1. Gravitation

2. 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

3. Force Force is proportional to the mass times mass
Force is inversely proportional to the distance squared or the radius squared

4. Elliptical Orbits

5. Elliptical orbits Perigee greatest force greatest velocity
smallest distance

6. Elliptical orbits
Apogee least force
least velocity
greatest distance

7. Circular orbits distance is constant velocity is constant
Fc is constant

8. 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

9. Equations
T=2π√(r3/Gm)
v=√(Gm/r)

10. 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

11. 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

12. 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

13. 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

14. 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