Chapter 12 Universal Gravitation

1
Chapter 12 Universal Gravitation
2
History of Gravity

• Ptolemy
• All objects go to their natural place
• Geocentric universe
• Main text for 1600 years
• Copernicus
• Heliocentric universe
• Brahe Keppler
• Keppler used Brahes observations to formulate 3
  laws of planetary motion
• Galileo
• Tested with gravitational affects on Earth,
  acceleration of gravity
• First to come up w/ idea for inertia
• Newton
• Law of Universal Gravitation
• Einstein
• Theory of General Relativity
• Punked out Isaac Newton

3
Isaac Newton

• First credited with the idea that Gravity extends
  through the universe
• Newton knew the concept of inertia, and that if
  something changed its speed or direction a force
  must be responsible
• Apple falling from tree apple changed its
  motion, so a force must be responsible-- Gravity
• More importantly, he also noticed the moon, and
  that it was traveling in circular motion
• Circular motion means changing direction and this
  also required a force
• He reasoned the same force was responsible for
  the Moon as was the apple

4
The Falling Moon- Satellite Motion

• Newton realized the moon must be falling or else
  it would travel away in a straight line
• So if it is falling, why is it never getting
  closer??
• He hypothesized the moon is just a projectile
  falling under the influence of gravity.
• And it never falls to Earth because of its speed.

5

• Launched projectiles will follow a curved path
  (see below) until they hit the ground
• But the ground also curves (Earth is not flat)
• Most projectiles have a curve that are much
  steeper than the curve of the Earth
• BUT, if you throw a projectile fast enough, then
  curved path of the projectile will match the
  curve of the Earth
• Then, the projectile will never reach the surface
  and forever be in an orbit
• Projectile must also be above the Earths
  atmosphere, so that air resistance does not slow
  it down

6
Projectile being thrown a different speeds, from
the top of a mountain above the atmosphere
7
Newtons Law of Universal Gravitation

• Force of gravity acting between 2 objects is
  directly proportional to their mass and inversely
  proportional to the square of the distance
  between them
• m1 and m2 represents the masses of the
  two objects involved
• d - distance between the center of the two
  objects
• G- Universal Gravitation Constant, value of
  6.67 x 10-11 Nm2/kg2
• F - represents the Force of Gravity between any
  2 objects
• Remember that Force of Gravity is the same thing
  as Weight

8
What this law means

• Whatever factor the mass is increased by, the
  force of gravity is increased by the same amount
• Ex. Triple the mass, force of gravity also is
  tripled
• Whatever factor the distance between 2 objects is
  increased by, the force of gravity is multiplied
  by the inverse of the square of that number
• Ex. Triple the distance, force of gravity is
  1/9th as much

9
Examples

• The force of gravity acting on you while on the
  surface of the Earth is 100 N.
• What would be the force of gravity acting on you
  if the Earths mass was doubled?
• Force Directly proportional to mass, So 200 N
• What would it be if your mass was doubled and the
  Earths stayed the same?
• Force Directly proportional to mass, So 200 N
• What would the force of gravity acting on you be
  if you were twice as far from the center of the
  Earth as you are now?
• Force is Inversely proportional to the square of
  the distance, so distance is increased by 2,
  inverse square of 2 is 1/22 or 1/4th , so force
  of gravity would be 1/4th as much or 25 N.

10
(No Transcript)
11
(No Transcript)
12
Keplers 3 Laws of planetary motion

• 1) The paths of the planets are ellipses, with
  the sun at one focus (the other focus is just a
  point in space)

http//www.sunsite.ubc.ca/LivingMathematics/V001N0
1/UBCExamples/Kepler/kepler.html
13

• 2nd Law
• An Imaginary line from the sun to a planet
  sweeps out equal areas in equal time intervals.
• This means planets move faster when they are
  closer to the sun and slower when they are
  further away

http//surendranath.tripod.com/Applets/Dynamics/Ke
pler/Kepler1Applet.html
14

• Third Law
• The square of the ratio of the periods of any two
  planets revolving about the sun is equal to the
  cube of the ratio of their average distances from
  the sun. Thus, if Ta and Tb are the planets
  periods, and ra and rb are their average
  distances from the sun we get
• (Ta/Tb)2 (ra/rb)3