Download Orbital Motion

© Simon Porter 2007
Orbital Motion
How far could you kick a dog?
From a table, medium kick.
How far can you kick a dog?
Gravity
Harder kick?
Harder kick
Gravity
Small cannon?
Woof!
(help)
Small cannon
Woof!
(help)
Gravity
Bigger cannon?
Bigger cannon
Gravity
Gravity
Even bigger cannon?
Even bigger cannon
Gravity
Gravity
Gravity
VERY big cannon?
VERY big cannon
Gravity
Humungous cannon?
Dog in orbit!
The dog is
now in orbit!
(assuming no
air resistance
of course)
Dog in orbit!
The dog is
falling towards
the earth, but
never gets
there!
Dogs in orbit!
Gravity
The force that
keeps an
object moving
in a circle is
called the
centripetal
force (here
provided by
gravity)
© Simon Porter 2007
Uniform Circular Motion
Remember we have already looked at
circular motion
Centripetal
acceleration = v2/r
Centripetal force = mv2/r
velocity
© Simon Porter 2007
Uniform Circular Motion
For orbital motion, the centripetal force is
provided by gravity
Earth’s
gravitational
attraction on moon
© Simon Porter 2007
Uniform Circular Motion
centripetal force = force of gravity
Mmv2/r = GMeMm/r2
v2 = GMe/r
Earth’s
gravitational
attraction on moon
© Simon Porter 2007
Period of orbit
v2 = GMe/r
Distance travelled in one orbit = 2πr
Speed = distance/time = 2πr/T
Earth’s
gravitational
attraction on moon
(T = period of orbit)
© Simon Porter 2007
Period of orbit
v2 = GMe/r
(2πr/T)2 = GM/r
T2 = 4π2r3/GM
T2 α r3
This is known as Kepler’s third law of planetary
motion.
© Simon Porter 2007
Energy of a satellite
A satellite has kinetic energy and gravitational
potential energy.
Total energy = ½mv2 - GMm/r
from slide 4
v2 = GM/r so Ek = GMm/2r
Total energy = GMm/2r – GMm/r = -GMm/2r
Total energy = -½mv2
© Simon Porter 2007
Energy of a satellite
Total energy of satellite = -GMm/2r
Kinetic energy = GMm/2r
Potential energy = - GMm/r
© Simon Porter 2007
Energy of a satellite
energy
Ek
distance
ET
Ep
© Simon Porter 2007
Weightlessness
Consider an astronaut
in a space ship
orbiting the earth
© Simon Porter 2007
Weightlessness
Remember both the ship and astronaut
are falling towards the earth (centripetal
acceleration)
v
mv2/r
© Simon Porter 2007
Weightlessness
Because they are both falling together, the
astronaut feels no reaction force from the
floor of the space craft so she feels
“weightless” (you get a small feeling of this
as a lift (elevator) starts to descend).
acceleration = v2/r
© Simon Porter 2007
Weightlessness
There is a
mathematical way to
look at this.
© Simon Porter 2007
Weightlessness
The forces on the astronaut are gravity
from the earth (GMm/r2) and the normal
reaction force (N) of the floor of the
spacecraft.
The net force must be equal to mv2/r if he
is in orbit.
GMm/r2 – N = mv2/r
© Simon Porter 2007
Weightlessness
GMm/r2 – N = mv2/r
N = GMm/r2 – mv2/r
N = (m/r)(GM/r – v2)
since v2 = GM/r, N = zero
© Simon Porter 2007
Weightlessness
So there is a force of gravity on the
astronaut, but no reaction force from the
floor so the astronaut feels weightless.
YouTube Zero G Puke
Bag
YouTube Greg Olsen
- Drinking
water on
the ISS
YouTube flying dog
YouTube Joe Francis
with hot
chicks
floating in
space!
© Simon Porter 2007
More questions!
I hate physics.
Page 152
Questions 1, 3, 4,
15, 24.
Page 153 Q7, 13
Pages 307
Questions
2, 4, 5, 6, 11, 12.
You can have
some time to
finish them in this
lesson, and then
you can finish the
rest for
homework, due in
Wednesday 30th
September
TEST on 6th
October