Download Newton’s law of Universal Gravitation

Newton’s law of
Universal Gravitation
We will be considering a lot of
individual topics.
Specific Topics
The inverse square law
How did Newton figure it out?
Universal law to W = mg
Gravitational Field
General “g” and Latitude
General “g” and Altitude; weightlessness
See the next slide
You mean, there is still more??
Yup
Kepler’s Laws
Discovery of New Planets
Explanation of Tides
Okay don’t get overwhelmed
I’ll be doing most of the math just to,
hopefully, prove to you that I’m not just
making it all up.
Mathematically, you need to know the
inverse square law, its ramifications, and
the gravitational field.
The rest is conceptual.
Inverse Square law
The force of gravity depends inversely on the
square of the distance between the two objects
interacting gravitationally.
Triple the distance, force decreases by 9
Halve the distance, force increases by 4
A few numerical examples (see the board)
How did Newton know?
Newton assumes that gravity both (1)
keeps the moon in orbit and (2) pulls the
apple to the ground (gives us “g”).
Calculate ac = amoon = v2/r
Calculate aapple = g (measure)
Compare ac/aapple to Rapple/Rmoon
Results agree “pretty nearly”. 
General gravitational field
Define general gravitational field
“g” = G M/R2 with G = 6.67 × 10–11 Nm2/kg2
See board for sample calculations.
The Force of gravity is Fgr = mass × “g”
So why does Weight = mg?
We can calculate the gravitational field at
surface of earth. Get “g” = 9.83 m/s2.
Why not 9.81 m/s2 ? Rotation of earth;
depends on latitude. Gives measured
acceleration due to gravity.
Orbital Motion
Only “some” of gravity is used to keep object
moving in a circle; the “rest” is used to
push an object against a scale.
If all of gravity is “used up” keeping the
orbiting object in a circular orbit, then there
is nothing left to push against a scale:
apparent weightlessness.
Kepler’s Laws (1 and 2)
Gravitational force is an inverse square
law leads to Kepler’s first law (ellipses)
Gravitational force is along the line
between the two bodies leads to Kepler’s
second law (equal areas  equal times)
Kepler’s Third law
Gravity provides the centripetal force for
orbiting bodies leads to Kepler’s Third law,
R3 / T2 = constant
The constant depends on the mass of the
central body (sun and planets, earth and
satellites)
Geosynchronous Orbit
Use Kepler’s third law, with Earth at the
center, and T = 23 hours 56 minutes to
determine where a sattelite should be put.
R = 42 million meters, height = 26,000 miles
Discovery of New Planets
Neptune and Pluto (?)
Planets around other stars
Broke down with Mercury (General
Relativity)
Explained Tides
Different pulls on “close side” of water;
earth’s center; and “far side” of water gives
two high and two low tides per day.
Bay of Fundy in Nova Scotia; tides can
change by about 15 meters (50 feet!)
p.89
p.89