The Beginning of Modern Astronomy

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The Beginning of Modern Astronomy
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Isaac Newton (1642-1727)

• did research on optics (the properties of light)
• invented calculus
• discovered the three laws of Motion
• discovered the law of universal gravitation

Motion Concepts

• inertia resistance to a change in motion.
• mass numerical measure of inertia, amount of
  material in the object.
• speed how fast something moves.
• velocity speed and direction.
• acceleration rate of change of
  velocity.Acceleration in the direction of motion
  speeds up the object. Acceleration perpendicular
  to the objects path changes the direction of its
  motion.
• momentum mass velocity.

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Newtons Laws of Motion

• An object moves with constant velocity unless
  acted on by an unbalanced external force.
• When an object is acted on by an unbalanced
  force, it accelerates in the direction of the
  unbalanced force. The magnitude of the
  acceleration is related to the magnitude of the
  net (unbalanced) force by the equation Fnet
  ma, where m is the mass of the object and a is
  its acceleration.
• When two objects interact, they exert equal and
  opposite forces on each other. FA on B - FB on
  A.

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Circular Motion, Centripetal Acceleration, and
Centripetal Force

• An object in uniform circular motion is
  accelerating even if its speed is constant.
• In this case, there is no acceleration along the
  path of the object the acceleration, called
  centripetal acceleration , is perpendicular to
  the path (toward the center of the circle).
• The force that causes a centripetal acceleration
  is called a centripetal force.

Example 1The average distance from Earth to the
Moon is 3.84108 m, and the moons average
orbital speed is 1022 m/s. Calculate its
centripetal acceleration.
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Newtons Law of Gravity
Any two particles in the universe attract each
other with a force that is directly proportional
to the product of their masses and inversely
proportional to the distance between them.
The minus sign reminds us that the force is
attractive.
G 6.67310-11 Nm2/kg2 M and m are the masses of
the two particles. r is the distance between
their centers.
A spherically symmetric object is one whose mass
is distributed equally in all directions. The
force on a particle outside an object with
spherical symmetry is the same as if all of of
the objects mass were concentrated at its
center. This allows Newtons law of gravity to be
used for things like planets, which are almost
spherically symmetric.
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Relation Between Weight and Mass
weight the gravitational force on an object.
Fnet ma
The acceleration due to gravity is directly
proportional to the mass of the planet and
inversely proportional to the square of the
distance from the planets center. It is usually
denoted by the symbol g.
W weight mg
Near earths surface, a g 9.8 m/s2.
When air resistance is negligible, the
acceleration of a falling body does not depend on
its weight.
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Newtons second law of motion and his law of
gravity enable us to determine the masses of
planets and stars.
Example 2 The acceleration due to gravity at the
surface of the Earth is 9.8 m/s2, and the radius
of the Earth is 6380 km. What is the mass of
Earth?
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Example 3 An astronaut whose weight is 150 lb on
Earth is launched to an altitude of twice earths
radius. What is his weight at that altitude?
The agreement between this theoretical value and
the experimental value was an important
confirmation of Newtons law of gravity.
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Conservation of Angular Momentum
P
O
When the net force on a particle is always
directed toward a fixed point, its angular
momentum relative to that point does not change
with time i.e., its angular momentum is
conserved.
The gravitational force of the Sun on a planet is
always directed toward the Sun, so the angular
momentum of the planet relative to the sun is
conserved.
It can be shown that the conservation of the
angular momentum of a planet is equivalent to the
statement that the line from the Sun to the
planet sweeps out equal areas in equal times, so
Keplers second law of planetary motion is
equivalent to the law of conservation of angular
momentum applied to a planet in orbit around the
Sun.
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Kinetic Energy, Radiative Energy, and Potential
Energy
Energy is the ability to move an object while
exerting a force on it.
The energy of an object due to its motion is
called kinetic energy. It is defined by the
equation
Potential Energy is the energy that a group of
objects has because of their relative positions.
There is no single formula for potential energy.
When you exert a force on an object and cause it
to move, you put energy into it. The process of
putting mechanical energy into an object is
called doing work on the object.
Radiative Energy is the energy of the electric
and magnetic fields in electromagnetic radiation.
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Example 5 The sidereal period of the Moon is
27.32 days, and its average distance from Earth
is 384,000 km. Calculate the mass of Earth.
Assume that the mass (m) of the Moon is
negligible compared to that of Earth (M).
P 27.32 days 2.7321018.64104 s 2.360106
s a 3.84105 km 3.84105103 m 3.84108 m G
6.67310-11Nm2/kg2
M 6.021024 kg
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Circular Velocity
Example 6 Calculate the orbital speed of a
satellite in a circular orbit 150 km above the
surface of Earth. Assume that the radius of earth
is 6380 km and its mass is 5.981024 kg.
r 150 km 6380 km 6530 km
r 6.53103 x 103 m
r 6.53106 m
M 5.981024 kg
Vc 28,500 km/hr 17,500 mi./hr
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Escape Velocity
Example 7 Calculate the escape velocity from the
surface of Earth.
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Tides
The length of a day increases by about 0.0023
seconds per century, and the Moon moves farther
from Earth by about 3.8 cm per year. Why?
900 million years ago, earths day was 18 hours
long.