Download Mercury`s Orbit

 Mercury •  Mercury is the smallest of the terrestrial planets with a radius of 2439 km or 0.38 R⊕. •  Its angular diameter varies between about 5 and 11 arc-­‐secs as viewed from Earth. At maximum elongaGon, a typical brightness is ∼0.5 magnitude and a diameter of ∼8 arc-­‐secs. •  Mercury is difficult to see because of its proximity to the Sun. Its maximum elongaGon is ∼28◦. Mercury, at a “maximum western” elonga*on (E). As the earth rotates CCW (counter clock wise), Mercury in this configuraGon rises before the Sun, hence west of the Sun in our sky. –  Mercury’s Orbit •  Mercury has a semi-­‐major axis of a = 0.38710 AU and the inclinaGon of its orbit to the eclipGc (i = 7◦. 005) is larger than all other planets (“dwarf” planets excluded). •  Mercury’s mean orbital velocity is 47.89 km/s. •  Mercury also has the highest eccentricity of all the (major) planets, e = 0.2056 •  As with the other planets, all of its elements vary with Gme. The closeness to the Sun produces an addiGonal source of perturbaGon on the Mercury’s orbit. •  So, for JDN 2450480.5 (31.01.1997): the longitude of its ascending node, Ω = 48◦. 3350 and the longitude of perihelion was ω = 77◦.4530. •  Due to its highly eccentric orbit, Mercury’s orbit has been a testbed for gravitaGonal theories. The line of apsides (major-­‐axis of the ellipse) rotates in the direcGon of orbital moGon at a rate of 0.4256 ± 0.0094 arc-­‐sec/yr, which is approximately the amount predicted by general relaGvity. In total, the calculated precession is 5.32 arc-­‐sec/yr but the observed precession is 5.75 arc-­‐sec/yr. The difference is account for the general relaGvisGc correcGon to Newtonian gravity. Example for non-­‐precessing orbit Example for Mercury's orbital precession –  Mercury’s Physical Proper=es •  Mercury has a heavily cratered surface •  RotaGon and orbital (revoluGon) period: ProtaGon = 58d.6462 PrevoluGon = 87d.969 •  Mercury rotates three Gmes on its axis for every two orbital revoluGons. •  As seen in the figure, for similar configuraGons of Mercury are seen from the Earth every two Mercurian sidereal years, which is equal to three Mercury rotaGons. •  Therefore during successive intervals of favorable maximum elongaGon (at aphelion), the same region of Mercury faces the Sun. •  So, on average, an observer on the Earth gets a relaGvely good look at the same region of Mercury only every fourth revoluGon. •  Slow rotaGon explains its small amount of fla.ening or oblateness, •  The plane of the rotaGon is inclined by only 0◦.01 to that of the orbit. •  Mercury has no moon. •  The mass of Mercury : M = 0.33022 x 1024 kg •  The combinaGon of mass and volume provides the mean density: <ρ> = 5430 kg/m3 •  This compressed mean density is higher than that of any other planet except Earth. •  Mercury has a low geometric albedo, 0.106, and mean color indices: (B-­‐V) = 0.93 and (U-­‐B) = 0.41. These colors are significantly redder than sunlight. •  Mercury’s mean density suggests that there is a substanGal amount of iron in the interior and large amounts of this iron must be in metallic form. • 
The surface of this airless planet is heavily cratered. • 
Large craters with central peaks are not rare on Mercury. • 
Its surface resembles the Moon more than it does any terrestrial planet. Indeed, aside from cratering impacts, the principal source of surface modificaGon for both objects for ages has been solar parGcles and radiaGon, meteorites of various sizes, and cosmic rays. • 
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Currently, Mercury shows signs of accreted water (ice) on its and when NASA’s MESSENGER spacecral flew past Mercury in 2008, it also discovered the presence of water vapor in the thin atmosphere that surrounds Mercury. This atmosphere, or more precisely “exosphere”, is created when parGcles from the Sun’s solar wind bombard Mercury and as a result atoms are released into its atmosphere. It’s possible that the solar wind vaporizes water from the ice deposits at Mercury’s poles, or maybe it’s coming from cometary fragments. Or maybe the solar wind is deposiGng the oxygen and hydrogen atoms on Mercury’s surface in the first place. •  Mercury's comet-­‐like tail as traced by neutral sodium atoms is shown on the right. The amount of sodium in Mercury's exosphere depends on the planet's posiGon in its orbit around the sun. •  The amount of the sodium tail is affected mainly by the distance of Mercury to the Sun. This changes the amount of radiaGon pressure exerted on the sodium atoms by the Sun and as a result the brightness of the sodium emission changes. •  Mercury’s exosphere contains: hydrogen, helium, oxygen, sodium, calcium, potassium and water vapor. •  Mercury has a magneGc field. The strength of the magneGc field is about 1.1% of Earth’s. It’s magneGc field is also created by is liquid outer core. Interior of the Mercury Mercury’s magneGc field •  The mean solar day length is found from the relaGve angular rate formula: from which we find Pmsd = 176 d •  At Mercury’s periods of revoluGon and rotaGon, the Sun would be above the equatorial horizon for half of this interval, or 89d. However, at perihelion Mercury’s large eccentricity causes it to sweep around the Sun faster than the rotaGon (ωrev > ωrtn). Therefore, the Sun on Mercury would normally seen to move from east to west, then, near perihelion, the following sequence would be observed: Sun becomes staGonary Sun moves eastward Sun becomes staGonary Then the Sun moves westward again, repeaGng the cycle Venus •  Venus someGmes appears as the brightest object in the sky aler the Sun and Moon, achieving −3.3 to −4.4 V magnitude at ∼39◦ elongaGon. As either a morning or an evening star. •  The bulk properGes of the planet are give in the table (see previous lecture notes) . Its orbital eccentricity (0.007) is smaller than that of the Earth, so its orbit is more circular. •  The orbit is also close to the eclipGc plane: i = 3.39◦. •  Venus orbits the Sun at an average distance of about 0.7 AU, and completes an orbit every 224.65 days. •  All the planets of the Solar System orbit in a counter-­‐clockwise direcGon as viewed from above the Sun's north pole: most planets also rotate counter-­‐clockwise but Venus rotates clockwise (called "retrograde" rotaGon) once every 243 Earth days—by far the slowest rotaGon period of any major planet. So, a Venusian sidereal day lasts longer than a Venusian year (243 versus 224.7 Earth days). •  Because of the retrograde rotaGon the length of a solar day (116.75d) on Venus is significantly shorter than the sidereal day (243 days). As a result of Venus's relaGvely long solar day, one Venusian year is about 1.92 Venusian days long. •  Transits of Venus are observable when inferior conjuncGons occur near a node passage. The planet reaches inferior conjuncGon every 584 days, on average. •  Venus, like Mercury, has no natural satellite and its mass is found to be 0.815 that of Earth. •  By direct measurement before and aler inferior conjuncGon, its radius is 6052 km, so that its mean density is 5200 kg/m3. This implies a large iron core. •  Yet, Venus has no detectable magneGc field unrelated to the solar wind. This may be due to Venus’ slow rotaGon, and/or the absence of a liquid core. It only has an induced magnetosphere formed by the Sun's magneGc field carried by the solar wind. •  The mean gravitaGonal acceleraGon on the surface of Venus at the equator is 8.96 m/s2, making it the most Earth-­‐like planet in terms of weight on the surface. •  Aside from the physical measurements, however, the environment on the surface of Venus is unmatched on Earth, except maybe in acGve volcanoes! •  The condiGons on the surface of Venus are beyond “harsh!” The Sun would be perceived only dimly through the super-­‐dense cloud decks, and the greenhouse effect produces a surface temperature of ∼750 K, under a pressure of ∼90 bar at the surface. –  Venus’s Atmosphere •  Troposphere: Only 2.5% of the incoming solar radiaGon reaches and is absorbed by the surface of Venus, but the thick CO2-­‐rich atmosphere is so efficient at absorbing the IR emiwed by the ground, which cause the surface temperature to rise to 730 K. •  Stratomesosphere: Venus’ atmosphere lacks ozone in any considerable quanGty, and the troposphere and thermosphere are separated by a roughly isothermal (no temperature change) stratomesosphere at about 200 K. Thermal structure of the atmospheres of the Earth (solid line), Venus (do.ed), and Mars (dashed). The atmospheric layers are labeled for the Earth •  Thermosphere : The dayside thermospheric profile of Venus is similar to that of Mars : absorpGon of solar EUV (Extreme Ultraviolet) by CO2 above ∼100 km alGtude accompanied by CO2 infrared emission, producing a thermospheric dayside temperature near 300 K. •  The thermosphere of Venus differs from that of Mars and Earth in several important ways arising from the much slower rotaGon period of the upper atmosphere: 4 days at the cloud tops and 6 days in the thermosphere. Because these are much shorter than the 243-­‐day (retrograde) sidereal rotaGon period of the solid planet, the atmosphere is said to superrotate. •  But thermospheric gases on Venus spend six Gmes longer on the nightside than on Mars or the Earth, and the temperature drops to a liwle over 100K. For this reason the nightside thermosphere on Venus is olen referred to as the cryosphere (“cold sphere”). •  Due to day–night thermospheric temperature difference there is a larger atmospheric pressure on the dayside than at the same alGtude on the nightside. •  This pressure difference creates a noon-­‐to-­‐midnight pressure gradient force. •  The dominant circulaGon pawern in the thermosphere is therefore a flow from the dayside to the nightside, as illustrated in the figure below. A similar circulaGon pawern occurs on Mars. Noon-­‐to-­‐midnight flow pawern on Venus and Mars –  Atmospheric Superrota7on : •  The atmosphere of Venus moves in the same direcGon as the planetary rotaGon (retrograde, east-­‐to-­‐west), but much faster than the solid planet. •  The sidereal rotaGon period for Venus is 243 days, whereas an air mass at cloud level takes only 4 days to circle the rotaGon axis, or 6 days for an air mass in the thermosphere. •  Thus, the air at cloud level is moving 60 Gmes faster than the planet under it. Typical wind speeds are of the order of 100 m/s at the top of the clouds and 65 m/s in the thermosphere.