The relations of the several planes can be best conceived by considering the points at which lines perpendicular to them, or their poles, meet the celestial sphere. By theory, the pole of the orbital plane of each satellite revolves round the pole of a certain fixed plane, differing less from the plane of the equator of Mars the nearer the satellite is to Mars. Lowell from a combination of his own observations with those of Schiaparelli, Lohse and Cerulli, found for the pole of the axis of rotation of Mars[12]:—
R.A. = 317.5°; Dec. = +54.5°; Epoch, 1905.
Tilt[13] of Martian Equator to Martian ecliptic, 23°. 59′. Hermann Struve, from the observations of the satellites, found theoretically the following positions of this pole, and of those of the fixed planes of the satellite orbits for 1900:—
| Pole of Mars: R.A. | = 317.25° | Dec. = 52.63° |
| Pole of fixed plane for Phobos | = 317.24° | = 52.64° |
| Pole of fixed plane for Deimos | = 316.20° | = 53.37° |
Lowell’s position of the pole is that now adopted by the British Nautical Almanac.
The actual positions of the poles of the satellite—orbits revolve around these poles of the two fixed planes in circles. Putting N for the right-ascensions of their nodes on the plane of the terrestrial equator, and J for their angular distance from the north terrestrial pole, N, and J, for the corresponding poles of the fixed planes, and t for the time in years after 1900, Struve’s results are:—
Deimos.
N1 = 46°.12′ + 0.463′ t; J =36°.42′ − 0.24′ t
(N − N1) sin J = 97.6′ sin (356.8° − 6.375° t)
J − J1 = 97.6 cos (356.8° − 6.375° t)
Phobos.
N1 = 47° 14.3′ + 0.46′ t; J1 = 37° 21.9′ − 0.24′ t
(N − N1) sin J = 53.1′ sin (257°.1′ − 158.0° t)
J − J1 = 53.1′ cos (257°1′ − 158.0 t)