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# Introduction to Astronomy (GT AA 100

CSU

GPA 3.98

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This 10 page Class Notes was uploaded by Mrs. Amina Graham on Tuesday September 22, 2015. The Class Notes belongs to AA 100 at Colorado State University taught by Roger Culver in Fall. Since its upload, it has received 30 views. For similar materials see /class/210209/aa-100-colorado-state-university in Astronomy at Colorado State University.

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Date Created: 09/22/15

Newtonian mechanics Mar 7 2012 Newton 1687 published quotPrincipia mathemitica philosophie naturalisquot after 15 yrs of work Didn t want to publish at first being scared of being laughed at as some ideas were too wild But it turned out to be a significant text He attempted to formulate all theories of natural phenomena gt formulation of motions referred to as Newtonian mechanics capstone of modern natural science Basic concepts 1 Frame of reference talks abt motions eg walking in the room how to know that someone s moving Based on frame of reference comparing to others motions A moving relative to B B moving relative to A gt because of common sense of humans gt earth seems to be stationary but actually Earth is hardly fixed 2 Fundamental quantities Time length mass Human beings have the tendency to estimate things but sometimes not very accurately Eg Mass someone s heavier than someone else Time quottime s upquot in exam but sometimes time passes slowly Units meter kilogram second used to be based on changing benchmarks gt now based on more accurate be 3 Defining degrees of motion a Velocity time rate of change of position if a thing moves faster than another thing that means either it can travel farther in a same period of time it can travel the same length in a shorter period of time gt Killie s road turtle starts to run gt Can Killie ever catch up with the turtle No Based on calculus human beings can solve such problems as the one above 5339 Acceleration quotquicknessquot time rate of change of velocity Acceleration 60mph5min 12 mphminute 4 Forces any agent which produces or prevents motion from occurence eg friction Important characteristics i Amoral No good or bad forces They re just there Principle of Universality nature treats everything everyone the same gt why should we How we should make use of forces is the problem ii Can be expressed mathematically in terms of observable quantities Drivers behind motions not God as ppl used to think 5 Mass ability of a given object to resist a force Based on the 5 basic concepts Newton formulated 3 statements of motions 1 If an object is moving at a constant velocity the object will continue to move at that velocity unless acted upon by additional forces Law of inertia Previously discovered by Galileo 2 If a force is exerted on an object the object will respond by accelerating in the direction of the force by amount equal to the force divided by the mass Force Mass x Acceleration or F ma gt the equation of motion 3 If a force is exerted on an object the object will also respond by exerting an equal and opposite force on the initial force producing agent action reaction gt The 3 statements help explain a lot of motions When Einstein came up with the discovery that light always travels at the same velocity the fundamental quantities became invalid Newtonian mechanics Mar 7 2012 Newton 1687 published quotPrincipia mathemitica philosophie naturalisquot after 15 yrs of work Didn t want to publish at first being scared of being laughed at as some ideas were too wild But it turned out to be a significant text He attempted to formulate all theories of natural phenomena gt formulation of motions referred to as Newtonian mechanics capstone of modern natural science Basic concepts 1 Frame of reference talks abt motions eg walking in the room how to know that someone s moving Based on frame of reference comparing to others motions A moving relative to B B moving relative to A gt because of common sense of humans gt earth seems to be stationary but actually Earth is hardly fixed 2 Fundamental quantities Time length mass Human beings have the tendency to estimate things but sometimes not very accurately Eg Mass someone s heavier than someone else Time quottime s upquot in exam but sometimes time passes slowly Units meter kilogram second used to be based on changing benchmarks gt now based on more accurate be 3 Defining degrees of motion a Velocity time rate of change of position if a thing moves faster than another thing that means either it can travel farther in a same period of time it can travel the same length in a shorter period of time gt Killie s road turtle starts to run gt Can Killie ever catch up with the turtle No Based on calculus human beings can solve such problems as the one above 5339 Acceleration quotquicknessquot time rate of change of velocity Acceleration 60mph5min 12 mphminute 4 Forces any agent which produces or prevents motion from occurence eg friction Important characteristics i Amoral No good or bad forces They re just there Principle of Universality nature treats everything everyone the same gt why should we How we should make use of forces is the problem ii Can be expressed mathematically in terms of observable quantities Drivers behind motions not God as ppl used to think 5 Mass ability of a given object to resist a force Based on the 5 basic concepts Newton formulated 3 statements of motions 1 If an object is moving at a constant velocity the object will continue to move at that velocity unless acted upon by additional forces Law of inertia Previously discovered by Galileo 2 If a force is exerted on an object the object will respond by accelerating in the direction of the force by amount equal to the force divided by the mass Force Mass x Acceleration or F ma gt the equation of motion 3 If a force is exerted on an object the object will also respond by exerting an equal and opposite force on the initial force producing agent action reaction gt The 3 statements help explain a lot of motions When Einstein came up with the discovery that light always travels at the same velocity the fundamental quantities became invalid March 23rd 2012 Earth Basic properties 1 Mass ofthe earth 6 x 1024 kg 2 Radius of the earth 6400km Eratosthenes 200BC noticed that on the first day of summer sunlight is perfectly perpendicular to Seyene and forms a 7 deegree angular with Alexandria gt radius of the earth Seyene Alexandria 500 stadia 4gt 500 stadia 7 degree circumference of the earth360 degree I4gt Circumference of the earth N 250000 stadia 25000 miles 40000km 3 Density mass per unit volume measured in gcm3 or kgm3 Typical ice 10 gcm3 or 1000kgm3 Typical rock 30 gcm3 or 3000 kgm3 Typical metal 80 gcm3 or 8000 kgm3 Mean density total mass total volume Assume that all objects are spherical in shape gt volume of a sphere T R3 Mean density of the earth 5500kgm3 Earth is composition of rock and metal denser than rock but lighter than metals Mean density of surface material 3300kgm3 mostly made up of rocks Mean density of surface lt mean density gt mean density of the rest must be higher gt the inner part must be denser 4 Magnetic field Earth also has magnetic field Common metals Fe and Ni nickel Seismology tsunamis mostly because of earthquakes nuclear weapons became banned gt tested underground primary waves travel thru both solids and liquids secondary waves do not travel through liquids the crust is very complicated Crust can be split up into plates Plate tectonics gt earthquakes Axis of rotation is no longer the axis of the magnetic field Liquid outer core gt magnetic field Other planets have magnetic fields Newtonian mechanics Mar 7 2012 Newton 1687 published quotPrincipia mathemitica philosophie naturalisquot after 15 yrs of work Didn t want to publish at first being scared of being laughed at as some ideas were too wild But it turned out to be a significant text He attempted to formulate all theories of natural phenomena gt formulation of motions referred to as Newtonian mechanics capstone of modern natural science Basic concepts 1 Frame of reference talks abt motions eg walking in the room how to know that someone s moving Based on frame of reference comparing to others motions A moving relative to B B moving relative to A gt because of common sense of humans gt earth seems to be stationary but actually Earth is hardly fixed 2 Fundamental quantities Time length mass Human beings have the tendency to estimate things but sometimes not very accurately Eg Mass someone s heavier than someone else Time quottime s upquot in exam but sometimes time passes slowly Units meter kilogram second used to be based on changing benchmarks gt now based on more accurate be 3 Defining degrees of motion a Velocity time rate of change of position if a thing moves faster than another thing that means either it can travel farther in a same period of time it can travel the same length in a shorter period of time gt Killie s road turtle starts to run gt Can Killie ever catch up with the turtle No Based on calculus human beings can solve such problems as the one above 5339 Acceleration quotquicknessquot time rate of change of velocity Acceleration 60mph5min 12 mphminute 4 Forces any agent which produces or prevents motion from occurence eg friction Important characteristics i Amoral No good or bad forces They re just there Principle of Universality nature treats everything everyone the same gt why should we How we should make use of forces is the problem ii Can be expressed mathematically in terms of observable quantities Drivers behind motions not God as ppl used to think 5 Mass ability of a given object to resist a force Based on the 5 basic concepts Newton formulated 3 statements of motions 1 If an object is moving at a constant velocity the object will continue to move at that velocity unless acted upon by additional forces Law of inertia Previously discovered by Galileo 2 If a force is exerted on an object the object will respond by accelerating in the direction of the force by amount equal to the force divided by the mass Force Mass x Acceleration or F ma gt the equation of motion 3 If a force is exerted on an object the object will also respond by exerting an equal and opposite force on the initial force producing agent action reaction gt The 3 statements help explain a lot of motions When Einstein came up with the discovery that light always travels at the same velocity the fundamental quantities became invalid Gravitation 1 F ma 2 There exists a mathematic relationship between acceleration and position a erdtz 3 A mathematical description of forces involved gt a description of how the objects will move gt a powerful tool to predict motions of various objects For astronomy use the same approach look at basic interactions in nature Universal law of gravitation mass 1 d mass 2 mass 1 gtlt mass2 Forceo ravit constanm f q y distanced2 mhml or F6 G 7 everything has gravitational effect on other things So a planet like Mars can exert some gravitational influence on you Astronomers find out that gravity is the most pervasive force in the universe planets are held together because of gravity 34 of the universe is made of dark matter unobservable gt only be detected by gravitational effect eg dropping an eraser Force on the eraser is gravity Fer maer 2 Far GmermearthRearth The mass of the earth can be considered to concentrate on the center gt the distance between the eraser and the earth is the radius of the earth 2 maer GmermemhRemh aer GmemhRemh2gt independent of the mass of the eraser gt dropping any masses their accelerations are the same Ciquot meathReath2 is the surface gravity of the earth 98msecsec mass In general the surface gravity of an object is given by Surface gravity G radius 2 Twobody system i There are only 2 objects ii The only forces acting are mutual gravitational forces eg a simple example of a 2body system can be the eraser and the earth If 2 bodies are let to freely interact a the path orbit of one object relative to the other must have one of the following shapes circle ellipse parabola hyperbola straight line Circle and ellipse orbits are capture orbits eg Earth orbiting around the sun gt capture orbit Newton with Newtonian mechanics said that there are encounter orbits which are parabola and hyperbola orbits What makes planets39 orbits spiral because of other forces other than gravitation b An object moves about the other in such a way that the line joining them sweeps out a constant area of orbit per unit time law of equal areas The triangles represent areas the object moves in a specific unit of time They must be of the same area eg motions of comets such as Halide comet Because when the object is closer to the sun the gravitation is higher gt acceleration is higher gt speed up Opposite for the other case c For capture orbits the mean distance sidereal period time for one orbit and the total mass mass 1 mass 2 are related as follows harmonic law mean distance3 sidereal period2 constant gtlt mass1 mass2 distances are measured in astronomical units or AU39s one astronomical unit mean earth sun distance 15x1011m time is measured in earth years masses are measured in solar mass units one solar mass 2x1030kg then the constant in the harmonic law is 1 Harmonic law is applied only to capture orbits Challenge of measuring masses of objects gt harmonic law offers a tool to calculate the masses eg Consider the earthmoon system mean distance 1400 AU 2510393 AU the sidereal period of the moon 112 8x102 year gt possible to calculate the mass of the earth based on harmonic law 25x10A33 W 1 Mearth Mmaan Mmoon can be considered to be 0 because mass of the moon is very small relatively to 1 solar mass unit I4gt Mass of the earth 2 2310396 solar mass units gt the mass of the earth is 23 millionth of that of the sun 25x10A33 8x10 2 So astronomers then can figure out masses of other objects by observing their orbits The 2body system is a bit too idealistic gt departures from the 2body systems 1 Smallscale departure gt Perturbation theory 2 Largescale departure gt nbody theory can explain why orbits are spiral dea example of 2body systems are systems of binary stars but then masses can39t be ignored although their masses might be small relative to solar mass units P a f a f If 39 111 rh xii3 6 Ufa 39 39 J 1 M8013 r 3 w E 7 v TN quot539 a gt 91 m 9 Vamwi 3313 I L 3 55 ZWr 3 mquot 07 mem c Low L a sari LP 31 I W 39s La I G emPXVMW3 Mrs Ms A39b i o 39 TOW Rd39m Lighiquot quotWhl I ggg Lari1quot AM a 12 r m 2 f 1 I r V v u s gt y 3 gt A 39 r r 39 a av P a f i v39m quotJ 39 HW W 3 U 2 40 w 0 W n s c i cwhtf w 7 m C U a39ifEmei Low cf Gf fv f givg m Force 65amquot 393 91 quhiquot 300 Mg mS c Skewcan s LoMtILIzz TaEN otr39HN g m MQSS Q elq Ky 903519 9 H c o m We 3 law Pomquotk m5quot gt 1 17ml 5 7 WW Ewpg 39 Para Edit3x 1 Law as anagf v Eclva 471mm gwg w yei 5 market Lmu 0W Eolrme 5 6 NM EC F55 quot inf3539 mef39w Vi m z Eq Nhrg 055 7 3a aw in f Ferfm 16 s G 2 g i o f K Smau 26 thmaz 39S m Maggi 39 Laf l a 39FCwnp i f lx m f 39 W 9614 0 5 5 s z HA sCW x Egg 27 Whip m s atvim 4 G gy 5 u 3 t3 r f 6 2 him 363 gagw WM 0 a ww 5 v lt9wwmw 39 u ilnL JNEL I r r warfizwwa WW F r 5M5 f f W l QL i J 5 P n g 7 15 3 1 quotW x P quotk s 5quot 1 A w how Ivrug 3 Ve cc 7 WWW w m bwzrJ2xr1 mum 139 r at J quot w fzfr 03005 4 1 z a 39 quot 413 i M f T t f WQ39QQCOEGI quot395 gc w rf Lam R g E qw wq 3a 3va V QEiUOv500 1C 2 56 3miu 4 0 00 g 6 W W T3 533R VF 10 T We 1 l lOAa x 10quotb lOquotab lOAa 10quotb lOAab 10quotaquotb lOAaxb 110quota 10quot a a 1 e P 39 o I h a 39 Luz 22 0 39Letitiittir39 l The flat 3 392 Arm723 5 139353 lugnggjiii uiet we the celestial sphere along a path called the ecliptic This ecliptic path intersects the celestial equator at two points called the equinox points The vernal equinox point is the point on the celestial equator at which the sun appears to cross the celestial equator moving from south to north The prime hour circle is then designated as the hour circle which contains the vernal equinox point 39 Focal length of primary lensmirrorFocal length of the eyepiece BlBZconstantdiameterquot2constantdiameterquot2 onstantdiameter of lensmirrorquot2 We w 79 117 qu r arrest 95ft Hamlet2e salinity numbers and mathematics Essie S TEljrs l represented with models Eyre 150 AD Ptolemy if an explanation is offered for a given phenomenon it must quotsave the phenomenon that is it must account for all of the observed characteristics of the phenomenon as possible William of Occam1400 AD if two or more explanations are equally successful at saving the phenomenon choose the simplest point on the celestial equator at which the sun appears to cross Total power5x10quot 2x3x10quot 1215xquot 14 Apparent Brightnesstotal powerimage area2xlOquot 1515xquot 14 image area Apparent brightnesstotal power image area 2x10A1515x10quot14 Image area 2x10A 15lmage an ew apparent brightness b new apparent magnitude Zt 2 23323 X10A 9X1125quot2 Type of telescopes Newtonian reflector Prime Focus Reflector Cassegrain Reflector gnaw 53 3 42 re 1 I 5 v a a I f g g j aquot a 3 r r g l 39 z I 39 7 a 1 i i tr f i i 1 l K 74 g 39M v i l w 1 M l i A A 5 39 v39 i 2 l 3 39 l i 4 Er 39 L i l i i E it i 39 aquot i W E x a W rAN iikv I i E n Wye3 We an March 23rd 2012 Earth Basic properties 1 Mass ofthe earth 6 x 1024 kg 2 Radius of the earth 6400km Eratosthenes 200BC noticed that on the first day of summer sunlight is perfectly perpendicular to Seyene and forms a 7 deegree angular with Alexandria gt radius of the earth Seyene Alexandria 500 stadia 4gt 500 stadia 7 degree circumference of the earth360 degree I4gt Circumference of the earth N 250000 stadia 25000 miles 40000km 3 Density mass per unit volume measured in gcm3 or kgm3 Typical ice 10 gcm3 or 1000kgm3 Typical rock 30 gcm3 or 3000 kgm3 Typical metal 80 gcm3 or 8000 kgm3 Mean density total mass total volume Assume that all objects are spherical in shape gt volume of a sphere T R3 Mean density of the earth 5500kgm3 Earth is composition of rock and metal denser than rock but lighter than metals Mean density of surface material 3300kgm3 mostly made up of rocks Mean density of surface lt mean density gt mean density of the rest must be higher gt the inner part must be denser 4 Magnetic field Earth also has magnetic field Common metals Fe and Ni nickel Seismology tsunamis mostly because of earthquakes nuclear weapons became banned gt tested underground primary waves travel thru both solids and liquids secondary waves do not travel through liquids the crust is very complicated Crust can be split up into plates Plate tectonics gt earthquakes Axis of rotation is no longer the axis of the magnetic field Liquid outer core gt magnetic field Other planets have magnetic fields

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