Projectile and Satellite Motion

1
Projectile and Satellite Motion

• Physics 1010
• Dr. Don Franceschetti
• October 11, 2005

2
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

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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.

4
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.

5
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

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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

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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.

8
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)

9
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

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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.

11
Review

• Q10.5 A rock is thrown upward at an angle. What
  happens to the horizontal component of its
  velocity as it rises? As it falls?
• Q10.6 A rock is thrown upward at an angle. What
  happens to the vertical component of its velocity
  as it rises? As it falls?

12
Review

• Q 10.14 Are the planets of the solar system
  simply projectiles falling around the sun?
• Q 10.18 Why does the force of gravity change the
  speed of a satellite in an elliptical orbit.

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Review

• Q10.25 Why is the kinetic energy a constant for
  a satellite in circular orbit?
• Q 10.26 Why is kinetic energy a variable for a
  satellite in an elliptical orbit?

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Review

• E10.4 In the absence of air drag, why does the
  horizontal component of a projectiles motion not
  change, while the vertical component does?
• E10.9 When a rifle is being fired at a distant
  target, why isnt the barrel lined up so that it
  points exactly at the target?

15
Review

• E10.15 Since the moon is gravitationally
  attracted to earth, why does it not simply crash
  into the Earth?
• E10.16 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?

16
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?