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The Phases of the moon New moon First Quarter Full moon Evening Sky The Phases of the moon Full moon Third Quarter New moon Morning Sky Eclipses of the Sun and 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 • The Umbra & Penumbra Moon’s shadow. 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. The Diamond Ring Eclipse: Solar From Space 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 Partial No eclipse YES 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. Partial Solar Eclipse : The Moon moves in front of the sun 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: 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 Penumbral No eclipse YES Umbral Total Lunar Eclipse 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 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 Light years 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 Parallax ~ Baseline Distance 1 1 Distance Parallax (Angle) Distance to Star Parallax ~ “Parsec” is short for parallax arcsecond 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. The formula is this simple. Sirius 28.036 pc or 8.6 ly 1 d p 1 pc = 3.26 ly P is in parsecs (pc) 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 Worked Problems 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 : 25 35 12 APPARENT LINEAR ANDof ANGULAR SIZE OF What is the angular size the Sun orOBJECTS Moon? Small angles measure the ratio of width/distance. Small Angle Approximation The angle , can be approximated as : Diameter/d. 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 Constant from the earth. To solve this problem use the θ = Dia ( 206,265) distance formula . The number 206,265 is a constant that defines the angle in arcseconds. Dia = ( Diameter) linear size of an object θ = angular size of the object, in arcsec d = distance to the object Dia (206, 265) d (3, 476)(206, 265) 384, 400 1,868arc sec s 1,868 31arc min 60 31 .51deg 60 The sharpest eye can distinguish objects about .01 apart or 0.5 . You could just tell if someone was holding up one or two fingers at 100 meters Magnitude 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 nonlinear detector, especially at low light levels. The Magnitude Scale Magnitude Description 1st The 20 brightest stars 2nd stars less bright than the 20 brightest 3rd and so on... 4th getting dimmer each time 5th and more in each group, until 6th the dimmest stars (depending on your eyesight) •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 61 Cygni 5.2 Procyon 0.38 faintest galaxies ~ 29 Inverse Squared Relationship • The brightness of a light source is inversely proportional to the square of the distance. Light Intensity with 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 1st mag. stars appears 100 times brighter than 6th mag. stars If two stars differ by 1 mag. their apparent brightness differ by a of factor 2.512 So a 1st magnitude star is : 2.512 times brighter than a 2nd magnitude star 2.512^2 = 6.31 times brighter than a 3rd mag star 2.512^3 =15.9 times brighter than a 4th mag star 2.512^4 = 39.8 times brighter than a 5th mag star 2.512^5 = 100 times brighter than a 6th mag star The apparent magnitude of a star depends upon two things. (1) How far away the star is (2) How large the star is If all stars were the same distance away,we could use their Apparent Brightness to judge their Actual Brightness. Finding Absolute Magnitude (M) If we could line up all the stars at the same distance, we could observe the true brightness , Absolute Magnitude, of the Stars. What distance ? It doesn’t matter but everyone needs to use the same distance. So 10 parsecs was chosen , which is 32.5 light years. 10 parsecs is just right! Simple, small, numbers Most Absolute Magnitudes are positive Few are very large Absolute Magnitude Absolute magnitude is the measure of the true brightness of a star if it were 10 pc away. Nothing special about 10 pc. This magnitude is called the Absolute Magnitude (M) a parsec = The distance formula: m – M = 5 log(d)-5 (3.26 LY) m is the apparent visual magnitude M is the absolute magnitude d is the distance to the star in parsec •mv-Mv = -5 + 5 logd Distance Modulus = mv-Mv Problem #1 M=-(5log250)+5-0.09 Log250=2.39794 M= -5(2.3794)+5-0.09 M= -11.897+5-0.09= -6.987 Example 2 A star has an absolute magnitude of –5.0 and is located 420 ly from Earth. Find the apparent magnitude. m – M = 5 log(d) - 5 m- (-5.0) = 5log(128.8) – 5 m = 5(2.1099) - 10 m = 0.55 Example 3 The bright star Sirius has an apparent magnitude of – 1.46 and an absolute magnitude of +1.4. How far is the star from the Earth? m – M = 5 log(d)- 5 1.46- 1.4=5log(d)-5 -2.86+5=5 log(d) 2.14/5 = log d or log d=0.428 d 10 d 2.679 pc or 8.7 ly 0.428 Thanks to the following for allowing me to use information from their web site : Nick Stobel Bill Keel Richard Pogge John Pratt NASA, JPL, OSHO