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## Total Eclipse of the Sun

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**0**New moon First Quarter Full moon Evening Sky The Phases of the moon**0**Full moon Third Quarter New moon Morning Sky The Phases of the moon**Solar Eclipses**• Solar eclipses only occur at New Moon. The Cause of Eclipses: Shadows • A solar eclipse occurs when the Moon comes between the Earth and Sun. The Earth enters the Moon’s shadow. • The Umbra & Penumbra Two types of shadows**Anatomy of a Solar Eclipse**Observers in the penumbra shadow will see a partial eclipse, Those in the Umbra shadow will see a total eclipse.**Totality:**• During a total Solar Eclipse there are a number of phenomena typically observed: • The sky darkens enough so that we can often see bright stars in the sky. • Animals become quiet • The Sun’s corona (and prominences if present) are observed • The diamond ring phenomena can occur. • Shadow fringes can be seen moving across the ground.**Eclipses**• In principal there should be an eclipse each new and full moon if the earth-moon-sun system was properly aligned, but the Moon’s orbital plane is inclined about 5° with respect to the Ecliptic. The Moon passes through the plane of the Earth’s orbit at two points on opposite sides called nodes.**Eclipses and Nodes**• To predict when an eclipse is likely to occur, we need to know where the line of nodes is in the sky. • Eclipses can occur when the line of nodes is pointing toward the Sun. • This happens twice a year, and lasts for ~ 1 month. • These two months are called the “Eclipse Seasons”**Some times the Moon rides above the Sun, sometimes below.**Solar Eclipse Occurs by Node**Solar Eclipse**Is the time of new moon within + or - 28 hours of node? YES NO Is it within +or – 20 hrs of node ? No eclipse NO YES Partial Central Is it within + or – 8 days of apogee ? YES NO Annular Total**Movement of the Nodes**• If the Moon’s orbit was fixed in the sky with Earth’s then the Eclipse season would always happen at the same time of year. • But the orbital nodes precess with a period of roughly 18.6 years. • This causes the Eclipse season to occur about 3 weeks earlier/year**Partial or Total?**• Our location within the Moon’s shadow determines whether we see a total or partial solar eclipse. • The Moon’s umbra makes a circle generally about 170 miles in diameter on the surface of the Earth and the Moon’s orbital motion causes that shadow to sweep rapidly along the surface of the earth, and totality usually only lasts a few minutes.**Annular Eclipses**• Because the Moon and Sun are not a constant distance from the Earth, their angular size changes.**Annular Eclipses**• When the Moon’s angular size is too small to completely cover the disk of the Sun, we observe an Annular Eclipse.**Lunar Eclipses**• The most common eclipse seen on Earth is a Lunar Eclipse • Lunar eclipses occur at Full Moon when the Moon enters the Earth’s shadow.**Description of a lunar eclipse**• As the Moon enters the Earth’s penumbra, the disk shows only a small amount of change. • When the Moon enters the Earth’s Umbra, the Lunar disk will appear to get smaller. Before the disk is completely dark it will become slightly redder,due to the scattering of light from the Earth’s atmosphere. • When the Moon enters the Earth’s Umbra completely, the eclipse is said to have reached “totality”. • An eclipse can last up to an hour and a half or even longer.**Lunar Eclipse**Is the time of new moon within + or - 28 hours of node? YES NO Is it within +or – 20 hrs of node ? No eclipse NO YES Penumbral Umbral**Partial Eclipses**• If the Moon does not completely enter the Earth’s Umbra, then we say that eclipse is a partial eclipse. • A penumbral eclipse occurs when the Moon only enters the Earth’s penumbra, they are not very impressive, and can be hard to observe**Distance, Parallax, Small Angle,**& Magnitude**AU (astronomical unit)**One AU is the average distance from which the Earth orbits the Sun. The AU is most commonly used for the distances of objects with in our solar system. The Earth is 1.0 au from the sun, and Neptune is a distance of 30.06 au from the Sun. • AVERAGE EARTH-SUN DISTANCE • 15O x 106 KILOMETERS • 93 x 106 MILES**Distances in Lightyears ly**The distance light travels in one year. 6 trillion miles = 1016 meters. We are 8.3 light minutes away form the Sun. Pluto is about 13 light hours. The nearest star is 4.2 light years away Sirius is 8.6 ly away The Andromeda Galaxy is 2.4 million ly away**Measuring Distance**• How can you measure the distance to something? • Direct methods, e.g. a tape measure. Not good for things in the sky. • Sonar or radar: send out a signal with a know velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, Mercury, Venus Mars & certain asteroids). • Triangulation: the use of parallax.**Parsec: where a star shifts by 1 arcsec over a 1/2 year**“Parsec” is short forparallaxarcsecond Baseline Parallax ~ Distance 1 1 Parallax ~ Distance Parallax (Angle) Distance to Star Baseline (Earth’s orbit)**Calculating distance using Stellar Parallax**Take photos of a nearby star 6 months apart. • Observe a star when the Earth is at point A -Star is in front of Star A • Observe it again 6 months later when the Earth is at point B -Star is in front of Star B Measure angle in arc seconds. Take ½ of the angle, this is p. 1pc = 3.26 ly The formula is this simple. P is in parsecs (pc) Sirius 28.036 pc or 8.6 ly**Stellar Distances**• Stellar Parallax is very small, a fraction of a second. 1 pc = 206,265 AU or about 3.26 ly Why is it so important to know the distance to a star? By knowing the distance to a star, one can find out a star’s luminosity, diameter, and mass. • Best resolution from Earth: • Measure angles as small as P = 0.03” • Then d = 30 pc = 98 ly • Results: about 2,000 accurate distances • Best resolution from satellite: • Measure angles as small as P =0.005” • Then d = 200 pc = 652 ly • Results: about 1 million accurate distances**The Small-angle**Formula**Angles in Astronomy are usually measured in deg, min, sec.**There are 60 min in a degree and 60 sec in a minute. 25 deg, 35 min & 12 seconds can be written :**What is the angular size of the Sun or Moon?**APPARENT LINEAR AND ANGULAR SIZE OF OBJECTS Small angles measure the ratio of width/distance. Diameter/d. Small Angle Approximation The angle , can be approximated as : When angles are extremely small, then the sine and tangent of the angle are approximately equal to the angle itself. Using the small angle formula, we can calculate the angular size. Diameter**The Moon has a diameter of 3,476 km and is 384,400 km from**Earth. Let’s use the small-angle formula to determine the angular size of the moon from the earth. Constant Dia ( 206,265) To solve this problem use the formula . The number 206,265 is a constant that defines the angle in arcseconds. θ = distance Dia = ( Diameter) linear size of an object θ = angular size of the object, in arcsec d = distance to the object**The sharpest eye can distinguish objects about apart**or . You could just tell if someone was holding up one or two fingers at 100 meters**The Magnitude Scale**• First introduced by Hipparchus (160 - 127 B.C.) • Brightest stars: ~1st magnitude • Faintest stars (unaided eye): 6th magnitude • The magnitude scale was originally defined by eye, but the eye is a non-linear detector, especially at low light levels. • Apparent Magnitude • The magnitude of a star as you see it in the sky.**The Magnitude Scales are backwards:**• A smaller number means brighter! • A larger number means dimmer!**Brighter**Vega 0.0 Procyon 0.38 61 Cygni 5.2 faintest galaxies ~ 29**Inverse Squared Relationship**• The brightness of a light source is inversely proportional to the square of the distance.**STELLAR PHOTOMETRY**• Astronomers determine the brightness of stars using an instrument called a photometer. • With modern equipment, we can measure more accurately. • 1st mag. stars apear 100 times brighter than 6th mag. stars • If two stars differ by 1 mag. their apparent brightness differ by a of factor 2.512