 miles distant from the center of Mars, would, when in the zenith of the observer, be only 3,633 miles distant from the surface of the planet. Hence it appears that, when this satellite is seen in the horizon of the observer on the surface of Mars, its diameter would subtend an angle of about 60', or nearly twice the apparent diameter which our moon presents to us; but, when it is in the zenith of the observer, it would subtend an angle of 94·3', or more than three times the apparent diameter presented by our moon. In other terms, in rising from the western horizon to the zenith, the apparent diameter of this moon would be increased nearly in the ratio of two to three; and, of course, its apparent area would be augmented nearly in the ratio of four to nine.
- ↑ Professor E. C. Pickering, of the Harvard College Observatory, has attempted to determine the real magnitude of the satellites of Mars, by comparing the intensity of the light reflected from the primary with that reflected from each of his satellites. He is thus led to estimate the diameter of the inner satellite to be about seven miles, and that of the outer one to be about six miles! ("Annual Report of the Director of Harvard College Observatory," November, 1877, page 17.) It is very questionable whether estimates, founded on photometrical comparisons in which the relative reflecting powers of the bodies compared are unknown, can inspire the confidence of astronomers in relation to the accuracy of the deduced diameters.
