Transcript The Law of Universal Gravitation

1)
What variables affect the force
of gravity between two objects?
2)
How does Einstein’s Theory of
General Relativity Compare to
Newton’s Law of Gravity?
Suppose Elvis (we found him!) is in orbit around Earth at a
distance twice as far from the planet’s center as the surface
of Earth is. Would you expect his weight to be greater than,
less than, or equal to his weight on the surface of the
planet? What variables determine your weight.
Answer: His weight would be less because of a lower
gravitational pull on his body. Variables that determine
your weight are your mass, the mass of the object pulling
on you and your distance from that object.
Your weight is just the measure of the force of gravity on
your body. Your weight changes depending where you are.
Your mass does not on your location, just on how many jelly
donuts you eat.
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Check out this website to see how your weight changes
throughout the universe. Notice your weight on Moon.
(Neil Armstrong, what a loser he was.) Notice your
weight on a Neutron Star (the blueberry muffin is really
going straight to the hips.)
http://www.exploratorium.edu/ronh/weight/
Thinking Question: Notice your weight on Jupiter.
Jupiter has a mass greater than 318 times the mass of
Earth. Why then is your weight not 318 times greater
on Jupiter? Think-pair-share with your partner.
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You may suspect that because Jupiter is 318 times as
massive as the Earth, you should weigh 318 times
what you weigh at home. This would be true if Jupiter
was the same size as the Earth. But, Jupiter is 11 times
the radius of the Earth, so you are 11 times further
from the center. The force of gravity is measured
from the center of objects, not their surface. This
reduces the pull by a factor of 112 resulting in about
2.53 times the pull of Earth on you. Standing on a
neutron star makes you unimaginably weighty. Not
only is the star very massive to start with (about the
same as the Sun), but it is also incredibly small
(about the size of San Francisco), so you are very
close to the center and r is a very small number.
 Sir
Isaac Newton (1642–1727) generalized
his observations on gravity in a law now
known as the law of universal gravitation.
 Universal
Gravitation Equation
F G
m1m2
d2
• m1 and m2 are the masses of the two objects
• d is the distance between the two objects
• G is the gravitational constant
 All matter is affected by gravity.
• Two objects, whether large or small, always have
a gravitational force between them.
 Gravitational
increases.
 Gravitational
force increases as mass
force decreases rapidly as
distance increases because distance is
squared.
1)
A satellite orbits the Earth the Earth at 300 km above the Earth’s
surface. If you double the satellites mass what will happen to the
gravitational force between the Earth and the satellite?
Answer: Gravitational force will double. When doing these type
of problems where you are only worried about the change you
can drop the constant G in Newton’s Law of Gravity. Just work
with the proportion:
F ∞ (m1m2) / d2
2)
If the satellite climbs to an orbit of 600 km how will that change
the gravitational force between Earth and the satellite?
Answer: Gravitational force will decrease by ¼ because the
distance is squared in the denominator of the Law of Gravity.

Newton’s Law of Gravity is a mathematical model
that works great in nearly all applications
important to us. NASA still uses it to plot the
trajectories of its spacecraft. Yet, it does not work
in all situations. Among other things:
Newton’s Law of Gravity does not fully explain
the precession of orbits for the planets,
especially of planet Mercury.[
It does not correctly predict the bending of light
by gravity.
It does not work well with objects travelling near
the speed of light
 Einstein’s
Theory of General Relativity
(1916) is an improvement on Newton’s Law
of Gravity because it is in closer agreement
with the observations.
In General Relativity objects with mass act by
curving space time. (Get it. Your one of the few.)
Fortunately for you the the mathematics of General
Relativity will not be on the FCAT.
 Planet
A and Plant B have identical masses.
Planet B three times farther from a star than
Planet A. How do the gravitational forces
between the star and the planets compare?
 A.
the force on A is 1/9 the force on B.
 B. The force on A is 1/3 the force on B.
 C. The force on A is three times the force on B.
 D. The force on A is nine times the force on B.
 Answer:
D