The Satellites Of Mars Predictions of Martian Moons

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In the year 1610, J. Kepler predicted that Mars had two satellites. This prediction turned out to be correct, although its basis was highly fortuitous. One of the earliest observations made by Galileo with his telescope was that Jupiter had 4 moons, although it is now known to have 12. Furthermore, it will be recalled from chapter III that Kepler had suspected there might be a missing planet between Mars and Jupiter. Consequently, he suggested the following simple sequence for the successive planets: Venus (no moons), Earth (one moon), Mars (two moons), missing planet (three moons), and Jupiter (four moons). What Kepler would have done had Galileo been able to detect all 12 satellites of Jupiter cannot be imagined.

The idea that Mars might have two satellites was introduced by the British writer Jonathan Swift in his famous satirical work "Gulliver's Travels," published in 1726. There is no doubt, from internal evidence, that Swift was familiar with Kepler's third law relating the period of a satellite to the dimensions of its orbit. Consequently, it is probable that he also knew of the prediction concerning the moons of Mars and adopted it in his description of Lemuel Gulliver's visit to the flying island of Laputa. The inhabitants of Laputa, wrote Swift, "have . . . discovered two lesser stars, or satellites, which revolve about Mars." The idea that Mars has two moons was also mentioned by Voltaire, apparently under the influence of Swift, in his novel "Micromégas," published in 1750.

Discovery of the Satellites

An unsuccessful search for the satellites of Mars was made by William Herschel in 1783 and his failure appears to have convinced astronomers that there were none. Nevertheless, during the 19th century, astronomers continued to look for Martian moons. One of the most careful searches was that of H. L. d'Arrest at the Copenhagen Observatory in 1864, but he was no more successful than his predecessors. The actual discovery of the two satellites of Mars was finally made in 1877 by Asaph Hall at the U.S. Naval Observatory in Washington, D.C.

"In the spring of 1877," wrote Hall, "the approaching favorable opposition of the planet Mars attracted my attention, and the idea occurred to me of making a careful search . . . for a satellite of this planet." The search was commenced in early August, and "on the night of the 11 th, and at half past two o'clock," said Hall, "I found a faint object ... a little north of the planet, which afterward proved to be the outer satellite." Cloudy weather and poor seeing conditions interfered with the observations on subsequent days, but "on August 16, the object was again found . . . and the observations . . . showed that it was moving with the planet. . . . On August 17, while waiting and watching for the outer satellite, I discovered the inner one. The observations of the 17th and 18th put beyond doubt the character of these objects."

In naming the moons of Mars which he had discovered, Hall stated:

Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr. Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars; but in the lines referred to [in the Fifteenth Book of the Iliad] they are personified by Homer, and mean the attendants, or sons of Mars. [According to Bryant's translation] "He [Ares, i.e., Mars] spake, and summoned Fear [Phobos] and Flight [Deimos] to yoke his steeds."

Characteristics of the Satellites of Mars

The moons of Mars differ from Earth's Moon in several respects, and this has led to the belief that they originated in a different manner. The Martian satellites are very small in size and their orbits are close to the parent planet. The planet and its satellites are shown in the photograph in figure 4.6. The positions are correct but the images of the satellites are larger than the actual sizes. Because of the small dimensions of the orbits, which are almost circular, the periods of revolution are quite short. Furthermore, the planes of the orbits of the Martian satellites are very close to the plane of the planet's equator. For Earth's Moon, however, there is an inclination of nearly 7 degrees between the orbital plane and Earth's equatorial plane.

The Martian satellites are too small for their sizes to be determined directly from measurements of the angular diameters. Highly approximate values have, therefore, been estimated from the brightness and an assumed albedo. In this manner, the diameter of Phobos, the inner moon, is found to be roughly 16 kilometers (10 miles) and that of Deimos, the outer moon, is only about 8 kilometers (5 miles).

The orbit of the inner satellite, Phobos, has a small eccentricity, namely 0.02, so that it is almost circular. The average radius of the orbit is 9450 kilometers (5850 miles). Phobos, therefore, is only about 6100 kilometers (3750 miles) from the surface of Mars. These distances may be compared with the average radius of 384 000 kilometers (239 000 miles) of the Moon's orbit around Earth.

It is of interest that the radius of the orbit of Phobos is about 2.8 times the radius of

FIGURE 4.6. The satellites of Mars; the image of the planet was superimposed. (Lowell Observatory photograph.)

Mars; this is almost as close as is theoretically possible. According to the calculations made by the French astronomer E. A. Roche in 1849, a satellite cannot approach closer to the center of its parent planet, having the same density, than 2.44 times the radius of the planet. At shorter distances, tidal forces would overcome the gravitational adhesion and the satellite would disintegrate.

Like the Moon, Phobos revolves around its parent planet in the same direction as the planet rotates (fig. 4.7). The sidereal period of revolution, the time required to make a complete orbit, is 7 hours 39 minutes, less than a third the length of a Martian day. Phobos is the only known satellite in the solar system with a period of revolution that is shorter than the rotational period of its parent planet.

In this connection, Asaph Hall wrote:

For several days the inner moon [Phobos] was a puzzle. It would appear on different sides of the planet in the same night, and at first I thought there were two or three inner moons, since it seemed . . . improbable that a satellite should revolve around its primary [i.e., parent planet] in less time than that in which the primary rotates. To decide this point I watched this moon throughout the nights of August 20 and 21, and saw that there was in fact but one inner moon, which made its revolution around the primary in less than one-third the time of the primary's rotation, a case unique in our solar system.

Because Mars rotates in the same direction as Phobos revolves in its orbit, the synodic period of the satellite, the time between two successive appearances at the same place in the Martian sky (p. 37), about 11 hours 6 minutes, is longer than the sidereal period.

Satellite (Phobos)

FIGURE 4.7. The motion of Phobos (south at top).

Satellite (Phobos)

FIGURE 4.7. The motion of Phobos (south at top).

Thus, to an observer on Mars, the moon Pho-bos would appear to rise and set twice each day. The interval between two successive moonrises or moonsets is the synodic period of a little over 11 hours. Because the period of revolution of the satellite is less than the rotational period of the planet, the observer would see Phobos rise in the west and set in the east. Artificial Earth satellites with sidereal periods of less than 1 day behave in the same manner.

As a result of the proximity of Phobos to its parent planet and of the fact that its orbital plane is inclined at an angle of only 1.13 degrees to the equatorial plane of Mars, the satellite is always below the horizon at high latitudes in both northern and southern hemispheres. Thus, because of the curved surface of the planet, an observer on Mars at a latitude above about 70° N or S could never see the inner moon.

In 1945, the American astronomer B. P. Sharpless reported that an analysis of the motion of Phobos indicated the orbit of this satellite to be slowly shrinking; it appeared as if this moon were gradually spiraling inward toward Mars. Although G. M. Clemence called attention to the doubtful accuracy of the measurements, the matter attracted some interest, especially when the Soviet astrophysicist I. S. Shklovskii suggested in 1959 that Phobos was hollow and was presumably of artificial origin.

From a careful analysis of the observational data obtained at various oppositions from 1877 on, G. A. Wilkins of the Greenwich Observatory in England concluded in 1966 that there is strong evidence against an abnormality in the orbit of Phobos. Nevertheless, he felt that it could not be ruled out completely. Most of the difficulties in interpreting the data arise from errors in the observations, and a final decision must await developments in the theory of orbital motion.

The orbit of Deimos, with an eccentricity of 0.0028, is even more circular than that of Phobos. The orbital radius is some 23 500 kilometers (14 500 miles) and the outer moon is thus roughly 20 000 kilometers (12 000 miles) from the surface of Mars. The sidereal period of revolution of Deimos, also in the same direction as the rotation of the parent planet, is 30 hours 18 minutes, and the synodic period is about 5/2 days.

Because Deimos revolves around Mars in a time period that is only a few hours longer than the planet's period of rotation, the outer moon would appear to a Martian observer to move slowly across the sky, rising in the east and setting some 2/2 days later in the west. Deimos would then be on the other side of Mars and would not be seen for about another 3 days. The time between two successive risings or settings of Deimos is the synodic period of 5yi days.

The angle of inclination of the orbital plane of Deimos to the equatorial plane of Mars varies to some extent as a result of the disturbing action of the Sun. The angle is always small, however, ranging from 0.85 to 2.69 degrees. Because Deimos is farther from Mars than is Phobos, the former can be seen up to latitudes of about 83° N and S. At higher latitudes, near the poles, both moons are always below the local horizon and would not be visible.

Because of their proximity to the parent planet and short periods of revolution, Phobos and Deimos frequently pass through the shadow of Mars cast by the Sun. To an observer on the planet, the moons would then suffer eclipse, Phobos about 1400 times and Deimos roughly 130 times each Martian year. The satellites also frequently pass directly between the Sun and Mars, but they are much too small to produce an eclipse of the Sun, as the Moon does when it is on (or close to) the line joining the Sun and Earth. At these times, a Martian observer would see the

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