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Gravity
Ancient Greece- Aristotelian Universe is Earth Centered (Geocentric system)
Copernican Revolution – Nicolas Copernicus figures out that the Sun is the center of the
Solar System (Heliocentric system)
Galileo- discovered that all things fall at a constant rate regardless of mass. We call this
local g (for the surface of the Earth g=9.80m/s2)
Tycho Brahe-Made meticulous charts of the planets and their orbits
Johannes Kepler- Used Brahe’s work to find 3 laws of Planetary Motion.
1st law- Planets orbits are ellipses with the sun at 1 focus.
2nd law-Planets sweep equal area in equal time. (the closer to the sun the faster
they move)
 ra

3rd law-Law of Periods  r
 b
3
  Ta 
   
  Tb 
2
Isaac Newton- Finds that the same force that causes an apple to fall to the earth also
caused the moon to constantly fall to the earth.
Newton’s Universal law of Gravitation
-
FGrav 
Gm1m2
r2
The constant (G=6.67 x 10-11N∙m2/kg2) allowed Newton to turn a proportionality (α) into
an equality (=)
1
The
r
2
makes it so that if the distance between the objects is doubled the Force is one-
fourth.
ORBITS- Any orbiting object (Earth) is falling at the same rate the object being orbited
(Sun) is curving away from it.
Weightlessness- In Space Astronauts feel weightless because they are accelerating
towards earth at the same rate as the space shuttle.
Weighing the Earth- Cavendish used a torsion pendulum to find Big G.
This can also be done using the orbital period of the moon and the equation
r3
T  2
GM E
.
The orbital velocity can be found using
v
GM E
r
Einstein Theory of Gravity
-Describes mass as causing curvature in space time. This is similar to a mass
causing a curve in a rubber sheet.
Local g
Local g is the acceleration due to gravity on the surface of
any planet or asteroid.
- Just like on earth it does not depend on the mass of
the object being dropped.
- The weight of an object is found by multiplying
mass x local g
F  ma
GMm
F 2
r
So
GMm
ma  2
r
GM
a 2
r
GM
g 2
r
M – the object being orbited
r – the distance from the center of the object being
orbited
Ex 1: Find local g on the surface of the Earth.
(ME=5.97 x 1024 kg, rE=6.37x106m.)
Ex 2: Find local g on a satellite 6.3x106m above
the surface of the earth.
(ME=5.97 x 1024 kg, rE=6.37x106m.)
Hint: r= rE + rabove Earth
Newton’s Universal law of Gravitation
GMm
F
r2
Ex 3: Find Mr. Eisenberg’s Weight on Jupiter
if his Mass is 75.0kg and my average radius is
0.3 m. (mJ=1.90 x 1027 kg, rJ=6.98 x 107 m)
Ex 4: Jupiter has a mass of 1.90 x 1027 kg and an
average radius of 6.98 x 107 m. What is the
Weight of Jupiter on Mr. Eisenberg?
(mEis=75.0 kg , rEis=0.3 m)
Ex 5: Find local g on Jupiter.
(mJ=1.90 x 1027 kg, rJ=6.98 x 107 m)