Transcript Universal Gravitation - stpats-sph3u-sem1-2013

Rewind
• An astronaut on the moon throws a wrench straight
up at 4.0 m/s. Three seconds later it falls downwards
at a velocity of 0.8 m/s.
a. What was the acceleration of the wrench after it left
the astronauts hand?
b. How high above the point from which it was released
was the wrench at 3.0 s?
c. How long would it take the wrench to return to the
position from which it was thrown?
Universal Gravitation
The Big Idea: Everything
pulls on everything else.
Discussion
Here are some questions and answers which lead towards
Newton’s Law of Universal Gravitation:
1. What causes the weight that each student feels?
2. What affects the size of the Earth’s pull on you? Why would
you weigh a different amount on the Moon?
3. If the Earth is pulling down on you, then what else must be
occurring, by Newton’s 3rd Law?
4. What happens to the strength of the pull of the Earth as you
go further away from it?
Newton’s Law of Universal
Gravitation
Newton discovered that gravity is
universal. Everything pulls on
everything else in a way that
involves only mass and distance.
Universal Gravitation
Newton’s law of universal gravitation states that
every object attracts every other object with a
force that for any two objects is directly
proportional to the mass of each object.
Newton deduced that the force decreases as the
square of the distance between the centers of
mass of the objects increases.
Universal Gravitation
The force of gravity between objects depends on
the distance between their centers of mass.
Universal Gravitation
Your weight is less at the
top of a mountain
because you are farther
from the center of Earth.
Universal Gravitation
The Universal Gravitational Constant, G
The law of universal gravitation can be expressed
as an exact equation when a proportionality
constant is introduced.
The universal gravitational constant, G, in the
equation for universal gravitation describes the
strength of gravity.
Universal Gravitation
The Universal Gravitational Constant, G
The force of gravity between two objects is found by
multiplying their masses, dividing by the square of the
distance between their centers, and then multiplying this
result by G.
>The magnitude of G is given by the magnitude of the
force between two masses of 1 kilogram each, 1
meter apart: 0.0000000000667 newton. In scientific
notation: G = 6.67 × 10−11 N·m2/kg2
>The units of G are such as to make the force
of gravity come out in newtons.
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
Universal Gravitation
The Mass of the Earth
>Once the value of G was known, the mass of
Earth was easily calculated.
>The force that Earth exerts on a mass of 1
kilogram at its surface is 10 newtons.
>The distance between the 1-kilogram mass and
the center of mass of Earth is Earth’s radius, 6.4
× 106 meters.
So the mass of Earth m1 = 6 × 1024
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
Problem
• Find the gravitational attraction, which exists
between a 60 kg boy and a 50 kg girl at a
distance of 3 m.
• Now find the gravitational attraction between
the 60 kg boy and the Earth using the Law of
Universal Gravitation.
• Is the result surprising?
Universal Gravitation
Gravitational Fields
Field lines represent the
gravitational field about Earth.
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
Universal Gravitation
Gravitational Fields Inside a Planet
As you fall into a hole bored through Earth, your
acceleration diminishes. The pull of the mass
above you partly cancels the pull below.
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
Universal Gravitation
Gravitational Fields Inside a Planet
Starting at the North Pole end,
you’d fall and gain speed all the
way down to the center, and
then overshoot and lose speed
all the way to the South Pole.
You’d gain speed moving toward
the center, and lose speed
moving away from the center.
Without air drag, the trip would
take nearly 45 minutes.
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
Universal Gravitation
Gravitational Fields Inside a Planet
At the beginning of the fall, your
acceleration would be g, but it would
decrease as you continue toward the
center of Earth.
As you are pulled “downward” toward
Earth’s center, you are also being
pulled “upward” by the part of Earth
that is “above” you.
When you get to the center of Earth,
the net force on you is zero.
There is no acceleration as you whiz
with maximum speed past the center
of Earth.
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
Universal Gravitation
Gravitational Fields Inside a Planet
In a cavity at the center of Earth, your weight
would be zero, because you would be pulled
equally by gravity in all directions.
Contributor: J. Flores
Source: Prentice Hall;
Conceptual Physics
• Pg 182 # 28 For this problem, use ratios only to obtain the
weight of a person at the following distances. Assume the
person weighs 980 N on the surface of Earth. Earth’s radius is
6.38 x 106 m.
a) Three times the distance from the centre of Earth
b) 128 000 km above the surface of Earth
Near Earth Approximation
• Close to the Earth the field strength, g, is
almost constant
GM
g 2
r
Fg  mg
• Pg 182 # 26. On or near the surface of Earth, g is 9.80 m/s2. At what
distance from Earth’s centre is the value of g 9.70 m/s2 ? At what height
above the surface of Earth does this occur?
Universal Gravitation
and Orbits