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