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GravitationGravitation
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Gravitational Force
the mutual force of attraction between particles of matter
Newton’s Law of Universal Gravitation
Fg=G(m1*m2/r2)
G= 6.67x10-11 Nm/kg2
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Force
Force is proportional to the mass times mass
Force is inversely proportional to the distance squared or the radius squared
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Elliptical Orbits
http://spaceweather.com/swpod2007/23oct07/orbit.gif
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Elliptical orbits
Perigee greatest force
greatest velocity
smallest distance
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Elliptical orbits
Apogee least force
least velocity
greatest distance
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Circular orbits
distance is constant
velocity is constant
Fc is constant
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Kepler’s Laws
First Law Each planet travels in an elliptical orbit around the sun with the sun as one focal point
Second Law- An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals.
Third Law- The square of an orbital’s period is proportional to the cube of the average distance between the planet and the sun T2 is
proportional to t3
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Equations
T=2π√(r3/Gm)
v=√(Gm/r)
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Circular Motion• = the movement of an object at constant
speed around a circle with fixed radius
• Axis – straight line around which rotation takes place
• Rotation – object turns around an internal axis
• Ex. Ice skater
• Revolution – object turns around an external axis
• Ex. Earth around the sun
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Rotational Speed
• Linear speed – distance/time
• Tangential speed – speed along a circular path
• Rotational speed – number of rotations per unit of time
• Example: Carousel horses travel at same rotational speed but different tangential speed
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Centripetal Force
• Force that causes an object to follow a circular path
• Ex. Force holding occupants safely in a rotating carnival ride
• Fnet = mv2
r
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Centripetal Acceleration
• Always points toward the center of the circular motion.
• Period (T) = time needed for an object to make one complete revolution
• Distance traveled = circumference
• Circumference = 2πr = πd
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Other formulas
• Centripetal Acceleration equals the velocity squared divided by the radius
• Ac = v2/r
• The number of revolutions equals the distance traveled divided by the circumference
• Revolutions = distance/circumference