Chapter 11 – Out Into Space
11.1 Rhythm of the heavens
Learning outcomes
· to make an object move in a circular path, a force must act perpendicular to its velocity
· a centripetal acceleration can be found by a=v2/r and the force required to cause it must be F=mv2/r or F=mw2r
· no work is done when a force on a body acts perpendicular to its motion
Lesson 1 The heavens above, Centripetal acceleration and force
Objectives: - reason for something to move in a circle
- definition of centripetal acceleration and force
SoftAct 10S 'Watching the planets go round'
Dis10O 'Eccentricity of planet orbits'
SoftAct 20S 'Retrograde motion'
Look at the book p. 34 - 36. Galileo’s insight, Descartes’ idea that a force is needed to change direction = Newton's first law of motion. Define centripetal acceleration and force
Exp 40E 'Testing - testing whether the actual force (tension) = the theoretical force (in the equation).
Lesson 2:. More on
Objectives: - understand that ALL objects that move in a circle require a force equal to
- realise that this force can be provided by gravity, a reaction force, tension…
Starter: SoftAct 60S 'Driving round in a circle' and linking it to last lesson, what provides the force?
Things moving in a circle are a special case derivation on p.37.
No work is done by the cork moving in the circle.
Speeds and accelerations in the solar system' on page 37
Warm 20W 'Orbital velocities and acceleration'
SAQ 30S 'Centripetal force'
Warm 70W 'Radians and angular speed'
Homework
SAQ 40S ‘Circular motion – more challenging’ Discussion of angular velocity w and what it means on p. 37
Comp 50C 'Centrifuges'
Extension: a) Question 5 on page 39
b) Data 10D 'Using Kepler’s third law' and
Reading 40T 'Kepler's second law and angular momentum'
c) Reading 10T 'Brahe and Hamlet'
Reading 20T Text to Read 'Hubble'
11.2 Newton's gravitational law
Learning outcomes
·
· the concept of gravitational field, and diagrams to represent it
· gravitational field strength and its graphical representation
·
· to calculate the orbit radius and time of a satellite or planet
Lesson 3 The Law
Objectives - from Newton
The rise of the clockwork universe continues. Why do we talk about clockwork?
The gravitational law - the equation and the Moon falling in - p. 40, link to apples falling.
Big G, who measured it, how, and why it was so hard.
http://en.wikipedia.org/wiki/Cavendish_experiment
SoftAct 70S ''Variations in gravitational force'
BUT look at the model window.
SoftAct 80S 'Gravitational universes'
SoftAct 90S 'Gravitation with three bodies'
Warm 80W 'Newton’s gravitational law'
Lesson 4 Gravitational field strength
Objectives - forces near a planet can vary depending on the object you put there – need to
use a standard object, a kilogram.
- this is field strength, g, in N/kg
Starter: revise and on whiteboards
Definition of g - look at page 42
Dis 100O OHT 'Apollo goes to the Moon'
The link between field strength and acceleration due to gravity.
SoftAct 240S 'Analysing data from the Apollo 11 mission to the Moon'
Dis 120O OHT 'Gravitational field pattern for the Earth-Moon system' try on whiteboards first.
SoftAct 110S Software Based 'Probing a gravitational field'
Lesson 5: Kepler and some questions on The Law
Objectives - by combing and you can derive extra laws that were originally deduced by Kepler (and Brahe)
Combine and to show Kepler 3 - R3 is proportional to T2
Applets of Keplers 3 laws.The role of Tycho Brahe (who developed an interest in alchemy after losing his nose in a duel and wanting a prosthetic).
http://home.cvc.org/science/kepler.htm
Geosynchronous orbits – what is special. Why have polar orbits?
http://www.thetech.org/exhibits/online/satellite/4/4b/4b.1.html
SAQ 110S Short Answer 'Finding the mass of a planet with a satellite'
Comp 90C 'Are there planets around other stars?'
Homework
Questions 1, 2, 3, 4 on page 46
Comp 60C 'How Cavendish didn’t determine G and Boys did'
Try reading: Reading 50T 'Training for movement in space'
Reading 60T 'Forces on real objects'
Reading 70T 'Gravity can pull things apart'
Reading 100T 'Supernovae and black holes'
Extension: a) Dis110O 'A geostationary satellite'
b) Comp 130C 'Variations in g'
c) Questions 5, 6, 7 on page 46
11.3 Mapping gravity
Learning outcomes
· gravitational potential energy difference in a uniform field = mgDh
· gravitational potential is gravitational potential energy per unit mass
· gravitational field strength = – gravitational potential gradient
· gravitational potential around a point mass
·
· the total energy of a body orbiting in a gravitational field is gravitational potential energy plus kinetic energy
Lesson 6: Gravitational potential in a uniform field
Objectives - we live in a uniform gravitational field
- the mgh we know only applies close to the Earth’s surface
- potential is energy per kilograms in J/kg
If you carry a kg mass around the room with a newton meter the reading doesn't change. Get up on the desk - it still doesn't.
It has taken energy to get up on the deskt. How do we work it out?
mgh because the field is uniform.
Demo 190D 'Exploring potential with a tennis ball'
Demo 200D ‘Loop-the-loop’
Warm 200W 'Pole vaulting'
Definition of gpe (= mgh in a uniform field only), and gravitaional potential Vg = gh (energy per kilogram). Gravitational potential difference and its similarity to electrical potential difference..
SAQ 210S Gravitational potential energy and gravitational potential'
Lesson 7: Potential wells
Objectives - Vg and Eg for spherical fields
- field is potential gradients
- gravitational fields are like springs
Remember Newton’s Law and graphs of F and g, including going to the Moon.
In a spherical field the potential is like a well.
Field is slope of graph of V vs r.
Potential is area under a graph of g vs r. Potential V = - GM/r
Demo 270D 'Measurements with gravitational slides'
Data 120D 'The gravitational field between the Earth and the Moon':
SoftAct 220S 'Storing energy with gravity'
SoftAct 230S 'Inferring fields'
Lesson 8: Getting a feel for field and potential
Objectives - know how to apply the big 4 equations to a variety of situations
SoftAct 250S Software Based 'Variations in field and potential'
SoftAct 260S Software Based 'Probing gravitational potential'
Dis 220O OHT 'Gravitational equations and graphs'
Data 220D 'Gravitational potential difference, field strength and potential'
Lesson 9: Getting out of here in a hurry (or not)
Objectives - know that the escape velocity needs to be reached to completely escape the field of planet.
- Know that the escape velocity doesn’t depend on mass
- Appreciate that this is why a black hole is black.
Remember the F/r graph for a spacecraft going to the Moon.
How do you escape from the Earth?
SoftAct 290S 'Setting up energetic orbits'
Data 240D 'Why is a 'black hole' black?'
Reading 120T Comets and the Rosetta mission'
Reading 130T 'The Cassini-Huygens mission to Saturn'
Homework
SAQ 250S r 'Summary questions for chapter 11'
Data 230D 'Changing orbits'
Extension: a) Questions 5, 6 on page 60
b) SoftAct 280S 'Relating field and potential'
c) Reading 110W Well Actually / But Also 'Gravitational potential due to spherical mass'