Orbital Motion © Simon Porter 2007
Orbital Motion © Simon Porter 2007. How far could you kick a dog? From a table, medium kick.
Dec 18, 2015
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Orbital Motion© Simon Porter 2007
How far could you kick a dog?
From a table, medium kick.
Even bigger cannon?
Even bigger cannon
GravityGravity
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!
The force that keeps an object moving in a circle is called the centripetal force (here provided by gravity)
Gravity
Uniform Circular Motion
Remember we have already looked at circular motion
Centripetal force = mv2/r
velocity
Centripetal acceleration = v2/r
© 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
© Simon Porter 2007
(T = period of orbit)
Period of orbit
v2 = GMe/r(2πr/T)2 = GM/rT2 = 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
v2 = GM/r so Ek = GMm/2r
Total energy = GMm/2r – GMm/r = -GMm/2r
Total energy = -½mv2
© Simon Porter 2007
from slide 4
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© Simon Porter 2007
Ep
Ek
ET
energy
distance
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)
© Simon Porter 2007
v
mv2/r
acceleration = v2/r
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).
© 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.
© Simon Porter 2007
YouTube - flying dog
YouTube - Greg Olsen - Drinking water on the ISS
YouTube - Joe Francis with hot chicks floating in space!
YouTube - Zero G Puke Bag
More questions!© Simon Porter 2007
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
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