PHYS 228 Astronomy & Astrophysics - Widener University

PHYS 228 Astronomy & Astrophysics
Lecture Notes from Zeilik et al. Chap. 1 Celestial Mechanics & the Solar System
Heliocentric Model of Copernicus
General Terms:
Zodiac
evening star
morning star
Inferior Planet - orbits closer to Sun than Earth (see Fig. 1-2)
elongation
superior conjunction
inferior conj
Superior Planet - orbits farther from Sun than Earth (see Fig. 1-2)
conjunction
quadrature
opposition
Orbital Periods of Planets
Synodic period -time taken by planet to return to same position in sky,
relative to Sun, as seen by Earth
Sidereal period- time taken by planet to complete one orbit w/ respect to
stars
Equations relating synodic and sidereal periods of a planet: Let S = synodic period of planet, P = sidereal period of planet, E =
sidereal period of Earth = 365.26 d
Then 1/S = 1/P - 1/E Inferior Planet 1/S = 1/E - 1/P Superior Planet
Defn: Astronomical Unit: Average orbital radius of Earth
Kepler's Three Laws of Planetary Motion
1. Elliptical Orbits 2. Radius vector of planet sweeps out equal periods in equal times 3. P2 = a3
Geometrical Properties of Elliptical Orbits r + r' = 2a = constant (1-1) by defn of ellipse b2 = a2 - a2e2 = a2(1-e2) (1-2) from Pythagorean theorem
where a = semimajor axis of ellipse
b = semiminor axis
e = eccentricity
r = a(1-e2)/(1 + e cos () (1-3) equation of ellipse A = (ab (1-5) area of ellipse e = (ra - rp)/(ra + rp) eccentricity of ellipse ra/rp = (1 + e)/(1 - e) ratio of aphelion distance to perihelion
distance ra + rp = 2a relation between aphelion/perihelion distances
and major axis rp = a(1 - e) relations between aphelion/perihelion
distances, semimajor
ra = a(1 + e) axis, and orbital eccentricity
Law of Areas and Angular Momentum dA/dt = rvt/2 = r2(d(/dt)/2 = H/2 = A/P = (ab/P Kepler's 2nd law
- of areas v2 = G(m1 + m2) [2/r - 1/a] vis viva equation (velocity at
any point r in orbit) vper = 2(a/P [(1+e)/(1-e)]1/2 velocity at perihelion vaph= 2(a/P [(1+e)/(1-e)]-1/2 velocity at aphelion
Newtonian Mechanics 1. Law of inertia 1. F = ma 1. Equal but opposite forces (action & reaction) Newton's Law of Universal Gravitation Fcent = mv2/r (1-14) v = 2(r/P Fgrav = G Mm/r2 (1-15) where G = 6.67 x 10-11 m3/kg . s2 Fgrav = (GM(/R(2)m = gm = mg W = mg Weight where g = 9.81 m/s2 Newton's Form of Kepler's 3rd Law P2 = 4(2/G(m1+m2) a3
PHYS 228 Astronomy & Astrophysics
Lecture Notes from Zeilik et al. Chap. 2 Solar System in Perspective
Planets
A. Motions:
ecliptic
prograde (direct) orbits - CCW seen from above Earth's orbital plane
synchronous rotation - sidereal rotation equals sidereal orbital period
oblateness of planet ( = (re - rp)/re Two Major Categories of Planets
Terrestrial Planets - Mercury, Venus, Earth, Mars
relatively small, low mass similar or smaller than Earth's
solid composition ( high density
orbit relatively close to Sun Jovian Planets - Jupiter, Saturn, Uranus, Neptune
large, high mass (15 to 318 M( )
liquid & gaseous comp ( low density
orbit far from Sun
B. Planetary Interiors
Differentiated - heavy elements sink to center, light elements rise to
surface
Explains Earth's Ni-Fe core, but light silicate rocks in crust
Expect Jovian planets to have rocky cores, surrounded by light H & He
Average density
((( = M/(4(R3/3) C. Surfaces Albedo A = amount reflected/amount incident
Blackbody radiation & Planck curve for warm objects Wien's law (max = 2898/T ((m) Ex. Sun T( 6000 K ( (max = 0.5 (m
Stefan's Law E = (T4 W/m
Subsolar Temperature (approx. equilibrium noontime temp near equator) Tss = (Rsun/rp)1/2 (1-A)1/4 Tsun ( 394 (1-A)1/4 rp-1/2 Planetary Equilibrium Temperature (derived from energy balance averaged
over entire planet) Te = (1-A)1/4 (Rsun/2rp)1/2 Tsun ( 279 (1-A)1/4 rp-1/2
D. Atmospheres Mercury, Moon - no atmospheres
Venus, Mars - CO2 atmosphere
Earth - N2 , O2
Jovian Planets - H, He Law for Perfect Gas
P = nRT Maxwellian Distribution - most probable speed
vp = (2kT/m)1/2 Average KE per particle
(KE( = ½ m (v2( Solve for root mean square speed
vrms = (v2(1/2 = (3kT/m)1/2 Escape speed from planet w/ mass M, radius R:
vesc = (2GM/R)1/2 Note: for vesc ( vrms, atmosphere escapes into space in few days. vesc ( 10 vrms Condition for atmosphere to be retained for billions
yrs or T ( GMm/150kR
Moons, Rings, & Debris (read on own, will be discussed in Chap. 7) A. Moons
B. Rings
C. Asteroids
D. Comets
E. Meteoroids
F. Interplanetary Dust
Newtonian Mechanics Applied to Solar System
A. Applications of Kepler's 3rd Law Modern form of Kepler's 3rd Law:
P2 = 4(2a3/G(m1+m2) B. Launching Rockets (read equations on own) Height of rocket found by equating total energy at ground w/ total energy
at maximum height h E = (KE + PE)ground = (KE + PE)h = const ½ mv2 + 0 = 0 + mgh h ( v2/2g (for small h) h = v2/2g{R(/[R(-(v2/2g)]} (for large h)
C. Orbits of Artificial Satellites Elliptical, parabolic, hyperbolic orbits PHYS 228 Astronomy & Astrophysics
Lecture Notes from Zeilik et al. Chap. 3 Dynamics of the Earth
Time and Seasons
A. Terrestrial Time Systems
celestial meridian
upper transit
celestial equator & poles
vernal equinox
sidereal time
6. local sidereal time
7. hour angle of the vernal equinox
Solar time
9. apparent solar time
10. mean solar time
Standard Time Zones
12. Greenwich mean time or universal time (UT)
Year
14. sidereal year - period w/resp. to stars -
15. tropical year - period w/ resp. to vernal equinox ( year of seasons
( Gregorian calendar
16. anomalistic year - period between successive perihelion passages
B. The Seasons Cause
Eccentricity e = 0.017 to small to affect seasons significantly
Seasons caused by tilt 23.50 of Earth's axis w/ orbital axis, resulting in
1. solar insolation varies due to angle of incidence: less in winter due to
energy spread out more, more concentrated in summer
1. fewer hours daylight in winter, more in summer
1. radiation must penetrate more atmosphere in winter due to lower angle,
more scattering Terms
vernal & autumnal equinoxes
summer & winter solstices
Tropics of Cancer & Capricorn
Arctic & Antarctic Circles - midnight sun
Evidence of Earth's Rotation (read on own) A. Coriolis Effect
21. Cyclones, Anticyclones
22. aCoriolis = 2 v x ( (constant acceleration)
A. Foucault's Pendulum
B. The Oblate Earth Evidence of the Earth's Revolution about the Sun (read on own) A. Aberration of Starlight
( ( tan ( = v/c B. Stellar Parallax
d = 206,265/(( (AU)
C. Doppler Effect
((( = ((-(()/(( = vr/c Differential Gravitational Forces
A. Tides Differential Tidal Forces:
Non- point source masses attract near faces of each other stronger than far
faces
Results in tidal stretching ( bulges (see Fig. 3-15)
Moon's tidal stretching of Earth & Earth's stretching of Moon (spring &
neap tides) dF/dr = -2GM/R3
or
dF = -(2GM/R3) dR where M, R = mass & radius of perturbing body (Moon here) B. Consequences of Tidal Friction 1. synchronous rotation of Moon with its orbit
1. slowing of Earth's rotation
1. recession of Moon C. Precession and Nutation Precession of equinoxes due to gravitational torque on rotating Earth by
Sun & Moon - 50(/yr
Nutation - wobbling of Earth's rotation axis due to Moon's orbit inclined
50 with ecliptic -sometimes above, sometimes below plane D. Roche Limit Limiting distance at which a body may approach another body without being
tidally disrupted. d = 2.44 ((M/(m)1/3 R Roche limit for a fluid satellite d = 1.44 ((M/(m)1/3 R Roche limit for a rigid satellite PHYS 228 Astronomy & Astrophysics
Lecture Notes from Zeilik et al. Chap. 4 The Earth-Moon System Dimensions (read on own) Eratosthenes - measured diameter of Earth c. 200 B.C. Dynamics
A. Motions
Months
2. sidereal month - w/resp. to stars 27.322 d
3. synodic month - w/resp to phases 29.531d
4. draconic or nodical month - w/resp. to line of nodes (intersect
ecliptic) 27.212 d
5. anomalistic month - w/resp to consecutive perigee 27.555 d
Synchronous rotation - tidal slowing
libration in longitude & latitude B. Phases
new (inf. Conj)
waxing crescent
first quarter (quadrature)
waxing gibbous
full (opposition)
third quarter (quadrature)
waning crescent B. Eclipses
Solar Eclipses
16. partial, total, & annular
Lunar Eclipses
18. partial & total
Interiors (read on own) A. The Earth Average
density ((( = 3M(/4(R(3 = 5520 kg/m3
Components Crust,
Mantle, Core Determinations of interior from earthquakes
longitudinal compression (P) waves
transverse distortion (S) waves
Hydrostatic Equilibrium
downward force of gravity balanced by upward pressure
otherwise object would expand or contract dP/dr = -(® [GM/r2] Equation of hydrostatic equilibrium (EHE) States that internal pressure becomes smaller as one moves from center to
surface. Ex. Use EHE to estimate central pressure inside planet or star: Consider region radius r w/ mass M and average density ((( inside a planet
.
Then must have
M = 4/3 (r3 ((( Simplify by taking ( to be uniform, & that surface P