physics of astronomy tuesday, winter week 6 (♥14 feb.06) math-a: giancoli ch.6 – gravity and...
TRANSCRIPT
![Page 1: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/1.jpg)
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
![Page 2: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/2.jpg)
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:
![Page 3: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/3.jpg)
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.
![Page 4: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/4.jpg)
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
![Page 5: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/6.jpg)
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
![Page 7: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/7.jpg)
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
![Page 8: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/8.jpg)
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
![Page 9: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/9.jpg)
Raff Ch.11.1.4 – Angular momentum
Homework: DO #11.4
Angular momentum L = p = M = r x p
![Page 10: 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](https://reader036.vdocument.in/reader036/viewer/2022082817/56649e225503460f94b0f67b/html5/thumbnails/10.jpg)
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