Universal Gravitation

1
Chapter 9

• Universal Gravitation

2
The Falling Apple and the Falling Moon

• Legend has it that Newton hypothesized about
  gravity when he watched an apple fall.
• He developed this idea further by comparing the
  falling apple to the falling moon.
• He proposed that a projectile, fired fast enough
  would fall around the earth rather than to the
  earth and would become a satellite like the moon.

3
How Gravity Affects Objects in Space

• The lines shown are tangent to the circle. They
  demonstrate the direction a satellite would move
  if gravity were turned off.
• Since the satellite is actually a projectile,
  which has gravity acting on it, it actually moves
  in a curved path which allows it to fall around
  the earth.

Without Gravity
With Gravity
4
Universal Gravitation

• Every object is gravitationally attracted to
  every other object in the Universe
• F Gm1m2/d2
• G universal gravitation constant
• 6.67 x 10-11 Nm2/kg2
• M1, M2 mass of each object
• R distance between the objects

5
Gravity and DistanceThe Inverse Square Law

• Gravity is reduced as distance increases, but
  this is not linear it is exponential
• If you double distance, gravity is reduced by the
  square of two, i.e. ¼
• If you triple distance, gravity is reduced by the
  square of three, i.e. 1/9 and so on.
• It is also important to remember that distances
  in this law are measured from the center of one
  object to the center of the second object.

6
Weight and Weightlessness

• As we learned earlier, weight is due to the
  acceleration of gravity on a mass.
• Scales do not actually measure weight, but rather
  the support force exerted on the scale.
• Hence when an elevator is accelerating downward,
  the support force is less and your weight appears
  to decrease
• When the elevator is accelerating upward, the
  support force increases and your weight appears
  to increase.
• Weightlessness is not a result of moving far from
  earth, but rather the result of being in a
  constant state of free fall

7
Tides

• Ocean tides are the result of the difference in
  gravitational pull between the earth and the moon
  on the opposites of the earth.
• This difference accounts for a high tide on
  either side of the earth, and a low tide one
  quarter turn from the high tide.
• Hence high tide occurs once every 12 hours and
  low tide occurs mid-way between high tides.
• Higher than usual tides occur when the Sun, Moon,
  and Earth align (new or full moon) these are
  spring tides
• When the moon is at right angles to the sun with
  respect to the earth, the gravitation affects
  cancel somewhat, which results in a somewhat
  higher low tide, and somewhat lower high tide
  these neap tides occur ½ way between a full or
  new moon.

8
Universal Gravitation and Astronomy

• We all know the earth is round, but why is it
  round? Universal Gravitation!
• Since everything is attracted to everything else,
  the earth pulled itself together before it
  became solid.
• Any corners have been pulled in so that earth
  (and most other celestial objects) are basically
  spheres.
• This also means that the earth is not just
  affected by the Suns gravity, but the gravity of
  other planets as well. This has important
  implications for astronomers and actually led to
  the discovery of the last two planets in our
  solar system.

9
Universal Gravitation and Astronomy

• When Saturn is near Jupiter its pull disturbs the
  otherwise smooth path of Jupiter. This deviation
  is called a perturbation.
• When Uranus was discovered, it appeared to
  deviate from Keplers Laws of Planetary motion
  something no planet before it had done.
• When studying this deviation two scientists,
  working independently, proposed that another
  planet, outside Uranus orbit, could be the cause
  Hence Neptune was found.
• Similar problems with Neptunes orbit were the
  motivation which led to the discovery of Pluto.
• Scientific work in one field often affects the
  work in all other fields.

10
Universal Gravitation and Astronomy

• Einstein defined gravity differently than Newton.
  He envisioned that a gravitational field was a
  warping of 4 dimensional space.
• This warping would cause and object to be
  attracted toward the center of the warp.
• A black hole is the result of the gravitational
  collapse of a star. This collapse causes the
  star to shrink, making its mass more condensed.
  This increases the effect of gravity according to
  the law of Universal Gravitation.
• Gravity becomes so strong, that light cannot
  escape hence the name black hole.

11
Chapter 10

• Part 2 Satellites

12
Fast Moving Projectiles Satellites

• A satellite is a fast moving projectile
• Since the projectile moves in a curved path, and
  the earth is a curved surface, if the projectile
  moved fast enough its motion would follow the
  curve of the earth
• Such a projectile would fall around the earth
  rather than to the earth
• Such a projectile becomes a satellite and orbits
  the earth.

13
Keplers Laws

• Kepler studied planetary motion. He found
• All planetary bodies move in elliptical orbits
• Planetary objects sweep equal areas in equal
  amounts of time
• If two satellites revolve around the same object
  they are related by the equation
• (t1/t2)2 (r1/r2)3

14
Escape Speed

• Escape Speed is the critical speed at which an
  object can escape a bodies gravitational pull.
  At this speed the object will not fall back to
  the planetary body, but will escape into space.
• For earth, escape velocity is 11.2 km/s