Gravitation
Makes the World Go ‘Round
Gravitational Force
● The Force of gravity is an attractive force felt
between all objects that have mass.
●
G=6.67x10-11N m2/kg2
Example 1: What is the Force of
Gravity on Earth due to the Sun?
Calculate the force of gravity on the Earth due
to the sun given the following:
Mass of the Sun: 1.99x1030 kg
Mass of Earth: 5.97x1024 kg
Radial Distance: 1.5x108 km
Example 2: The Mass of Mars
Calculate the mass of Mars given the following:
Mass of Sun: 1.99x1030 kg
Radial Distance: 2.28x108 km
Force of Gravity of Mars on the Sun: 1.64x1021N
Newton’s (Mind) Cannon
● The
idea was not Newton’s idea.
● Gravity being a force between ALL
OBJECTS was Newton’s idea.
● Newton's Cannon
The One Direction
● Until now Gravity pointed “downward”
● ...But it really points “inward”
The One Direction
● Since the force of gravity is always pointed
inward…
● ...Gravity is a centripetal force!
Example 3: The Acceleration of
Gravity
Calculate the acceleration of gravity on the
Earth given the following:
Mass of Earth: 5.97x1024 kg
Radius of Earth: 6371 km
Example 4: The Orbital Speed of
Earth
How quickly is the Earth moving right now in its
orbit around the sun?
Mass of the Sun: 1.99x1030 kg
Mass of Earth: 5.97x1024 kg
Radial Distance: 1.5x108 km
Example 5: How Far is the Moon
From Earth?
Determine the distance the moon is from Earth
given the following:
Mass of Earth: 5.97x1024 kg
Mass of the moon: 7.35x1022 kg
Speed of moon in orbit: 1025 m/s
Homework/Classwork
● Worksheet
● There will be an additional 2 problems based
on vertical loops posted online
● ALSO, if you do not have a grade for
something in Genesis, I DON’T HAVE IT! I
will not hunt you down. Come see me.
Kepler’s Laws of Planetary Motion discovery
worksheet is done between these two lessons
Introduction to Kepler’s
Laws
Discovery worksheet completed here:
Kepler's Laws Applet
Kepler’s Laws of
Planetary Motion
Ellipses
● An ellipse is a geometric shape in which the
sum of the distances from two foci is
constant.
Focus
● A focus is one of the points from which the
above distances are measured.
Semimajor Axis
● The distance from the center of an ellipse to
the furthest point along the major axis of the
ellipse.
Eccentricity
● Deviation of a curve or orbit from circularity
Period
● The amount of time it takes a planet to
revolve once around the sun
Kepler’s First Law:
The Law of Ellipses
● The general shape of a planetary orbit is an
ellipse.
● The sun is at one focus.
Kepler’s Second Law:
The Law of Areas
● Each triangular area is the same
● Planets move faster when they are closer to
the sun than when they are farther away.
e=0
e=0.35
e=0.70
Planetary Velocity Decreases as
Planetary Distance Increases
● Another relationship that can be shown by
using
Max/Min Orbital Velocities
● What are the maximum and minimum orbital
velocities of earth in its rotation around the
sun?
o
o
minimum distance from sun
 rmin=1.47x1011 m
maximum distance from sun
 rmax=1.52x1011 m
Kepler’s Third Law:
The Law of Harmonies
● T2/R3 = constant = k
● Equation is normally written T2 = kR3
● This relationship applies to any orbiting
system
o
o
Planets orbiting the sun
Jupiter’s moons orbiting Jupiter
Units Really matter for k
● What is k when T is measured in seconds
and when R is measured in meters?
● An astronomical unit (AU) is a unit of
distance equal to the semimajor axis of
Earth. What is the value of k when T is
measured in years and R in AU?
So what exactly is k?
● Yet again derivable from
● Verify that this new form of k yields the same
results as on the previous slide.
Homework Slide
● Complete the worksheet
● ALSO, if you do not have a grade for
something in Genesis, I DON’T HAVE IT! I
will not hunt you down. Come see me.
Geosynchronous
Satellites
Geosynchronous
● Geo: of, or relating to Earth
● Synchronous: at the same time
● Geosynchronous: Having an orbital period
that is synchronized with Earth’s rotation.
Examples of Geosynchronous
Orbits
● Satellites!
Telephone
Television
Weather
o Global positioning
o Radio
o Internet
o Military
o
o
o
Objects in orbit around Earth
Example 1: How Far Away Are
Geosynchronous Satellites?
● How far above the Earth’s Surface are these
satellites? (Ans: 35864 km)
● Let’s begin with (again)
Example 2: How Quickly Must
Geosynchronous Satellites Travel?
● Finally, a calculation that involves another
equation! (Ans: 3070 m/s)
Homework
Calculate the distance above Mars’ surface a
Geosynchronous satellite would have to be and
with what speed it must move in order to
maintain that orbit.