Physics of AstronomyTuesday, 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 orbitsF=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 10-11 N.m2/kg2

•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/r2

Force on m is F = ma a = v2/r

Solve for period T v=2r/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 momenta Torques change angular momenta

F=dp/dt (= ma) where =dL/dt = r F = I where

Linear momentum p = mv is Angular momentum L = mvr = I is

conserved if F=0 conserved if =0

s=R, v=R, atan=Rmr2

Klin=p2/(2m) = ½ Mv2 Kang=L2/(2I) = ½ I2

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: 1st order, scalar differential equations instead of

F=ma: 2nd order, vector differential equations. DO #11.2

xx x x

dv dxT m dx m dv mv dv

dt dt F dx

Raff Ch.11.1.3 – Hamilton’s EOM2

( ) ... :2

pH T V V x treat p and x independently

mdH

dp

dH

dx

xx x x x

x

dp dxT F dx dx dp v dp

dt dtdT

dv

F dx

Generalized x-coordinate becomes q… DO #11.6

Raff Ch.11.1.4 – Angular momentum

Homework: DO #11.4

Angular momentum L = p = M = r x p

Raff Ch.11.1.3 – Hamilton’s EOM

2 2

,

: ( , , ), ( , , )

: ( , ), , , ( , )

q

q

q x y z

r

x y

rr

dpdH dq dH

dp dt dq dt

Cartesian q x y z p mv mv mv

dr dPolar q r v v p

dt dt

v v

T

dT dTp p

dv dv

Homework: apply this technique to #11.5