Download The Law of Universal Gravitation

• Who discovered gravity?
• How in the world can we
determine the mass of Earth? I
mean, you can’t put it on a
scale or balance!
• Is gravity a strong force?
Objectives
1. Historical perspective
2. Determining Newton’s Law of
Universal Gravitation
3. Defining the Universal
Gravitational Force equation
involving two objects
4. Confirming acceleration due to
gravity is 9.8 m/s2.
Earth’s Radius
• There is a water well that is directly under the
sun at noon on the Summer Solstice in Syene,
Egypt.
• There is a tower of a known distance from the
water well in Alexandria, Egypt.
• In 235 B.C. the angle of the shadow of the tower
was measured on the Summer Solstice. It was
approx. 1/50th of 360 degrees (7.1 degrees).
Thus the distance from the tower to the water
well is 1/50th of the circumference of Earth.
Law of Universal
Gravitation
The Law of Universal Gravitation
Newton (1642-1727) proposed that the
force which makes an apple fall from a
tree towards the earth is the same force
which keeps the moon orbiting Earth
and Earth orbiting the Sun. In fact, he
claimed that this same force called
gravity governs the Universe. (1686)
In his terms… any two bodies exert a
force upon each other.
Say WHAT!?!
Newton’s Law of Gravitation
m1m2
Fg 2
r
m1m2
Fg   const _ of _ proportionality  2
r
Gm1m2
Fg 
2
r
Unit analysis…
G = 6.67 X 10^¯11 N•m²/Kg²
• G is the Universal Gravitational Constant. It
was needed to complete the calculations of
Universal Gravitation. But it’s SO SMALL!
How can we measure something so small?
• In 1798 Henry Cavendish developed an
experiment which did indeed measure
something so small.
Earth’s Mass
• Once G is known, the mass of any object can
be determined.
• Solve for mearth.
• Fg (?) = G(√) m₁(√) mearth(?)
rearth (√)
• Fg = m₁ g
• Now solve for g!!!!
• Mearth = 5.98 * 10 ²⁴ Kg.
• HOLY SMOKES!!!!
• Compare this mass to everyday
objects.
Applications
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Tides
Black holes
Planet/ Star formation
Satellite motion (GPS, weather, spying!)
Homework
• Pg 242 Practice C
• Due tomorrow