Transcript Day-16

Astronomy 1010
Planetary Astronomy
Fall_2015
Day-16
Kill time
Course Announcements
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Dark Sky nights – Mon. 10/5 & Wed. 10/7 starting at
7:30pm – at the Observatory.
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Exam-2 will be Friday, Oct. 9
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SW-chapter 4 posted: due Mon. Oct. 5
First Thursday Art Walk 5-8pm tomorrow; downtown
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Definitions & Terms -1
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Tide: (1) A laundry detergent
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(2) A gravitational interaction which goes as d3
Lecture – Tutorial
Newton’s Law of Gravity: pg 29
 Work with a partner!
 Read the instructions and questions carefully.
 Discuss the concepts and your answers with one
another.
 Come to a consensus answer you both agree on.
 If you get stuck or are not sure of your answer, ask
another group.
 If you get really stuck or don’t understand what the
Lecture Tutorial is asking, ask one of us for help.
i-Clicker Question
Renaissance Astronomy: Gravity Calculations 1
PROCESS OF SCIENCE
 For a theory to be
“scientific”, it must
be testable.
 Old theories that
are disproven lead
to greater insight.
Newton’s Law and Gravitation
• All my favorite Projectiles behave like this!!!

Velocity
Force
Acceleration
 Kepler’s laws of
orbits and Newton’s
laws of motion and
gravity are only the
beginning.
 Gravity is very
important for shaping
objects and orbits.
 Internal forces
 Tides
 Orbital resonances
 The gravitational
force results in an
acceleration.
 All objects on Earth
fall with the same
acceleration known
as g.
 g = 9.8 m/s2
F
g
w
eight m
 Gravity is an attractive force between any two
objects with mass, acting along the line
between them.
 It depends on the objects’ masses.
 It depends on the distance between them.
 G is the universal gravitational constant.
 The m terms are the two masses.
 More mass = more force.
 The distance between the objects is r.
 A greater r = smaller force.
 Gravity is governed by an inverse square
law.
i-Clicker Question
Renaissance Astronomy: Gravity Calculations 4
 In the Earth-Moon system, the gravitational
force of Earth on the Moon is equal to the
gravitational force of the Moon on Earth.
 The accelerations are different!
 Remember Newton’s second law: F = m a.
 The more massive object will have a smaller
acceleration, while the less massive object
will have a larger acceleration.
 It is the same in the Sun-Earth system.
CONNECTIONS 4.2
 The gravitational
interaction of three
bodies leads to
Lagrangian
equilibrium points.
 These are special
orbital resonances
where the object at
that point orbits in
lockstep.
 SOHO is near L1.
 Orbits describe one body
falling around another.
 The less massive object
is a satellite of the more
massive object.
 The two bodies orbit a
common center of mass.
 For a much smaller
satellite, the center of
mass is inside the more
massive body.
 An astronaut inside an
orbiting space shuttle
will experience free fall
because he is falling
around Earth at the
same rate as the shuttle.
 He is not weightless.
 Gravity provides the
centripetal force that
holds a satellite in its
orbit.
 Uniform circular
motion: moving on a
circular path
at constant speed.
 Still experiencing an
acceleration since the
direction is constantly
changing.
 Planets in real-world
scenarios move on
elliptical orbits.
 The gravitational
force changes both
the direction and the
speed of the planet
as it moves in its
orbit.
 Results in Kepler’s
law of equal areas.
 Circles and ellipses are bound orbits.
 Objects with higher orbital speeds can
escape bound orbits to be in unbound orbits.
 Parabolas and hyperbolas are examples.
 Newton derived Kepler’s laws from his law
of gravity.
 Physical laws explain Kepler’s empirical
results:
 Distant planets orbit more slowly; the
harmonic law and the law of equal areas
result.
 Newton’s laws were tested by Kepler’s
observations.
i-Clicker Question
Renaissance Astronomy: Graph Orbital Velocities
Renaissance Astronomy: Graph Kepler’s 3rd Law
MATH TOOLS 4.2
 The velocity of an object traveling in a
circular orbit can be found by equating the
gravitational force and the resulting
centripetal force.
 This yields:
 You can solve for the period by noting that
 This yields
Kepler’s third law:
 Tides are a
consequence
of gravity.
 Something closer
to an object
experiences a
stronger gravitational
pull than something
else farther away.
 The centers of Earth
and the Moon orbit
like point masses.
 Parts of Earth are
closer to the Moon
than other parts.
 This produces a
stretch on the Earth,
called a tide.
 Tides cause bulges
to appear on either
side.
 Earth’s oceans flow in response to the tidal
forces.
 The oceans have a tidal bulge: They are
elongated in a direction that is nearly pointed
at the Moon.
 Earth rotates
under the tidal
bulge.
 We get two high
and two low tides
each day.
 The behavior is
complicated by
Earth’s
landmasses and
solar tides.
 Tides can affect the solid part of Earth,
too.
 A gravitational pull can stretch and deform
a solid body.
 Results in friction, which generates heat.
 Friction also opposes the rotation of Earth,
causing Earth to very gradually slow its
rotation.
 Days lengthen by about 0.0015 seconds
every century.