Thursday, December 25, 2008

Orbit and rotation of mercury


Orbit of Mercury (yellow)

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 left 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.

Mercury’s orbit is inclined by 7° 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.Functionally, Mercury’s axial tilt is nonexistent,with measurements as low as 0.027°.This is significantly smaller than that of Jupiter, which boasts the second smallest axial tilt of all planets at 3.1 degrees. This means an observer at Mercury’s equator during local noon would never see the Sun more than approximately 1/30 of one degree north or south of the zenith. Conversely, at the poles the Sun never rises more than 2.1′ above the horizon.

Orbit of Mercury as seen from the ascending node (bottom) and from 10° above (top)

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 prior to 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.

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