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Physics of Astronomy, week 4, winter 2004 Astrophysics Ch.2

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).

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Physics of Astronomy, week 4, winter 2004 Astrophysics Ch.2

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  1. 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

  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.

  3. #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

  4. #2.2: Find the area of an ellipse. so y goes between and x goes from (-a to +a) Area =

  5. 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

  6. 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

  7. 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

  8. Force and Angular momentum

  9. Center of Mass reference frame Total mass = M = m1+ m2 Reduced mass = m Total angular momentum L=m r v = m rp vp

  10. 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.

  11. 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)

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