Saturday, 19 March 2011

Orbit and rotation

Mercury has the most eccentric orbit of all the planets; its eccentricity is 0.21 with its distance from the Sun ranging from 46 to 70 million kilometers. It takes 88 days to complete an orbit. The diagram on the right illustrates the effects of the eccentricity, showing Mercury’s orbit overlaid with a circular orbit having the same semi-major axis. The higher velocity of the planet when it is near perihelion is clear from the greater distance it covers in each 5-day interval. The size of the spheres, inversely proportional to their distance from the Sun, is used to illustrate the varying heliocentric distance. This varying distance to the Sun, combined with a 3:2 spin-orbit resonance of the planet’s rotation around its axis, result in complex variations of the surface temperature.[17] This resonance makes a single day on Mercury last exactly two Mercury years, or about 176 Earth days.[71]

Mercury’s orbit is inclined by 7 degrees to the plane of Earth’s orbit (the ecliptic), as shown in the diagram on the right. As a result, transits of Mercury across the face of the Sun can only occur when the planet is crossing the plane of the ecliptic at the time it lies between the Earth and the Sun. This occurs about every seven years on average.[72]
Orbit of Mercury as seen from the ascending node (bottom) and from 10° above (top)

Mercury’s axial tilt is almost zero,[73] with the best measured value as low as 0.027 degrees.[7] This is significantly smaller than that of Jupiter, which has the second smallest axial tilt of all planets at 3.1 degrees. This means that to an observer at Mercury’s poles, the center of the Sun never rises more than 2.1 arcminutes above the horizon.[7]

At certain points on Mercury’s surface, an observer would be able to see the Sun rise about halfway, then reverse and set before rising again, all within the same Mercurian day. This is because approximately four days before perihelion, Mercury’s angular orbital velocity exactly equals its angular rotational velocity so that the Sun’s apparent motion ceases; at perihelion, Mercury’s angular orbital velocity then exceeds the angular rotational velocity. Thus, the Sun appears to move in a retrograde direction. Four days after perihelion, the Sun’s normal apparent motion resumes at these points.[17]
Spin–orbit resonance
After one orbit, Mercury has rotated 1.5 times, so after two complete orbits the same hemisphere is again illuminated.

For many years it was thought that Mercury was synchronously tidally locked with the Sun, rotating once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces the Earth. However, radar observations in 1965 proved that the planet has a 3:2 spin–orbit resonance, rotating three times for every two revolutions around the Sun; the eccentricity of Mercury’s orbit makes this resonance stable—at perihelion, when the solar tide is strongest, the Sun is nearly still in Mercury’s sky.[74]

The original reason astronomers thought it was synchronously locked, was that whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury's rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury’s 3:2 spin–orbit resonance, a solar day (the length between two meridian transits of the Sun) lasts about 176 Earth days.[17] A sidereal day (the period of rotation) lasts about 58.7 Earth days.[17]

Simulations indicate that the orbital eccentricity of Mercury varies chaotically from nearly zero (circular) to more than 0.45 over millions of years due to perturbations from the other planets.[17][75] This is thought to explain Mercury’s 3:2 spin-orbit resonance (rather than the more usual 1:1), since this state is more likely to arise during a period of high eccentricity.[76] Numerical simulations show that a resonant orbital interaction with Jupiter may cause the eccentricity of Mercury's orbit to increase to the point where the planet may collide with Venus within the next five billion years.[77]
Advance of perihelion
Main article: Perihelion precession of Mercury

In 1859, the French mathematician and astronomer Urbain Le Verrier reported that the slow precession of Mercury’s orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps instead a series of smaller 'corpuscules') might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation.[78] (Other explanations considered included a slight oblateness of the Sun.) The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place faith in this possible explanation, and the hypothetical planet was even named Vulcan. However, no such planet was ever found.[79]

The perihelion precession of Mercury is 5600 arc seconds per century. Newtonian mechanics, taking into account all the effects from the other planets, predicts a precession of 5557 seconds of arc per century.[80] In the early 20th century, Albert Einstein’s General Theory of Relativity provided the explanation for the observed precession. The effect is very small: the Mercurian relativistic perihelion advance excess is just 42.98 arcseconds per century, therefore it requires a little over twelve million orbits for a full excess turn. Similar, but much smaller, effects operate for other planets: 8.62 arcseconds per century for Venus, 3.84 for Earth, 1.35 for Mars, and 10.05 for 1566 Icarus.[

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