physics of astronomy week 2 – thursday 15 jan 2004 celestial mechanics star date boas: spherical...
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Physics of Astronomyweek 2 – Thursday 15 Jan 2004
Celestial Mechanics
• Star Date
• Boas: Spherical Coordinates
• Gravity lecture and applications
• Workshop moons of Jupiter
• Learning plans and assignments
Boas: Spherical coordinates
Guiding Questions: Celestial Mechanics
1. How did ancient astronomers explain the motions of the planets?
2. Why did Copernicus propose that the Earth and the other planets revolved around the Sun?
3. What did Galileo see in his telescope that supported the geocentric model?
4. How did Tycho Brahe attempt to test the ideas of Copernicus?
5. What phenomenological laws did Kepler induce from Tycho’s data?
6. How do Newton’s laws explain Kepler’s conclusions?7. Why don’t the planets fall into the Sun?
Derive Kepler’s 3d law from Newton’s second law:
F=ma
Gravitational force acceleration in circular orbit
F=GmM/r2 a = v2/r
Solve for v2:
Speed v = distance/time = 2r/T. Plug this into v2 and solve for T2:
This is Kepler’s third law: T = period and r = orbit radius.
Apply Kepler’s 3d law: For objects orbiting the Sun,
a=radius in AU and p=period in years
A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How far is the satellite from the Sun? 2
3 2 10 a = p = _______
12
a ______
NB: This simple form of K3 only works for our solar system. Why?
A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How often does the satellite pass between the Earth and the Sun?
1 1 1
'
1 1 1
1 1 110 1
121
________________
________________
sidereal period Earth s sidereal year synodic period
P P S
S
SS
Sidereal and Synodic periods
We can use Newton’s gravity to approximate the size of a black hole!
21
2____________
Gravitational energy kinetic energy
GmMmv
rSolve for r
Not even light can escape (v=c) if it is closer than r to a black hole. This is the Schwarzschild radius:
R=_____________________
42r3 = GM T2 a3=p2 for planets around the SunOrbit radius: r(m) or a(AU); Period T(sec) or p(years)
http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html
Keplerian orbits: close = faster
Solve 42r3 = GMT2 for central mass M=_______
Earth data: period = 1 year ~ 3 x 107 sec
orbit radius = 1 AU ~ 150 x 109 m
M= M=
Saturn data:
period ~ 30 year = __________________ sec
orbit radius = 10 AU ~ ________________ m
M= M =
Use Kepler’s 3d law to weigh the Sun
Use Kepler’s 3d law to weigh Jupiter.
Then, use Kepler’s 3d law to weigh galaxies and discover dark matter
Mon.19.Jan: Holiday; Tuesday Boas HW due.
Tues.20.Jan: ML on Universe Ch.3: Moon & Eclipses
Thus.22.Jan: ML on Universe Ch.4: Gravity & Orbits
Mon.26.Jan: Workshop on Jupiter’s moons & Dark matter
Tues.27.Jan: HW due on Universe 3+4; Quiz
Review Physics Ch.3+4; ML Physics Ch.6
Thus. 28.Jan: Lecture and ML on Astrophysics Ch.2
Tues.3.Feb: HW due on Physics Ch.6; CO Ch.2; Quiz
Learning Plan for weeks 3-4:
Tues.20.Jan: Universe Ch.3: Moon & Eclipses (Boas due)
Team 1: Ch.3.1, Motion of Moon, # 23
Team 2: Ch.3.2, Motion of Moon, # 43
Team 3: Ch.3.3-4, Lunar Eclipses, # 30
Team 4: Ch.3.5, Solar Eclipses, #33
Team 5: Ch.3.5, Distances: demonstrate and diagram Eratosthenes’ calculation
Thus.22.Jan: Universe Ch.4: Gravity & Orbits
Team 1: Ch.4.1-2, Retrograde motion, #48
Team 2: Ch.4.3, Galileo’s observations, #50 or 52
Team 3: Ch.4.4-5, Tycho + Kepler, #35
Team 4: Ch.4.6-7, Newton + orbits, #39
Team 5: Ch.4.8, Tides #44 (or Physics Ch.6 #54)
Assignments for week 3:
Mon.26.Jan: Workshop on Jupiter’s moons & Dark matter
Tues.27.Jan: HW due: Physics Ch.6 # 54
Universe Ch.3 # 23, 43, 30, 43, Ch.4 # 48, 52, 35, 39, 44
Review Physics Ch.3+4; ML Physics Ch.6, Gravitation:
Team 1: Ch.6.1-3, #13, 14
Team 2: Ch.6.4-5, #28
Team 3: Ch.6.6-8, #47
Thus. 28.Jan: Lecture on Astrophysics Ch.2
Team 4: Ch.2.1, #2.1 & 2.2
Team 5: Ch.2.3, #2.7
Tues.3.Feb: HW due: Physics Ch.6 # 13, 14, 28, 47, 57, 60
CO (Astrophysics) Ch.2 # 1, 2, 7, 8, 11
Assignments for week 4: