Physics of astronomy week 4 winter 2004 astrophysics ch 2
Download
1 / 11

Physics of Astronomy, week 4, winter 2004 Astrophysics Ch.2 - PowerPoint PPT Presentation


  • 54 Views
  • Uploaded on

Physics of Astronomy, week 4, winter 2004 Astrophysics Ch.2. Star Date Ch.2.1: Ellipses (Matt #2.1, Zita #2.2) Ch.2.2: Shell Theorem Ch.2.3: Angular momentum (J+J, #2.7) #2.11: Halley’s comet Learning plan for week 5. Ch.2.1: Ellipses (Matt #2.1, Zita #2.2).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Physics of Astronomy, week 4, winter 2004 Astrophysics Ch.2' - mitch


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Physics of astronomy week 4 winter 2004 astrophysics ch 2
Physics of Astronomy, week 4, winter 2004Astrophysics Ch.2

Star Date

Ch.2.1: Ellipses (Matt #2.1, Zita #2.2)

Ch.2.2: Shell Theorem

Ch.2.3: Angular momentum (J+J, #2.7)

#2.11: Halley’s comet

Learning plan for week 5


Ch 2 1 ellipses matt 2 1 zita 2 2
Ch.2.1: Ellipses (Matt #2.1, Zita #2.2)

Make an ellipse: length of string between two foci is always r’ + r = 2a.

Eccentricity e = fraction of a from center to focus.


2 1 derive the equation for an ellipse
#2.1: Derive the equation for an ellipse.

Distance from each focus to any point P on ellipse:

r2=y2+(x-ae)2 r’2=y2+(x+ae)2

Combine with r+r’=2a and b2 = a2(1-e2) to get


2 2 find the area of an ellipse
#2.2: Find the area of an ellipse.

so y goes between

and x goes from (-a to +a)

Area =


Ch 2 2 shell theorem p 36 38
Ch.2.2: Shell Theorem (p.36-38)

The force exerted by a spherically symmetric shell acts as if its mass were located entirely at its center.

The force exerted by the ring of mass dMring on the point mass m is

Where s cosf = r - R cos q and s2 = (r - R cos q )2 + (R sin q )2 and

dMring = r(R) dVring and

dVring = 2 p R sinq R dq dR


Physics of astronomy week 4 winter 2004 astrophysics ch 2

Substitute this into dF and integrate

Change the variable to u = s2 = r 2 + R 2 - 2rR cos q. Solve for

cos q =

sin q =

Substitute these in and integrate over du to get


Physics of astronomy week 4 winter 2004 astrophysics ch 2

Density = mass of shell / volume of shell

r(R) = dMshell / dVshell

So dMshell = r(R) dVshell = 4 p R2r(R) dR

Which is the integrand of

So the force on m due to a spherically symmetric mass shell of dMshell:

The shell acts gravitationally as if its mass were located entirely at its center.. Finally, integrating over the mass shells, we find that the force exerted on m by an extended, spherically symmetric mass distribution is

F = GmM/r2



Center of mass reference frame
Center of Mass reference frame

Total mass = M = m1+ m2

Reduced mass = m

Total angular momentum L=m r v = m rp vp


Virial theorem
Virial Theorem

<E> = <U>/2

where <f> = average value of f over one period

Example: For gravitationally bound systems in equilibrium, the total energy is always one-half of the potential energy.


Learning plan for week 5 hw due mon 9 feb
Learning Plan for week 5 (HW due Mon.9.Feb):

Mon.2.Feb: Introduction to Astrophysics Ch.3

Universe Ch.5.1-3, #6, 11 (Jared + Tristen)

Universe Ch.5.4-5, #25 (Brian + Jenni)

Universe Ch.5.6-8, #27, 29 (Erin + Joey)

Universe Ch.5.9, #34, 36 (Matt + Chelsea)

Universe Ch.19.1, #25 (Annie + Mary)

Tues.3.Feb: HW due on Physics Ch.6

Universe Ch.19.2-3, #34, 35 (Jared + Tristen)

Universe Ch.19.4-5, Spectra -> T,Z, #43 (Erin + Joey)

Universe Ch.19.6, L(R,T), #46, 50 (Annie + Mary)

Universe Ch.19.7,8, HR, #52 (Brian + Jenni)

Thus.5.Feb: HW due on Astrophysics (CO) Ch.2

CO 3.1, Parallax, #3.1 (Jared + Tristen)

CO 3.2, Magnitude, #3.8 (a-d) (Erin + Joey)

CO 3.3 Wave nature of light, #3.6 (Matt + Chelsea)

CO 3.4, Radiation, #3.8 (e-g) (Brian + Jenni)

CO 3.6, Color index, #3.13 (Annie + Mary)