Title: Understanding Orbits
1Understanding Orbits
2Understanding Orbits
- Orbital Motion
- Baseballs in Orbit
- Analyzing Motion
- Newtons Laws
- Laws of Motion
- Weight, Mass and Inertia
- Momentum
- Changing Momentum
- Action and Reaction
- Gravity
3Orbital MotionBaseballs in Orbit
- If a baseball player throws a baseball
horizontally from a mountain top - Gravity pulls the ball toward the ground.
- The faster a ball is thrown horizontally, the
farther it will go before gravity pulls it to the
ground. - When an object moves fast enough, it will go far
enough as it falls to miss the Earth and stay
in orbit.
4Orbital MotionBaseballs in Orbit (contd)
- The Earths curvature causes a 5 meter decrease
in altitude for every 8 kilometers across the
ground. - If the ball is moving fast enough across the
ground so it falls 5 meters or less every 8
kilometers, it will never hit the ground (as long
as theres no air resistance).
5Orbital MotionBaseballs in Orbit (contd)
- A ball thrown fast enough to cover exactly 8
kilometers in the time it takes the ball to fall
5 meters will be in a circular orbit. - Increasing velocity (adding more energy) will
make it an elliptical orbit.
6Orbital MotionAnalyzing Motion
- To analyze objects in motion, follow a Motion
Analysis Process (MAP) Checklist - Define a coordinate system.
- Develop an equation of motion.
- Apply simplifying assumptions.
- Assign initial conditions.
- Perform error analysis.
- Test the model.
7Newtons LawsLaws of Motion
- Newtons Laws of Motion are unbreakable.
- Newtons Laws of Motion can explain
- The motion of the heavens
- The paths of the stars
- The future position of Earth
8Newtons LawsWeight, Mass, and Inertia
- A scale measures how much Earths gravity is
pulling an object's mass. - Mass tells us
- How much matter an object has.
- How much the object resists motion (inertia).
- How much gravitational attraction it has to other
masses (gravity).
9Newtons LawsMomentum and Inertia
- Newtons First Law of Motion
- A body continues its state of rest or of uniform
motion in a straight line unless compelled to
change that state by forces impressed on it. - Objects at rest stay at rest.
- Objects in motion continue in straight-line
motion. - UNLESS acted upon by an outside force, like
gravity.
10Newtons LawsMomentum and Inertia (contd)
- For an object at rest, resistance to movement is
its inertia, which is determined by how much mass
it has. - For an object moving, its resistance to change in
that movement (speed or direction) is its
momentum.
11Newtons LawsLinear Momentum
- An objects linear momentum is its resistance to
changes in its straight-line motion. - Depends on both its mass and its velocity.
- The direction of the objects linear momentum is
the same as the objects velocity (speed).
12Newtons LawsLinear Momentum (contd)
- A spacecraft in orbit is in motion.
- Motion is not in a line.
- Because motion isnt in a straight line,
something must be acting on itgravity.
13Newtons LawsAF Linear Momentum Example
- Which scenario would require a pilot to
anticipate speed changes more during aerial
refueling? - A jumbo C-5 transport
- An F-15 fighter aircraft
- A fully loaded C-5 has about 20 times the mass of
an F-15more momentum.
14Newtons LawsAngular Motion
- Objects at rest resist spinning .
- The resistance to start spinning for an object is
its moment of inertia. - An objects angular momentum is its resistance to
changes in direction or speed of its spinning
motion. - Depends on how spread out mass is from the
center of spinning (mass moment of inertia). - Depends on how fast the spin is (angular
velocity).
15Newtons LawsAngular Momentum
- Angular momentum keeps the spin direction (as
determined by the right-hand rule) pointed in the
same direction. - If you curl the fingers of your right hand in the
spin direction, your thumb will point in the
direction of the angular momentum. - Quarterbacks put a spiral on a football to give
it angular momentum and keep it from tumbling. - Barrels of rifles and handguns have rifling to
spin a bullet and keep it from tumbling.
16The Right-Hand Rule
- Use the right-hand rule to find the direction of
the angular velocity and the angular momentum. - Curl the fingers of your right hand in the
direction of spin and the thumb points in the
direction of the angular velocity and angular
momentum.
17Newtons LawsChanging Momentum
- Newtons Second Law of Motion The time rate of
change of an objects momentum equals the applied
force. - Changing an objects momentum requires a force.
- How quickly the momentum is changed determines
the size of the force. - Newtons Second Law when mass is constant Force
equals mass times acceleration.
18Newtons Laws Changing Momentum (Example)
- Bulldozer and baby carriage are traveling at the
SAME SPEED. - Momentum is mass times velocity.
- A bulldozer has much higher momentum because it
has more mass traveling at the same velocity. - To stop both objects in the same amount of time,
we must apply a much higher force to the
bulldozer (higher rate of momentum change).
19Newtons Laws Action and Reaction
- Newtons Third Law of Motion When body A exerts
a force on body B, body B will exert an equal,
but opposite, force on body A.
A
B
20Newtons Laws Gravity
- Newtons Law of Universal Gravitation The force
of gravity between two bodies is directly
proportional to the product of their two masses
and inversely proportional to the square of the
distance between them. - If we double the distance between the two masses
(R) in the upper part of the figure to (2R) in
the lower figure, the gravity force (Fg) is
decreased by four (Fg/4).
21Newtons Laws Gravity (contd)
- Acceleration due to gravity on an object near
Earth depends on - Earths mass times the universal gravitational
constant. - Square of the distance between the object and the
Earth. - The farther you are from Earths center, the less
the acceleration due to gravity.
22Newtons Laws Gravity (contd)
- Acceleration of gravity has nothing to do with
the falling objects mass. - Galileo was correct objects of different masses
will fall at the same rate.
23Summary
- Orbital Motion
- Baseballs in Orbit
- Analyzing Motion
- Newtons Laws
- Laws of Motion
- Weight, Mass, and Inertia
- Momentum
- Changing Momentum
- Action and Reaction
- Gravity
24Next
- Based on tools developed in this lesson well
describe the path that spacecraft make as they
fly over the Earth. - Well also figure out how spacecraft change from
one orbit to another.