Gravity

1
Gravity

• Dr. Don Franceschetti
• Physics 1010
• October 4, 2007

2
Aristotle

• Heavy objects (predominantly earth and water)
  seek to come to rest on earth surface.
• Earth Center of Universe
• Celestial objects execute orbits around center of
  Earth.

3
Newton realized

• Every mass in the universe attracts every other
  with a force given by

4
Law of Universal Gravitation

• Everything attracts everything else.
• Earth not special.
• An inverse square force. (Double distance, force
  reduced to ¼)

5
Determining big G

• Use balanced masses and bring large mass near.
• Done by Cavendish and Jolly.
• G6.67x10-11 Nm2/kg2

6
Determine mass of the earth

7
Comparing G and g

• MgGMME/RE2
• ME g RE2 /G
• And so we now know the mass of the Earth! About
  6x1024kg

8
And we know a lot more

• Mass of sun from radius of orbit and length of
  year.
• Mass of planets that have moons.
• Locate undiscovered planets Neptune and Pluto
  through gravitational effects

9
Weight and weightlessness

• You feel weightless in free fall.
• Force of gravity on the space shuttle in orbit is
  about as much as weight of shuttle on earth
  surface.
• Satellites fall around the Earth.

10
Tides

• Tides occur because force of gravity decreases
  with distance.
• There are tides in the atmosphere and in the
  moon, too.

11
Gravitational Field

• A field is a way to avoid thinking of action at a
  distance.
• Mass 1 sets up gravitational field in the space
  around it. Mass 2 responds to the field of Mass
  1 and vice versa.
• Gravitational field of Earth at Earth surface is
  Earth force on object (mg) divided by mass (m) of
  object, or 9.8 N/kg.

12
20th (and 21st) Century Theories of Gravitation

• 1905, Einstein Special Theory of Relativity
• Speed of light in always measured to be 300,000
  km/sec in vacuum regardless of motion of source
  or observer.
• Length and distance measurements made by
  observers in relative motion must be different in
  such a way that 1 is true.

13
Special Relativity leads to

• Time dilation
• Length Contraction
• Twin Paradox
• E mc2

14
General Relativity

• Principle of Equivalence. Gravity is equivalent
  to uniform acceleration.
• Light bends in a gravitational field.
• Interpret as curvature of space-time caused by
  mass.

15
Black holes

• Squeeze enough mass into a small enough space and
  even light cannot escape.
• Described by equations of General Relativity.
• Fate of the most massive stars.
• Detectable by gravitational effects and x-rays
  emitted by in-falling matter.
• Probably at the centers of most galaxies
  including ours.

16
Expanding Universe

• Hubble discovered that distant galaxies are
  running away from us, with the more distant
  moving faster.
• Predicted by Einsteins equations but he didnt
  want to believe it.
• Big Bang Theory--confirmed by discovery of
  microwave background radiation
• Expansion may reverse if enough mass in universe.

17
Inflation theory

• Extra fast expansion needed in early universe to
  account for present uniformity.
• Hubble telescope suggest Inflation may be
  continuing.

18
Modern Gravity Mysteries

• Dark matter -- gravitational effects suggest much
  more matter than we can see.
• Dark energy -- what is the source of power for
  current inflation?
• Effects could disappear as more data is gained or
  could lead to new laws of physics.

19
Projectile and Satellite Motion

• Physics 1010
• Dr. Don Franceschetti

20
Projectiles

• A projectile is any object that is projected by
  some means and continues in motion by its own
  inertia.
• Main classes are weapons bullets, arrows,
  artillery shells, bombs, rocks and balls
  baseballs, footballs, golf balls

21
Projectiles

• Are in free fall, neglecting air resistance
• The horizontal component of velocity does not
  change because the net force acting has zero
  horizontal component
• The vertical component changes in response to the
  gravitational force.

22
Projectile motion by superposition

• Projectiles launched horizontally
• Upwardly launched projectiles
• Range is same for angle and complementary angle.
• Greatest range for projectiles launched at 45
  degrees.

23
Fast moving projectiles satellites

• Circular orbits
• Near earth 90 minute period
• Orbital sped 8km/s, near Earths surface
• Geosynchronous, 24 hour period, orbital speed is
  less
• Elliptic orbits
• Keplers laws apply

24
Keplers laws

• Tycho Brahelast of the great naked eye
  astronomers, recorded planetary positions every
  night for years and years.
• Kepler, mathematician tried to explain Brahes
  data, came up with

25
Keplers 3 Laws

• Orbits of planets are ellipses with sun at one
  focus.
• The line connecting the sun and each planet
  sweeps out equal areas in equal time.
• The square of the period of a planet is
  proportional to the cube of the semimajor axis.

26
Keplers 2nd Law

27
Newton

• Orbits of planets are ellipses with sun at one
  focus. (laws of motion plus law of universal
  gravitation)
• The line connecting the sun and each planet
  sweeps out equal areas in equal time.
  (Conservation of Angular momentum)
• The square of the period of a planet is
  proportional to the cube of the semimajor axis.
  (laws of motion plus law of universal
  gravitation)

28
Newtons Cannon
29
Energy Conservation and Satellite Motion

• Terminology
• Apogee, most distant point from Earth
• Potential energy is greatest
• Kinetic energy is least, motion is slowest
• Perigee, closest approach to Earth
• Potential energy is least
• Kinetic energy is greatest, speed is hight
• Perihelion, aphelion, apply to planet and Sun

30
Escape speed

• Minimum speed needed to escape planet
• from Earth is 11.2 km/s.
• From Sun at Earth orbit is 42.2 km/s
• Pioneer 10 left Earth in 1972 at 15km/s used
  gravitational assist from Jupiter.

31
Review

• Q. Since the moon is gravitationally attracted to
  earth, why does it not simply crash into the
  Earth?
• Q. When the space shuttle coasts in a circular
  orbit at constant speed about the Earth, is it
  accelerating? If so, in what direction? If not,
  why not?

32
Review

• E10.18 Does the speed of a falling object depend
  on its mass? Does the speed of a satellite in
  orbit depend on its mass?