Transcript Universal Gravitation

Universal Gravitation
• 1546-1601 Tycho Brahe
• 1571-1630 Johannes Kepler
• 1. Law of Ellipses :
– If e = 0, then the two foci are at the same location and it is a
circle
• 2.
• 3.
• Kepler provided a framework for describing the motion
and paths of the planets about the sun but not the
WHY!!!
Con’t
• Newton wanted to know the cause of the
elliptical motion of planets and the circular
motion of the moon:
– 1.
– 2.
– 3.
– 4.
– Universal Gravitation
Moon as a Projectile
• Orbiting moon ~ cannonball ~ apple
• Laws of mechanics apply universally
Newton’s Evidence for Gravity: Inverse
Square Law
• INVERSE SQUARE LAW: Fgrav~1/d2
Newton’s Law of Universal
Gravitation
• Distance is not the only variable affecting the magnitude
of a gravitational force
• Fnet=ma
• Force causing the apple to fall must be dependent
(directly proportional) on the mass of the apple
• Same force causes Earth’s upward acceleration
(Newton’s 3rd law)
• Force is also dependent (directly proportional) on mass
of Earth
• Force is inversely proportional to square the distance
• UNIVERSAL not just here on Earth
Effect of Mass on Fgravity
• Fgravity=Gm1m2/d2
G=6.67x10-11 Nm2/kg2
G constant
• Fgravity=Gm1m2/d2
• G=6.67x10-11 Nm2/kg2
Universality
• ALL objects attract in proportion to their mass
• Ex. Jupiter approaches Saturn in its orbit, it
deviates from its smooth path (perturbation)
• Uranus had an orbit that Newton’s law of gravity
did not correctly predict
• Proposed that another planet was attracting
Uranus in addition to the sun (Giant: Neptune)
Value of g
• Fgravity=Gm1m2/d2
• mg=Gm1m2/d2
• g=GMEarth/d2
Fgravity=mg
MEarth: 5.98x1024 kg
dEarth: 6.38x106 kg
Inverse Law
• Value of g varies
inversely with the
distance from the
center of the earth
• g=G Mplanet/Rplanet2
Equations
• Fgravity=Gm1m2/d2
Fgravity=mg
• F=ma (F is gravitational Force) (a is centripetal
acceleration)
• ac=(4pi2)/(T2)
Fc=mp(4pi2)/(T2)
• mg=Gm1m2/d2
(Ta/Tb)2=(Ra/Rb)3
• Fc= (Mpv2)/R
(Mpv2)/R=Gmpms/R2
• v=(2piR)/T
T2/R3=(4pi2)/(GMs)
• T2=(4pi2/GMs) R3
• g=GMEarth/d2