Transcript 1.1 - Newtonian Gravitation and Orbits - K

Newtonian Gravitation
and Orbits
SPH4U – Grade 12 Physics
Unit 1
Recall:
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The force of Gravity, FG is one of the
fundamental forces of nature. It is incredibly
important in understanding the universe. It is a
vector, and it has magnitude and direction.
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FG is NOT the same as g ,which is the
acceleration due to gravity. (also called the
gravitational field intensity).
Recall:
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The force of gravity exists between any two
objects in the Universe. It is not just about
planets and satellites and other things in space!
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Because the force of gravity is calculated
between two objects, both objects exert a force.
This means that if planet Earth is exerting a
force of gravity down on you, you in turn are
exerting a force of gravity up on the Earth.
Universal Law of Gravitation
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For any two objects of mass m1 and m2, whose
centers are separated by a distance of r, the force of
gravity will be determined by this formula, which is the
Universal Law of Gravitation.
In order for the
force of gravity to
be noticeable, at
least one of the
objects must
have a large
mass relative to
the distance
between the
object centers.
Force of Gravity
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The force of gravity is always attractive. Every
mass attracts every other mass. Therefore the
direction will always be towards the center of the
other mass.
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The magnitude of m1 on m2 is equal in strength
to the magnitude of m2 on m1.
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The Acceleration due to Gravity: g .
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As already stated, g and FG are not always the
same thing.
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In grade 11 Physics, we said that g was equal
to 9.81m/s2.
In truth, this
 is just an approximation, and the
value of g varies at different points on the earth
depending on how far one is from the earth’s
surface. This is because of the inverse-square
relationship of the Universal Gravitational Law.
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The Acceleration due to Gravity: g.
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In grade 11 Physics, we calculated
the
force
of


gravity using the equation FG  mg
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In truth, this is only valid for the force of gravity
that is near the surface of the Earth. It
represents just a particular instance of the
Universal Law of Gravitation.
Also see table 1 on
page 289 of your
textbook.
Acceleration due to gravity - g
Gravitational Fields
Gravitational Fields
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Recall from grade 11 physics, that a field is a
region in space where a force can be felt.
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In this course, we will describe a field as a
collection of vectors, one at each point in
space, that determines the magnitude and
direction of the force.
Notice that the arrows
are drawn bigger
near the center. That
is no accident!
Vectors should always
be drawn to represent
the strength of the
force. The force is
stronger in this region,
so the arrows are
bigger.
Gravitational Field Strength/
Intensity
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The gravitational field strength is the force of
attraction per the unit mass of an object that is
placed in the field.
It is equal to the gravitational force on the object
divided by the object’s mass.
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Near the surface of the Earth, this is of course g
Gravitational Field Strength/
Intensity
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To calculate the gravitational field strength as a
function of a spherical mass we combine the
universal law of gravitation and Newton’s second
law to get this equation:
g
6.67x10-11
Nm2/kg2
Gm planet
r2
G=
r = radius of the planet
mplanet = mass of the planet
g = magnitude of the gravitational field strength on the surface
Example 1
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Calculate the magnitude of the gravitational field
strength of a white dwarf with a radius of
7.0x106m and a mass of 1.2x1030kg.
Satellites and Orbits
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A satellite is an object or a body that revolves
around another body due to gravitational
attraction.
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An artificial satellite is an object that has been
intentionally placed by humans into orbit around
Earth or another body. (Natural satellites, like
the moon, are not placed there by humans).
Satellites and Orbits
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Orbits are an example of centripetal motion,
which we will study later in the course.
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When an object is orbiting something like a
planet there is a force of attraction between the
object and the planet. The orbital velocity
however, keeps the object from falling into the
planet. Both of these components, the orbital
velocity and the gravitational force, are
necessary for an object to orbit something.
Satellites and Orbits
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Orbits are typically elliptical, not circular, but we
approximate the orbits by assuming they are
circular.
Satellites and Orbits
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You can solve for a satellites orbiting speed
using the following equation:
Gm
v
r
v = orbiting speed
G = 6.67x10-11 N·m2/kg2
m = mass of the planet or large body
r = orbital radius from center of satellite to the center of the planet
Example 2
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An asteroid has a mean radius of orbit around
the Sun of 4.8x1011m. What is its orbital
velocity?
Satellites and Orbits
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A geosynchronous orbit is when a satellite
orbits the Earth with a speed that matches the
Earth’s rotational speed. A geosynchronous
satellite will appear to travel through the same
point in the sky every 24 hours.
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A geostationary orbit is an orbit is a type of
geosynchronous orbit where the satellite orbits
directly over the equator. The satellite will appear
to observers on the earth to remain fixed in the
sky at all times.
General Relativity and Gravity
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The Universal Law of Gravitation that we have
been studying is based on Newtonian physics.
It accurately describes a lot of phenomenon.
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It is important to note however that General
relativity, proposed by Einstein, has a different
way of describing the force of gravity and
explains gravity in terms of geometry and
space. General relativity is able to describe all
of the phenomena that the Newtonian model
could, but it can also explain things like black
holes, which the Newtonian model is limited in.
General Relativity and Gravity
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This tends to be true for a lot of Newtonian
physics. Newtonian physics describes some
phenomena quite well, but not everything, and it
does not work for other things at all. It is still
good for us to learn, but as you advance in
physics you will learn more about how General
Relativity is used to describe gravity because it
tends to explain things we see in the universe
more accurately.
General Relativity and Gravity
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General Relativity is the main way that scientists
view gravity today, but it also does not answer all
the questions we have about the Universe.
Perhaps in the future it will be replaced in turn by
another theory…
Homework
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Read Sections 6.1, 6.2, and 6.4
 Make
additional notes to supplement the
lesson notes.
 Complete the following questions:
Pg. 296 # 1, 2, 4, 5, 9, 11
 Pg. 303 # 1, 4, 5, 6, 7, 8
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Don’t forget to finish
your Tribal Coat of
Arms!