Rotation of Early Earth Moon System Faster than Today and Mars

Due to tidal dissipation and angular momentum conservation, the Earth-Moon distance is increasing presently (the Moon moves away from the Earth at a rate of approximately 4 cm/year, see Dickey et al. 1994), and the rotation of the Earth is decreasing (the length-of-day is longer at present than in the past; it increases by about 20 microseconds per year due to the Moon, and by another 25 microseconds per year due to the Sun). The reason for these changes is the so-called tidal friction effect. Tidal friction is the time-averaged, global dissipation mechanism of rotational energy and angular momentum by tides. It is caused by the non-instantaneous effects of tidal forces on mass redistribution and on ocean currents and heights (if there is an ocean). Today, the precise mechanism of tidal energy dissipation is still an open question and, despite a better knowledge of time-scales and sophisticated mathematical modelling techniques, ocean tides are still not known with the desired accuracy to compute this effect, but are believed to be the major actors in this process. If mp and ms are the masses of the primary and secondary bodies, ^ is the rotation rate of the primary planet, D is their semi-major axis in the mean ellipse of their relative distances, Qp is the dissipation factor inside the planet (QEarth ~ 12), k2 is the tidal Love number, a is the radius of the primary planet, and n the angular rotation rate of the secondary body (the Moon, in the Earth's case) around the planet, one has (Murray and Dermott 2000):

mp QpD11/2

Using ancient observations of solar eclipses, Stephenson and Morrison (1984) have shown that the Earth length of the day is increasing by 2 milliseconds per century, on average.

The day was shorter by about 2 hours and the year "longer" by about 35 days during the Devonian period (400 million years ago, i.e. 0.4 Gyr ago). There was thus a more rapid rotation of the Earth in the geologic past. A linear extrapolation shows that the length of day would be 19 h, 1 Gyr ago, and that the Moon was very close to the Earth 1.2 Gyr ago (15,000-20,000 km).

A full computation, taking into account that Earth is not a perfect sphere (Kopal 1972), that its rotation axis is not perpendicular to the orbit of the Moon, and the contribution of the Sun, leads to a predicted decrease of the rotation of the Earth of approximately 2.3 milliseconds per century. Extrapolating all this to the past indicates that the Earth's rotation period was at a few hours after its birth. However, the linear extrapolation with the present dissipation rate is not very realistic (Williams 2000; Varga et al. 2006). The dissipation rate in the oceans depends on the rotation rate of the planet as well as on the distribution of the continents. The motion of the continents (Kvale et al. 1999), intense global glaciations (Evans et al. 1997; Kirschvink et al. 2000), or higher mantle activities (Melezhik et al. 2003; Greff-Lefftz and Legros 1999), are among the geophysical processes that could have further influenced the rotation rate of Earth. It is believed that the initial rotation period of the Earth could have been as low as 13.1 h (MacDonald 1964), and an initial rotation rate of 10 hours is consistent with the relation between the planetary angular momentum, density, and planetary mass observed in the solar system (Hubbard 1984, Chap. 4). These numbers provide a good starting point for our simulations.

The present rotation of Mars may be, in contrast, much more similar to the planet's primitive rotation. Phobos and Deimos are indeed much smaller than the Moon compared to Earth-Moon system due to the smaller masses of the martian satellites (mPh0bos = 1.47 x 10-7 mMoon and mDeimos = 1.47 x 10-8 mMoon). Hence, the rotation period of Mars is essentially unaffected by Phobos and Deimos. The solar tides have changed the rotation rate of Mars by only a couple of minutes over the age of solar system. Tidal friction could have reduced the rotation significantly only if Mars had a larger moon in the past. Large impacts near the end of the accretion phase are likely to determine the initial spin position and rotation rate. These initial conditions remain unknown (Lissauer et al. 2001), and, therefore, one cannot exclude the possibility that Mars has kept the present rotation rate throughout its past. In the Noachian (3.5-4.5 Gyr ago), the planet probably had a magnetic field, a more massive atmosphere and a wetter climate. During the same period, Mars suffered heavy impact bombardment, and creation of a large impact basin could have important consequences on the climate as well as on the rotation. Geophysical processes such as volcanic events and uplifts, construction of the large Thar-sis province or of giant impact basins, or formation of mass anomalies associated with mantle convection could also have affected the rotation rate of Mars. Recently discovered geological evidences point towards important climatic changes as well (Head et al. 2003, 2005, 2006; Neukum et al. 2004). Mars present obliquity is similar to that of the Earth, but it has been probably much larger in the past (Laskar et al. 2004b; see also Laskar 1994, 1996, 1997; Laskar et al. 2002, 2004a). Climate models have predicted that at high obliquities (>45°, polar ice may sublimate rapidly from the poles and be re-deposited in the tropics, resulting in periodic large-scale surface mass redistributions (Levrard et al. 2004; Forget et al. 2006). However, the effects of climate change-induced surface ice redistribution on the rotation are likely to be small. Zuber and Smith (1999) showed that if the whole north polar deposits (with an estimated volume of 1.2 x 106 km3) (Zuber et al. 1998) were removed, the change in Mars' mean moment of inertia would be AI/I = 3.88 x 10-6. Consequently, it is difficult to explain any diminution in the rotation rate of Mars throughout its past unless a large impact scenario (such as the one formed Hellas basin 4 Gyr ago) is considered.

Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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