Transcript Chapter 4 Gravitation and the Waltz of the Planets

Physics of Astronomy
week 4, winter 2004
Celestial Mechanics
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Star Date
Review motion of Moon and Mars
Starry Night animations
Jupiter’s size and distance – workshops
Gravity review: Physics Ch.3-6
Figures for Astrophysics Ch.2
Learning plan
Use Kepler’s 3d law to weigh Jupiter
Gravity review: Physics Ch.3-6
Ch.3: Kinematics in 2D: Vectors
• Review vectors.
Add component by component.
• Forces in the y direction do not affect motion in the x direction
v2
• Uniform circular motion: a 
r
• Galilean relativity: Motion of an object depends on the motion
of its reference frame
Physics Ch.4: Newton’s Laws
SForce = mass * acceleration, where a = dv/dt
• N1: Law of Inertia: Every body continues in its state of rest or of
uniform speed in a straight line as long as no net force acts on it.
• N2: SF=ma: The acceleration of an object is directly proportional to the
net force acting on it and is inversely proportional to its mass. Acceleration is in
the same direction as the net force.
• N3: Action & Reaction: Forces are INTERACTIONS: Whenever
one object exerts a force on a second object, the second exerts an equal and
opposite force on the first.
Physics Ch.6: Gravitation & Newton’s Synthesis
F
GmM
rˆ
2
r
We derived Kepler’s 3d law (phenomenological)
from Newton’s 2d (theory)
Near the surface of the Earth, F=mg. Derive g from
the mass M and size R of Earth:
g is approximately constant close to the surface of
the Earth, but weakens with altitude.
Newton’s law is indistinguishable, in most cases,
from Einstein’s insight that gravity is due to the
curvature of space near massive objects.
Astrophysics Ch.2:
Learning Plan for weeks 3-4:
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
Assignments for week 4:
Tues.27.Jan: HW due: Physics Ch.6 # 54
Universe Ch.3 # 23, 24, 33, 30, 43, start 45
Ch.4 # 36, 48, 52 (50), 35, 39, 44
Review Physics Ch.3+4; ML Physics Ch.6, Gravitation:
Team 1: Ch.6.1-3, #13, 14: Brian & Mary
Team 2: Ch.6.4-5, #28: Erin & Jenni
Team 3: Ch.6.6-8, #47: Annie & Tristen
Thus. 28.Jan: Lecture on Astrophysics Ch.2
Team 4: Ch.2.1+2.2, #2.1 & 2.2: Matt & Zita
Team 5: Ch.2.3, #2.7: Joey & Jared
Tues.3.Feb: HW due: Physics Ch.6 # 13, 14, 28, 47, 57, 60
CO (Astrophysics) Ch.2 # 1, 2, 7, 8, 11