Sun at Center
Orbits are Circular
Tycho Brahe
1546-1601
Tycho was the greatest
observational astronomer of his
time. Tycho did not believe in
the Copernican model because
of the lack of observational
parallax. He didn’t believe that
the Earth Moved.
Tycho: Where’s the Parallax?
Tycho Brahe
1546-1601
Kepler worked for Tycho as his
mathematician. Kepler derived
his laws of planetary motion
from Tycho’s observational
data.
Orbits are Elliptical
Kepler’s 3 Laws of
Planetary Motion
1: The orbit of each planet about the sun is an ellipse with the sun
at one focus.
2. Each planet moves so that it sweeps
out equal areas in equal times.
3.
T12 r12
= 2
2
T2 r2
Isaac Newton
(1642 -1727)
Universal Law of Gravity
Every particle in the Universe attracts every other particle
with a force along a line joining them. The force is directly
proportional to the product to their masses and inversely
proportional to the square of the distance between them.
d
m
mM
F~ 2
d
M
Gravitational Force is
Universal
The same force that makes the apple fall to Earth, causes the
moon to fall around the Earth.
Universal Law of Gravity
G = 6.67 x10
d
m
GmM
F=
2
d
−11
2
Nm
2
kg
M
Measuring G: Cavendish
mM
F~ 2
d
G = 6.67 x10
GmM
F=
2
d
−11
2
Nm
2
kg
G is the same everywhere in the
Universe.
Inverse Square Law
GmM
F=
2
d
Gravitational Force
How would the force of gravity and the acceleration due to
gravity change as you fell through a hole in the Earth?
Quiz Questions
GmM
F=
2
d
1. If the moon was instantly transported twice the distance away
from the Earth, how would the gravitational force between them
change?
a) Increase by a factor of 2 b) Decrease by a factor of 2
c) Increase by a factor of 4 d) Decrease by a factor of 4
2. If the mass of the Moon instantly doubled, how would the
gravitational force between the Earth and Moon change?
a) Increase by a factor of 2 b) Decrease by a factor of 2
c) Increase by a factor of 4 d) Decrease by a factor of 4
Problem
Calculate the force of gravity between the Earth and the Moon.
Assume a circular orbit.
GmM
F=
2
d
F=
−11
2
2
24
22
6.673
x
10
Nm
/
kg
6.00
x
10
kg
7.4
x
10
kg )
(
)(
)(
( 3.84 x10 m )
8
2
F = 2.01x10 N
20
Problem
Calculate the acceleration of the Earth due to the Earth-Moon
gravitational interaction.
F
a=
m
20
2.01x10 N
a=
24
5.98 x10 kg
a = 3.33 x10−5 m / s 2
Problem
Calculate the acceleration of the Moon due to the Earth-Moon
gravitational interaction.
F
a=
m
20
2.01x10 N
a=
22
7.35 x10 kg
−3
a = 2.73 x10 m / s
2
Problem
The acceleration of gravity at the Moon due to the Earth is:
−3
a = 2.73 x10 m / s
2
The acceleration of gravity at the Earth due to the moon is:
−5
a = 3.33 x10 m / s
2
Why the difference?
FORCE is the same. Acceleration is NOT!!!
Force is not Acceleration!
FEarth on Moon = − FMoon on Earth
The forces are equal but the accelerations are not!
Problem
Calculate the acceleration of gravity acting on you at the
surface of the Earth.
F=
Gm you M E
d
6.673 x10
(
a=
F = m you a
2
GM E
a=
2
d
)( 5.98 x10
( 3.84 x10 m )
−11
2
Nm / kg
2
8
a = 9.81 m / s 2
2
24
kg )
Gravitational forces produce the tides and
keep the same side of the Moon always facing
the Earth in a Synchronous Rotation.
The gravitational force between
Earth and Moon results in tides
Large spring tides occur when
the Sun and Moon are aligned
such that they BOTH pull on the
Earth’s water.
Smaller neap tides occur when
the Sun and Moon are misaligned
such that they pull on the Earth’s
water in different directions.
Earth’s Ocean Tides
Neap Tides
Spring Tides
How many High and Low Tides
per day?
Earth- Moon System: Tidal Lock
Moon pulls on Earth and causes
tidal bulges in Oceans. Earth
pulls on moon causing tidal
bulge in Moon such that the
CM is off from CG.
Earth’s pull on the moon at its
center of gravity produces a
torque which rotates it. The moon
is ‘tidally locked’ so that it rotates
at the same rate at which it
revolves, showing Earth only one
face.
Questions!
Which exerts a greater gravitational force on the Earth, the moon or
the Sun? Which has a greater effect on the Earth’s tides? Why?
The Sun exerts a greater
force on the Earth. It also
causes tides, though it has
about half the effect as the
moon. Tides are due to
differences in force on
opposite sides of the Earth.
The sun is so far away
relative to the size of the
Earth that the difference in
force is not as significant
as the difference due to the
Moon since it is closer!
Spring
Spring
Neap
Bouncing laser
beams off the
Moon
demonstrates
that it slowly
moving away
from the Earth
~.25 cm/month
Earth- Moon System is Changing!
•Earth Rotation Slowing due to friction of ocean on bottom
•.0023 s per century: 900 Million yrs ago, Earth day was 18 hrs!
•Decrease of Earth’s spin angular momentum, increases the
orbital angular momentum of the Moon!
•Earth is slowing down and Moon is moving further away!
Eventually the Earth's rotation period
will be identical to the Moon's orbital
period. This situation is called
synchronous (1:1) rotation. In the
distant future (many billions of years
from now), the Earth will have a day
which is 47 current days long, and the
Moon will only be visible from one side
of the Earth!!
2-D Motion
2-D Motion
Horizontal and vertical components are independent of each other!
Gravity acts in the vertical direction but not in the horizontal direction!!
Speed in vertical direction speeds up!
Speed in horizontal direction stays the same!
Projectile Motion
No Change
change
Projectile Motion
Which hits the ground first?
SAME!
Both falling the same height!
Horizontal speed doesn’t effect the time to hit the ground!
If it takes 1 second to hit the ground, how tall is the tower?
Projectile Motion
d = 5t = 5(1) = 5m
2
2
If it takes 1 second to hit the ground, how tall is the tower?
Question
The ball is thrown horizontally at 20 m/s.
How long does it take to hit the ground? 1 Second!!
How far does it travel in the horizontal direction?
d
Question
The ball is thrown horizontally at 20 m/s.
How long does it take to hit the ground? 1 Second!!
How far does it travel in the horizontal direction?
m
d = vt = 20 1s = 20m
s
Question
The ball is thrown horizontally at 30 m/s.
How long does it take to hit the ground? 1 Second!!
How far does it travel in the horizontal direction?
d
m
d = vt = 30 1s = 30m
s
Question
The ball is thrown horizontally at 100 m/s.
How long does it take to hit the ground? 1 Second!!
How far does it travel in the horizontal direction?
Curvature of Earth
Every 8000 m, the Earth curves by 5 meters
Curvature of Earth
If you threw the ball at 8000 m/s, how far would travel
in the vertical and horizontal directions in 1 second?
horizontal : d = vt = ( 8000m / s )(1s ) = 8000m
vertical : d = 5t = 5 (1s ) = 5m
2
2
Orbital Velocity
If you can throw a ball at 8000m/s, the Earth curves away
from it so that the ball continually falls in free fall around the
Earth – it is in orbit around the Earth!
Ignoring
air
resistance.
Above the atmosphere
Orbital Velocity
As the ball falls around the Earth in orbit, does the
acceleration due to gravity speed it up?
Circular Orbital Velocity
As the ball falls around the Earth in a circular orbit, does the
acceleration due to gravity speed it up?
Circular Orbital Velocity
The force of gravity is perpendicular to the velocity of the ball
so it doesn’t speed it up – it changed the direction of the ball.
It provide a centripetal acceleration the keeps it in a circle!
At a speed of 8km/s
Orbital time is ~ 90 minutes
Escape Velocity
8km/s: circular orbit
Between 8 & 11.2 km/s: elliptical orbit
11.2 km/s: escape Earth
42.5 km/s: escape solar system!
Elliptical Orbits
Does the force of gravity change the
speed of on object in an elliptical orbit?
Because there is a
component of force in the
direction of motion!
Do Workbook 45-47
Orbits
Circular Orbit
Elliptical Orbit
Where does the satellite move faster in the elliptical orbit?
Near the Earth or far from Earth? Why?
Geosynchronous Orbit
Elliptical Orbit
Satellite Orbits
Global Geostationary Satellite
Coverage
USA
USA
Euro
Japan
USSR
China
With an orbital period of
about 100 minutes, these
satellites will complete
slightly more than 14
orbits in a single day.
Sun-Synchronous Near Polar Orbits
Orbiting Space Trash
Man-made debris orbits at a speed of roughly 17,500 miles/hour (28,000 km/h)!
More than 4,000 satellites have been launched into space since 1957. All that activity
has led to large amounts of space trash. More than 13,000 objects that are at least
three to four inches (seven to ten centimeters) wide. Of those objects, only 600 to 700
are still in use. 95 percent of everything up there that the United States is tracking is
trash. There are millions of smaller parts that are too small to track.
Orbiting Space Trash
Fast Trash Go Boom
Australia, in 1979.
Orbiting Space Trash
What Goes Up Must Come Down
This is the main propellant tank of the
second stage of a Delta 2 launch vehicle
which landed near Georgetown, TX, on
22 January 1997. This approximately
250 kg tank is primarily a stainless steel
structure and survived reentry relatively
intact.
Skylab crashed onto
Australia in 1979.
Radioactive Space Junk
Cosmos 954
Nuclear Power in Space
Mission to Mars
The NASA Mars Exploration Program (MEP) will launch a
spaceflight mission to Mars in late 2009 that will land a
nuclear powered roving Mars Science Laboratory on the
surface of the planet.
Our Spaceship Earth
One island in one ocean...from space
“...we’re all astronauts aboard a little spaceship called Earth”
- Bucky Fuller