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GravitationGravitation
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
Force
Force is proportional to the mass times mass
Force is inversely proportional to the distance squared or the radius squared
Elliptical Orbits
http://spaceweather.com/swpod2007/23oct07/orbit.gif
Elliptical orbits
Perigee greatest force
greatest velocity
smallest distance
Elliptical orbits
Apogee least force
least velocity
greatest distance
Circular orbits
distance is constant
velocity is constant
Fc is constant
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
Equations
T=2π√(r3/Gm)
v=√(Gm/r)
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
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
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
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
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