Astronomy 1010-H
Planetary Astronomy
Fall_2015
Day-16
Definitions & Terms -1
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Tide: (1) A laundry detergent
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(2) A gravitational interaction which goes as d3
Kill time
Course Announcements
•
How is the sunset/sunrise observing going?
•
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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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
Concept Quiz—Gravity and
Weight
Your weight equals the force between you and Earth.
Suppose you weigh 600 newtons. The force you exert on
Earth is:
A. 600 newtons.
B. much smaller than 600 newtons because your mass is
much less than Earth’s.
C. exactly zero, since only massive objects have gravity.
 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.
Concept Quiz—Earth’s Position
Assume Earth were moved to a distance from the Sun
twice that of what it is now. How would that change the
gravitational force it would experience from the Sun?
A.
B.
C.
D.
E.
It would be half as strong.
It would be one-fourth as strong.
It would be twice as strong.
It would be four times as strong.
It would not change.
 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.
Concept Quiz—Earth and Moon
Earth and the Moon have a gravitational force between
them. The mass of the Moon is 1.2 percent of that of
the Earth. Which statement is incorrect?
A. The force on the Moon is much larger than that on
Earth.
B. The forces are equal size, even though the masses are
different.
C. The Moon has a larger acceleration than Earth.
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.
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.
 Earth’s mass is large
compared to the
Moon’s, so tidal
forces on the Moon
are strong.
 Moon’s rotation and
orbital period are
locked: tidal locking.
 This means the
Moon’s rotation
period equals its
orbital period.
 Because of tides, Earth is not a perfect sphere.
 Earth’s leading edge creates an acceleration
on the Moon in its orbit, resulting in a bigger
orbit.
 The lunar month increases by 0.014 seconds
per century.