© Simon Porter 2007 Orbital Motion.

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Presentation transcript:

© 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! The force that keeps an object moving in a circle is called the centripetal force (here provided by gravity) Gravity

Uniform Circular Motion © Simon Porter 2007 Uniform Circular Motion Remember we have already looked at circular motion Centripetal acceleration = v2/r Centripetal force = mv2/r velocity

Uniform Circular Motion © Simon Porter 2007 Uniform Circular Motion For orbital motion, the centripetal force is provided by gravity Earth’s gravitational attraction on moon

Uniform Circular Motion © Simon Porter 2007 Uniform Circular Motion centripetal force = force of gravity Mmv2/r = GMeMm/r2 v2 = GMe/r Earth’s gravitational attraction on moon

Period of orbit v2 = GMe/r Distance travelled in one orbit = 2πr © 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)

This is known as Kepler’s third law of planetary motion. © 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.

Total energy = GMm/2r – GMm/r = -GMm/2r © 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 from slide 4

Energy of a satellite Total energy of satellite = -GMm/2r © 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

Weightlessness There is a mathematical way to look at this. © 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

Weightlessness GMm/r2 – N = mv2/r N = GMm/r2 – 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 - Joe Francis with hot chicks floating in space! YouTube - flying dog

More questions! Page 152 Questions 1, 3, 4, 15, 24. Page 153 Q7, 13 © Simon Porter 2007 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 More questions! I hate physics.