Astronomy 421 Concepts of Astrophysics I. Astrophysics Talks at UNM. Course Logistics. Backgrounds. Other Opportunities

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Astonoy 421 Concepts of Astophysics I Couse Logistics Goals: - Ipove knowledge of astophysics - develop eseach skills ain Aeas of Study: - Obital echanics - Radiation and atte - Relativity - Stas -

1 Astonoy 421 Concepts of Astophysics I Couse Logistics Goals: - Ipove knowledge of astophysics - develop eseach skills ain Aeas of Study: - Obital echanics - Radiation and atte - Relativity - Stas - Stella Renants (including Black Holes) G.B. Taylo Fall 2013 Lectue topics and eading can be found on the syllabus Poble solving (hoewoks and in class) Pee eview execise Te pape (and pesentation) will be a significant pat of the couse (see handout) 1 Astophysics Talks at UN Please eview ateial in Ch 1 of Caoll +Ostlie (The Celestial Sphee) but it won t be in lectues, hoewoks o tests. HW 1 due Thusday, Aug 29. Thusdays 2-3P in oo 190 (see schedule on dept web pages) Astonoy specific seinas Geat oppotunity to lean oe about a wide ange of topics in astophysics Fee Donuts! Fidays 11a Noon NRAO Colloquiu Seies by Video fo Roo 190 Astonoy specific Colloquia Fiday 4-5p Colloquia a PandA (see schedule on dept web pages) Physics and Astonoy Colloquia 3 4 Othe Oppotunities UN uns a Univesity Radio Obsevatoy The Long Wavelength Aay - You can get telescope tie on this wold-class facility ASTRON/JIVE sue student poga gaduate and advanced undegads weeks in the Nethelands - Application deadline is Feb. 1 NRAO Sue Student poga undegads and gads weeks in Socoo (!!!), Geen Bank, o Chalottesville - Application deadline Feb. 1 Backgounds Pof. Geg Taylo, PhD UCLA 1991 Cluste agnetic Fields Eployent: NRAO pedoctoal Fellow Postdocs at Aceti and Caltech NRAO Socoo staff scientist UN Pofesso and Diecto of the LWA Reseach Aeas: Galactic and Extagalactic Astonoy, Cosic Explosions, Radio Intefeoety Instuentation and Techniques You Backgound? NRAO Synthesis Iaging Wokshop in June days of Apetue Synthesis Techniques See e fo oe details 1

Keple s Laws Newtonian echanics echanics - Outline Keple's laws: Celestial echanics (C+O

Enegy, Potential Enegy, Kinetic Enegy, Escape Velocity Newtonian Explanation of Keple s

A line connecting a planet to the Sun sweeps out equal aeas in equal tie intevals. 3.

2 Keple s Laws Newtonian echanics echanics - Outline Keple's laws: Celestial echanics (C+O Chapte 2) 1. A planet obits the Sun in an ellipse, with the Sun at one focus of the ellipse. Enegy, Potential Enegy, Kinetic Enegy, Escape Velocity Newtonian Explanation of Keple s Laws Viial Theoe 2. A line connecting a planet to the Sun sweeps out equal aeas in equal tie intevals. 3. The squae of the obital peiods of a planet is popotional to the cube of the seiajo axis of its elliptical obit. Tidal Foce, Roche Liit Collision Physics These ae kineatical elations - descibe the otions without efeence to the dynaical foces. We shall see that they can be deived and efined fo Newton's law of gavitation. 7 8 Keple's fist and second laws illustated Keple's thid law illustated P 2 a 3 Seiino axis Seiajo axis 9 10 Bode s Law oden View a = * 2 whee = 0, 1, 2,... 9 Devised by Bode in 1772, no longe accepted

oe geneally, obital otions follow conic sections, depending on total

A conic section is the suface foed by cutting a cone with a plane.

13 14 Cuves with e = 1 ae paabolas Exaple 2.1.1 Deteine the vaiation

whee p is the distance of closest appoach to the focus (at angle 0).

0934 Cuves with e >1 ae hypebolas Cuves with 0 e < 1 ae ellipses Cuves

3 oe geneally, obital otions follow conic sections, depending on total enegy. A conic section is the suface foed by cutting a cone with a plane. (see C+O 2.1) Copae closed and open cuves Cuves with e = 1 ae paabolas Exaple Deteine the vaiation in distance of as fo the focus though its obit. whee p is the distance of closest appoach to the focus (at angle 0). Seiajo axis of as's obit = AU e= Cuves with e >1 ae hypebolas Cuves with 0 e < 1 ae ellipses Cuves with e = 0 ae cicles Futhest distance fo focus is a + ae = a(1 + e) = 1.67 AU. Closest distance is a ae = a(1 - e) = 1.38 AU. Now, let's ove onto Newton's desciption! Newtonian echanics Newtonian echanics

4 Newtonian echanics Linea oentu Newton's laws: 1. An object at est will eain at est and an object in otion will eain in otion in a staight line at a constant speed unless acted upon by an extenal foce. => Consevation of linea oentu in absence of unbalanced foce. Angula oentu θ plane The law of inetia Foce is the change of oentu with tie. 3. The law of action-eaction, o consevation of total linea oentu. In any inteaction, of e.g., two paticles, the changes in oentu obey If tie inteval of inteaction is, then the ate of oentu change is Fist law is thus a special case of second Newton's Law of Gavitation (see C+O 2.2 fo deivation, fo Keple III and centipetal foce) { { When. a toque exists = 0 = 0 fo cental foces. Why? Fo point asses, this attactive foce is a cental foce. Still tue fo spheically syetic bodies (see C&O exaple 2.2.1). Gavitational acceleation Note that g is independent of

Gavitational potential enegy: Fo In 3-D, geneally Enegy (o wok) necessay to aise an object against a gavitational foce is given by: Kinetic enegy Likewise we can use

Then plug in in fo F, and integating, we find U at any othe to be: 25 which is change in kinetic enegy between the ties t 1 and t 0.

26 Total enegy Fo definitions of KE and U, any change in U is balanced by opposite change in KE: Suaizing: and thus the total enegy E is constant: Gavitational

Kinetic enegy Total enegy Any change in U balanced by opposite change in KE: total enegy of 27 28 A consequence of enegy consevation: Escape velocity If ass oves to

5 Gavitational potential enegy: Fo In 3-D, geneally Enegy (o wok) necessay to aise an object against a gavitational foce is given by: Kinetic enegy Likewise we can use Newton 2 and integate the RHS, f i Only changes in U elate to F. Zeo point of U abitay. So define U to be zeo at infinity. Then plug in in fo F, and integating, we find U at any othe to be: 25 which is change in kinetic enegy between the ties t 1 and t 0. Call these the kinetic enegies K 1 and K 0 espectively. 26 Total enegy Fo definitions of KE and U, any change in U is balanced by opposite change in KE: Suaizing: and thus the total enegy E is constant: Gavitational potential enegy If we conside the ass to be fixed, then the only KE is due to the ass,. This is fine fo, e.g. satellites obiting the Eath, but we will genealize this late. Kinetic enegy Total enegy Any change in U balanced by opposite change in KE: total enegy of A consequence of enegy consevation: Escape velocity If ass oves to and slows to v=0 (i.e. "escapes"), then KE = U = 0, so E = 0 at. Then eveywhee. Execise Escape Velocity poble: What velocity is needed fo a ocket to escape the gavitational influence of the Eath? Eath = x kg eath = 6378 k In this case, v=v escape Note: independent of. What is physically? Does it have to be the adius of a planet? 29 5

Gravitation. AP/Honors Physics 1 Mr. Velazquez

Gravitation. AP/Honors Physics 1 Mr. Velazquez Gavitation AP/Honos Physics 1 M. Velazquez Newton s Law of Gavitation Newton was the fist to make the connection between objects falling on Eath and the motion of the planets To illustate this connection