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# ASTR 100 Week 7 Notes ASTR 100

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This 5 page Class Notes was uploaded by Sarah Gardner on Friday February 26, 2016. The Class Notes belongs to ASTR 100 at Ball State University taught by Dr. Bob Berrington in Fall 2016. Since its upload, it has received 20 views. For similar materials see Introduction to Astronomy: Solar System and Beyond in Astronomy at Ball State University.

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Date Created: 02/26/16

Week 7 Notes ASTR 100 I. Galileo Galilei a. Born Feb 15, 1564 in Pisa Italy b. First to utilize telescope for astronomical observation i. Telescope invented by Hans Lippersay in 1608 c. Persecuted by Catholic Church i. Died under house arrest ii. Passionate about the heliocentric model d. Published Sidereus Nucius (“Sidereal Messenger”) e. Provided early efforts toward a theory of motion (classical mechanics) i. Recognized uniform acceleration of objects due to earth’s gravity ii. Drop 2 objects from the same height, hit the ground at the same time (account for air resistance – a flat sheet of paper will not strike the ground at the same time as a basketball, but a crumbled up piece of paper will) iii. No matter the mass, objects will fall at the same rate in a vacuum f. Pardoned by the Catholic Church in 1992 (23 yrs ago) g. Gelileo’s middle finger is a relic in a museum in Florence, Italy (bonus: the finger faces Rome) II. Telescopic Observations a. Moons of Jupiter i. Galileon Satellites 1. Lo, Europa, Ganymede, Castillo (Jupiter’s moons) ii. Provided evidence that other centers of revolution exist 1. Both Jupiter and the earth keep their moons with them in orbit iii. Contradicted that the earth was the center of the universe b. Craters on the Moon i. Mountains and valleys on the surface of the moon 1. The laws of physics that apply here apply on the moon ii. Showed planets’ surfaces are not perfect (no perfect circles) c. Sunspots i. Galileo viewed the sun as it was setting so it didn’t destroy his eyes ii. The surface of the sun was marred with “spots” iii. “Heavens not perfect” – went against the church iv. Made a way to track the rotation of the sun d. Saturn’s rings i. Called ears of Saturn 1. Interpreted the rings as 2 bodies orbiting Saturn 2. Spherical lens blurred the image 3. Observations showed the bodies vanished every 5 years a. Earth passing through the plane of the ring of Saturn (orbit) e. Phases of Venus i. Disproved Ptolemaic model ii. Geocentric model the only allowable phases were crescent phases iii. Observed gibbous phases iv. No way for all phases of the moon to be seen in a geocentric model 1. Strong support for heliocentric model III. How did they know the Earth rotated? a. Focault’s Pendulum i. Plane of the pendulum wants to maintain the same orientation ii. Earth’s rotation causes the plane of the pendulum to rotate iii. For a pendulum at the north pole the plane will rotate once every 24 hrs iv. First demonstration took place in Feb 1851 IV. Johannes Kepler a. 1571-1630 b. Lived in Germany and was a Theologian and Musician i. Learned of the Copernican hypothesis while studying at his university ii. Went to Denmark to work with Tycho Brahe iii. Inherited Tycho’s detailed observations c. Kepler proved himself to Tycho i. Modeled the motions of the planets using math and Copernican models (he was great at math – more like a numerologist though [studys patterns]) ii. Resulted in published work Astronomia Nova (The New Astronomy) in 1609 1. Contains first two of three laws of planetary motion V. Kepler’s laws of planetary motion a. 1 law of Planetary Motion i. The planets follow elliptical orbits 1. Ellipses are a family of curves knows as a conic section (includes circles) 2. There is a formal definition (equation), but we don’t need to know it ii. Ellipse (cont.) 1. Set of points whose distance to two foci is constant 2. Sun is at one of the 2 foci but nothing is at the second focus b. 2 law of Planetary Motion i. The planets sweep out equal areas of orbit in equal time ii. Planets move faster when close to the sun iii. Sweep out equal areas in equal amount of time c. 3 law of Planetary Motion i. After Kepler got the job with Tycho, he got more data ii. He figured out the square of a planet’s period (time to revolve the sun) is proportional to its semi-major axis cubed (see semi-major axis below) 2 3 1. P ∝ a 2. ∝ means “proportional to” iii. If the units of the semi major asxis is in AUs then the period is in years 1. P yr = a AU iv. Kepler published his third law in Harmonices Mundi (1919) VI. Semi-Major axis a. Half of the major axis i. For a circle it’s the radius ii. For an ellipse, it is the length across it 1. Perihelion distance = closest to the sun 2. Aphelion distance = furthest from the sun iii. The vertical axis is called the minor axis, but we will never use it b. Example 1 i. What is the semi major axis of a planet whose orbital period is 8 years? 2 3 ii. Period = 8 yrs; use P yr = a AU iii. P = (8 yrs) = 64 yrs 3 iv. √64 = 4 AU v. A planet that is 4x distant to the sun has a period of 8 yrs c. Example 2 i. What is the orbital period of Jupiter if the semi-major axis of the orbit is 5.2 AU? 3 3 2 ii. A = (5.2 AU) = 140.608 = P iii. √P ≈ 12 yrs d. The period is dependent only on the semi-major axis VII. Sir Issac Newton a. 1643 – 1724, lived in England b. Math Professor at Cambridge University i. Held Lucasian Chair of Mathematics (was held by Stephen Hawking) c. Published Principia in 1687 i. Established laws of motion ii. Universal law of gravity d. Also established modern optics and created calculus e. All done at his home while hiding from the Bubonic Plague VIII. Newton’s Laws of Motion a. 1 law, the Law of Inertia i. An object in uniform motion will continue along in its motion (or lack of ) until acted upon by external force b. 2 Law i. The rate of change of momentum of an object is equal to the external force applied to it ii. For constant mass objects, the accerleration of an object is proportional to the amount of force it receives iii. F=ma (force = mass x acceleration) c. 3 Law of Motion i. Known as action/reaction law ii. Every action has an equal and opposite reaction iii. For every force applied by one body on another, an equal and opposite force is applied on the first body by the second iv. F 1 (-F 2 IX. Universal Law of Gravitation a. Inverse square law of gravity i. Curved orbits imply a force which we know to be gravitational 2 ii. Fg = GMm/r b. Using calculus proved that the orbits of planets are ellipses i. Actually able to calculate planetary orbits using mathematics ii. Now had a physical reason for planetary orbits X. Acceleration due to earth’s gravity a. Universal Law of Gravity i. Fg = GM(earth symbol)m /r(ebrth symbol) 2 nd b. Newton’s 2 law i. F= Fg = bm a c. If we equate the two, we get i. m b = GM (earth) b/ r(earth) 2 ii. Solving for a 2 1. A = GM(earth)/r(earth) XI. Weight and Mass a. Ojects have mass consistent with their weight F = mg i. Weight should be unit of force (force of gravity) ii. The pound lb is a unit of force iii. “g” is the acceleration due to gravity iv. The kilogram is the metric unit of mass v. The English unit of mass is a slug b. Planetary Orbits i. Planetary Orbits can be any of the conic sections 1. Depends on velocity ii. Bound orbits 1. Circular 2. Elliptical iii. Unbound orbits (have enough inertia to escape the gravitational pull) 1. Parabola 2. Hyperparabola

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