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2

 speed – rate at which an object moves, i.e. the distance traveled per
unit time [m/s; mi/hr]
 velocity – an object’s speed and direction, e.g. “10 m/s moving east”
 If you are moving in a straight line, speed and velocity are used
interchangeably
 acceleration – a change in an object’s velocity, i.e. a change in either
speed or direction is an acceleration [m/s^{2}]

3

 As objects fall, they accelerate.
 The acceleration due to Earth’s gravity is 10 m/s each second, or g = 10
m/s^{2}.
 The higher you drop the ball, the greater its velocity will be at
impact.
 Gravity of the moon is 1/6 as much..on Mars its 1/3…

4

 Galileo demonstrated that g is the same for all objects, regardless of
their mass!
 This was confirmed by the Apollo astronauts on the Moon, where there is
no air resistance.

5

 Forces change the motion of objects.
 momentum – the (mass x velocity) of an object
 force – anything that can cause a change in an object’s momentum
 As long as the object’s mass does not change, the force causes a change
in velocity, or an…

6

 mass – the amount of matter in an object
 weight – a measurement of the force which acts upon an object

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9

 Invented the reflecting telescope
 Invented calculus
 Connected gravity and planetary forces
 Philosophiae naturalis
principia mathematica

10

 Newton used Galileo’s law of Inertia and…
 Galileo’s formula for calculating centriptal accelration and…
 His formula relating Force and Accleration to
 Derive Kepler’s laws
 Formulate the law of Universal gravitation

11

 A body at rest or in motion at a constant speed along a straight line
remains in that state of rest or motion unless acted upon by an outside
force.

12

 The change in a body’s velocity due to an applied force is in the same
direction as the force and proportional to it, but is inversely
proportional to the body’s mass.

13

 For every applied force, a force of equal size but opposite direction
arises.

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15

 Between every two objects there
is an attractive force, the magnitude of which is directly proportional
to the mass of each object and inversely proportional to the square of
the distance between the centers of the objects.

16

 Extending Kepler’s Law #1, Newton found that ellipses were not the only
orbital paths.
 possible orbital paths
 ellipse (bound)
 parabola (unbound)
 hyperbola (unbound)

17

 angular momentum – the momentum involved in spinning /circling = mass x
velocity x radius
 torque – anything that can cause a change in an object’s angular
momentum (twisting force)

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20

 In the absence of a net torque, the total angular momentum of a system
remains constant.

21

 Since gravitational force decreases with (distance)^{2}, the
Moon’s pull on Earth is strongest on the side facing the Moon, and
weakest on the opposite side.
 The Earth gets stretched along the EarthMoon line.
 Greatest force pulls water away from Earth towards moon.
 Both Earth orbits center of mass of Earth Moon System
 Weaker force allows water to slide away from Earth on side opposite moon

22

 This fight between Moon’s pull & Earth’s rotation causes friction.
 Earth’s rotation slows down (1 sec every 50,000 yrs.)
 Conservation of angular momentum causes the Moon to move farther away
from Earth.

23

 …is when the rotation period of a moon, planet, or star equals its
orbital period about another object.
 Tidal friction on the Moon (caused by Earth) has slowed its rotation
down to a period of one month.
 The Moon now rotates synchronously.
 We always see the same side of the Moon.
 Tidal friction on the Moon has ceased since its tidal bulges are always
aligned with Earth.

24

 orbital energy = kinetic energy + gravitational potential energy
 conservation of energy implies:
 orbits can’t change spontaneously
 An object can’t crash into a planet unless its orbit takes it there.
 An orbit can only change if it gains/loses energy from another object,
such as a gravitational encounter:
