Lunar and Solar Eclipses: Periods, Phases, and Orbits, Lecture notes of Astrophysics

Download Lunar and Solar Eclipses: Periods, Phases, and Orbits and more Lecture notes Astrophysics in PDF only on Docsity! The Moon orbits the Earth and returns to the same right ascension every 27.32 days. (It moves eastward against the background of stars.) This is the sidereal (si-DER-e-al) period of the Moon (“time with respect to the stars”). During this time the Earth has moved along on its orbit around the Sun. The lunar phases repeat every 29.53 days. This is the synodic period of the Moon. Moon, Sun, and eclipses Since the Moon takes 27.32 days to return to the same right ascension, its mean motion is 360 degrees / (27.32 days X 24 hours/day) = 0.549 deg/hour If you are standing outside looking at the Moon, it is moving 15 degrees per hour from east to west owing to the rotation of the Earth. But it's also moving 0.549 deg/hour from west to east against the background of stars. ----------------------------------------------------------------> <--- Its net motion is still from east to west in the horizon system of coordinates. Waxing gibbous Waning fele)oleutsy © 2005 Brooks/Cole - Thomson Midnight First quarter Sunset North Pole Noon Earth’s rotation Sunrise Third quarter Waxing crescent d New Waning crescent SUNLIGHT Because the Moon is close to being spherical, the Earth-Moon-Sun angle completely dictates what the lunar phase is. Simply put, the first quarter Moon is due south at sunset. The full Moon rises at sunset, and sets at sunrise. The third quarter Moon rises at midnight. The first quarter Titel Rel week through its 4-week cycle. (eT SNe) from the Latin word for humpbacked. y the Moon) Grow The full moon is two RB i - ey HW to (Ul), it ks weeks through its C1) aes ei (om 9 tae) muon) USC e Sal mL URI] Las Tg © 2005 Brooks/Cole - Thomson  If the Moon passes completely into the dark part of the Earth's shadow, which can only occur at full Moon, there is a total lunar eclipse. If only part of the Moon enters the umbra, we have a partial lunar eclipse. At the average distance of the Moon from the Earth, the Earth's umbral shadow is 2.65 times the angular diameter of the Moon, or about 1.37 degrees. But a lunar eclipse does not occur every full Moon because of the tilt of the Moon's orbit with respect to the ecliptic. eevee ome ec Line of nodes. Full Unfavorable for eclipse arom ue elo d UL Mela Ue eles Feet LC ee seams] um Line of nodes ele Rome reel} Full moon passes south of Earth's shadow; no eclipse Earth, moon, and shadows drawn to scale © 2007 Thomson Higher Education New moon shadow passes north of Earth; no eclipse Some definitions apogee – the point in the orbit of the Moon or an artificial satellite when it is farthest from the Earth perigee – orbital position where the Moon or artificial satellite is closest to the Earth aphelion – point in the orbit of a planet when it is furthest from the Sun perihelion – point in the orbit of a planet when it is closest to the Sun Because the Moon's orbit around the Earth is elliptical, the angular diameter of the Moon changes somewhat. Similarly, because the Earth's orbit about the Sun is also elliptical (but less so), the Sun's angular diameter changes. A simple sighting device that can be used to measure the Moon’s angular size. The distance between Earth and Moon varies between 356,400 and 406,700 km. That's because the Moon's orbit is elliptical, not perfectly circular. Sometimes it’s less than 30 arc minutes in angular size, sometimes it’s greater than 30 arcmin in angular size. The distance between the Sun and Earth varies between 147.1 and 152.1 million km. The Earth's orbit is less elliptical than the Moon's orbit around the Earth. Given the Sun's diameter of 1,392,000 km, its angular size varies from 31.46 to 32.53 arc minutes. In order for a total solar eclipse to occur, the new Moon must be aligned with the Sun, and the Moon must have a larger angular size. If the Moon is at one of its nodes at new Moon, a solar eclipse can occur. There are several kinds of solar eclipses: partial total annular annular-total If the Sun and Moon are aligned and the Moon's angular diameter is greater than that of the Sun, we have a total solar eclipse. Note corona and prominences. Some solar eclipses are such that they are annular at the start and end of the track, and total in the middle. The radius of the Earth is just big enough to make a total solar eclipse in the middle. The Mars rover Curiosity obtained these images of an annular eclipse caused by the moon Phobos passing in front of the Sun’s disk on August 20, 2013. In the previous millennium (1001 to 2000 AD) the following number of solar eclipses visible on Earth occurred: 625 total 837 partial 767 annular 156 annular-total The Babylonians discovered that there was a pattern to the occurrence of solar eclipses. They repeat with a period of 18 years 11 1/3 days (give or take a Leap Day). This is called the saros cycle. The basic rule is this: if a total solar eclipse occurs on a given date at a given place, odds are very good that another total solar eclipse will occur 223 new Moons later, or 6585 1/3 days. The next eclipse in the cycle will occur 1/3 of the way around the Earth to the west. Three eclipse tracks following the total solar eclipse of March 7, 1970. The saros cycle that includes the total solar eclipses of August 11, 1999, and August 22, 2017, began with a very unimpressive partial solar eclipse visible near the North Pole on January 4, 1639. After 14 partial solar eclipses, an annular eclipse occurred on June 6, 1891, followed by an annular-total eclipse on June 17, 1909. Then the cycle includes 41 total solar eclipse whose tracks Keep moving south on the Earth. Then there are 20 partial solar eclipses of decreasing fractional cut, ending on April 17, 3009, with a partial solar eclipse visible near the South Pole. The cycle lasts 1370 years. Other saros cycles can progress from south to north.