Physics of Astronomy Tuesday, winter week 6 (♥14 Feb.06) Math-A: Giancoli Ch.6 – Gravity and orbits Math-B: Giancoli 11, Raff Ch.11.1 HW setup Excel workshop tomorrow (Wednesday) – what time? Energy and momentum conservation lab Thursday Looking ahead

Phys-A: Giancoli Ch.6: Gravity and orbits  F=ma If you know all the forces operating, you can find the acceleration. What forces have we worked with so far? What other forces can move objects? Gravitational force near Earth: Gravitational force more generally:

G and orbits Cavendish experiment found the universal gravitational constant G = 6.67 x N.m 2 /kg 2 What is G in fundamental SI units? Let’s derive g from G (assuming we know the mass of the Earth) Each team choose one: Ch.6 # (p.151) 4,6,8,11,13,14,18 But how could we know the mass of the Earth? Kepler’s laws Derive the Earth’s mass from the Moon’s orbit.

Newton’s 2d → Kepler’s 3d F = GmM/r 2 Force on m is F = ma a = v 2 /r Solve for period Tv=2  r/T Each team choose one: (p.152) 22,27,28,36,38; (p.153) 42, 47, 53, 54, 57, 59; (p.154) 60, 62

Looking ahead Tomorrow (Wednesday): EXCEL workshop in CAL for A+B time? see template worksheet on syllabus and in CAL/…/Handouts Thursday (Physics B): Energy + Momentum lab in CAL 1234 beforehand: complete Excel workshop and Pre-Lab on syllabus review kinetic energy, angular motion, and momenta

Phys.B: Giancoli Ch.9-11: Momenta and Angular motion Forces change linear momentaTorques change angular momenta  F=dp/dt (= ma) where  =dL/dt = r  F = I  where Linear momentum p = mv isAngular momentum L = mv  r = I  is conserved if  F=0 conserved if   =0 s=R , v=R , a tan =R    mr 2 K lin =p 2 /(2m) = ½ Mv 2 K ang =L 2 /(2I) = ½ I  2 Ex: Each team choose one: Ch.11  =r  F (p.295) #6-8, 10, 18, 29, 37, 38, 49, 54, 63

Raff Ch.11.1 – Classical Mech Potential energy V = U : F = -dV/dx only conservative forces have potential energy (Gravity and Electric yes - Friction and Magnetic no) Kinetic energy K = T = Work done Hamiltonian = Kinetic energy + Potential energy H = T + V Easier: 1 st order, scalar differential equations instead of  F=ma: 2 nd order, vector differential equations. DO #11.2

Raff Ch – Hamilton’s EOM Generalized x-coordinate becomes q… DO #11.6

Raff Ch – Angular momentum Homework: DO #11.4 Angular momentum L = p  = M = r x p

Raff Ch – Hamilton’s EOM Homework: apply this technique to #11.5