# Chapter 4 - DOC 7

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"Chapter 4 - DOC 7"

Chapter 11 – Out into space
Specification Section 5.4.1.2 Out into space

General learning outcomes for each section are given in the teaching notes from the CD-ROM.
For information on Key Skills see the Specification section on the CD-ROM.

Types: Students should demonstrate:      (a) knowledge and understanding of phenomena, concepts and relationships by describing and
explaining cases involving...
(b) comprehension of the language and representations of physics: by making appropriate uses of the
terms…; by expressing in words and vice-versa...; by sketching, plotting from data and interpreting…
(c) quantitative and mathematical skills, knowledge and understanding by making calculations and
estimates involving…

Lesson         Content                                                           Activities                   Homework
11.1                (a) motion in a horizontal circle and in a circular
Rhythms of          gravitational orbit,
the heavens         (b) changes of gravitational and kinetic energy, work done
where the force is not along the line of motion
2         2         2             2
(c) v = r ω, a = v /r, F= mv /r, a = ω r and F = mω r
 Explain observations of the motion of planets, stars,
the Moon and the seasons in terms of the heliocentric
model of the solar system.
 Appreciate the simplification resulting from the
replacement of the geocentric model by the
heliocentric one.
 Explain the retrograde motion of Mars and the phases
of Venus in terms of the heliocentric model.
Lesson 1: In advance of this lesson, students should read         Activity 10S “Watching the   Reading 10T “Brahe and Hamlet”
Section 11.1 from the textbook, and one or more of Readings       planets go round             Reading 20T “Hubble”
10T, 20T, 30T. Begin with a brainstorm of how unaided             Activity 20S “Retrograde     Reading 30T “The problem of
observations of the motions/appearance of the Sun, Moon and       motion”                      longitude”
stars, the seasons etc. are explicable in terms of the accepted
model of the solar system. Some students will not even be
aware of how the stars move at night, so some time may need
to be spent in eliminating misconceptions. Discuss the
historical development of our understanding of motion in the
solar system, from Ptolemy via Copernicus to Tycho Brahe

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Lesson   Content                                                               Activities                  Homework
and Kepler, stressing how the heliocentric model makes
calculation and explanation of motions much simpler.
Demonstrate or have students run Activity 10S. Use the
examples of the retrograde motion of Mars (Activity 20S) and
the phases of Venus (p36) to illustrate the heliocentric model
in action.

     Appreciate how Kepler’s first law led to precise fitting
of planetary orbit data.
 Appreciate the origin of Kepler’s second law in terms
of kinetic and potential energy exchanges.
 Use data on planetary orbit radii and orbital periods to
derive Kepler’s third law.                                                                                     rd
Lesson 2: Strictly speaking, the teaching of Kepler’s Laws is         File 30T “Planetary orbit   Qs 10D “Using Kepler’s 3 law”
optional, so if you are pushed for time, you could limit the work     data”
of this lesson, and spend more time on the work of lesson 1. It
is worthwhile considering Kepler’s laws as they are revisited
later in the chapter.
Discuss Kepler’s work showing that planets followed elliptical,
not circular orbits (Kepler’s first law), and discuss qualitatively
Kepler’s second law in terms of KE/PE exchanges. You could
mention comets as orbiting bodies with orbits so elliptical that
they are only close to the Sun for a short time during each
orbital pass. Students can now try to obtain Kepler’s third law
for themselves using the data in File 30T.
 Know that a body describing uniform circular motion is
being accelerated towards the centre of its motion.
 Know the meaning of the terms centripetal
acceleration and centripetal force.
 Know the meaning of the terms angular speed and
 Use the relationship a = v /r in calculations involving
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uniform circular motion.
 Recall and use the relationships v = 2Πr/T, ω = 2Πf
and ω = 2π/T in calculations involving uniform circular

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Lesson          Content                                                                Activities                       Homework
motion.
 Recall and use the relationship v = rω in calculations
involving uniform circular motion.
 Recall and use the relationships a = ω r, F = mv /r, F
2          2
2
= mω r in calculations involving uniform circular
motion.
 Know that for a body describing uniform circular
motion, there must be an agent providing the
centripetal force.
 Identify the origin of the centripetal force for a range of
situations involving circular motion.
Lesson 3-4: Begin with a recap of Newton’s first law, using            Activity     30D    “Galileo’s   Qs 20W “Orbital velocities and
Galileo’s “pin and pendulum” experiment (Activity 30D) and/or          frictionless experiment”         acceleration”
the thought experiment of p36 in the BOOK. Lead into                   Activity 40E “Testing F =        Qs 30S “Centripetal force”
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discussion of what causes an object to follow a circular path,         mv /r”                           Qs 40S “Circular motion- more
noting that while the magnitude of the tangential velocity is          Activity 60S “Driving round      challenging”
constant, the velocity itself is continually changing, and is          in a circle”                     Qs 50C “Centrifuges”
always centripetally directed. Derive the relationship a = v /r
2       Qs 20W “Orbital velocities       Qs 70W “Radians and angular
and, using v = rω, the corresponding relationship a = ω r.
2       and acceleration”                speed”
Discuss how Newton’s second law leads to the corresponding             Qs 30S “Centripetal force”       BOOK Qs p39
2                2
force relationships F = mv /r and F = mω r. Activity 40E can           Qs 40S “Circular motion-
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be used to test the relationship F = mv /r experimentally, while       more challenging”
Activity 60S enables circular acceleration to be modelled.             Qs 50C “Centrifuges”
Discuss the origin of the centripetal force in a variety of            Qs 70W “Radians and
situations (see BOOK p38, and get students to brainstorm               angular speed”
others). Mention the absence of work done in circular motion,          BOOK Qs p39
as the force is perpendicular to the direction of motion.
Students should be given plenty opportunity to practise using
the various relationships: see BOOK questions p39 and the
question sets listed right.

11.2            (a) motion in a uniform gravitational field, the gravitational field
Newton’s        of a point mass
Gravitational   (b) gravitational field, diagrams/graphs of gravitational fields
2                     2
law             (c) F = -GMm/r , g = F/m, g = -GM/r

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Lesson   Content                                                             Activities                       Homework
 Appreciate the thought processes that led Newton to
promulgate his Law of Universal Gravitation.
 Recall and use the equation describing Newton’s Law
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of Universal Gravitation: F = -Gm1m2/r .
 Understand how Kepler’s third law may be derived
from a consideration of Newton’s Law of Universal
Gravitation and the expression for centripetal force.
 Make calculations on satellites orbiting massive
bodies to determine, for example, the mass of the
massive body, the orbital period, the orbital radius.
Lesson 5-6: Introduce Newton’s Law of Universal Gravitation         Activity 70S “Variations in      Activity     80S       “Gravitational
(NLUG) using the treatment of BOOK p40, where the Moon’s            gravitational force”             universes”
centripetal acceleration is just the acceleration at the Earth’s    Activity 80S “Gravitational      Activity 90S “Gravitation with three
2
surface diluted by distance . Lead into F = -Gm1m2/r ,
2   universes”                       bodies”
illustrating the equation with Activity 70S and sample              Activity 90S “Gravitation        Qs 80W “Newton’s gravitational
calculations. The inverse square nature of the law can be           with three bodies”               law”
understood in terms of gravity diluting over a surface of area      Qs       80W         “Newton’s   Qs 60C “How Cavendish didn’t
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4пr (see BOOK p41). Discuss how the gravitational force             gravitational law”               determine g and Boys did”
gives rise to the centripetal force. It is worthwhile showing how   Qs 110S “Finding the mass        Qs 90C “Are there planets around
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Kepler’s third law arises by equating Gm 1m2/r = m2ω r, and
2       of a planet with a satellite”    other stars?”
inserting ω = 2п/T. Activities 80S and 90S can be used to                                            Qs 110S “Finding the mass of a
explore the nature of the gravitational force further, possibly                                      planet with a satellite”
setting for homework if time is limited.
In the second session, students should do problem solving,
using, for example, Qs 80W, Qs 110S, and/or Activities 80S
and 90S.

   Know that a gravitational field is a region in space
where a mass feels a force due to another mass.
   Know the meaning of the term gravitational field
strength.
   Recall and use the equation for radial gravitational
2
fields g = F/m = -GM/r , to make calculations involving
gravitational fields.
   Draw the pattern of gravitational field lines around a
mass such as a planet.

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Lesson          Content                                                               Activities                      Homework
 Sketch the variation in gravitational field strength with
distance from a body.
 Sketch the variation in total gravitational field strength
with distance from the surface of the Earth to the
surface of the Moon, identifying key features.
 Make calculations on satellites orbiting massive
bodies to determine, for example, the mass of the
massive body, the orbital period, the orbital radius.
Lesson 7-8: Introduce the concept of the gravitational field,         Activity 110S “Probing a        Activity    110S       “Probing a
recapping work from Chapter 9 on the gravitational field at the       gravitational field”            gravitational field”
surface of the Earth, and generalizing to any body with mass.         Qs 110S “Finding the mass       Qs 110S “Finding the mass of a
Show the relationship between the equation for gravitational          of a planet with a satellite”   planet with a satellite”
force and that for field, noting how they are linked through F =      BOOK Qs p46                     BOOK Qs p46
mg. Discuss the graphical depiction of a gravitational field,                                         Qs 120D “The gravitational field
noting that the field lines show the direction of the gravitational                                   between the Earth and the Moon”
force that acts on a mass placed in the field. Discuss the                                            Qs 130C “Variation in g”
launching of a satellite into orbit (BOOK p42), noting that the                                       Reading 60T “Forces on real
gravitational field is accelerating the satellite towards the Earth                                   objects”
always, but it remains in orbit due to high speed. It is also                                         Reading 70T “Gravity can pull
worth pointing out that objects in free fall are not weightless,                                      things apart”
but that they are being accelerated towards the centre of the                                         Reading 100T “Supernovae and
Earth. Go through the calculation of geostationary orbit radius,                                      black holes”
and then get students to do Qs 110S (could be homework), if
Students can carry out Activity 110S which uses Apollo data to
determine the variation in field strength with distance from the
Earth to the Moon. Alternatively, just use display material
100O as a basis for discussion, and do Activity 110S for
homework. Display material 120O illustrates the variation of
the field strength from the Earth to the Moon, which can be
explored quantitatively using Qs 120D.
11.3 Arrivals   (a) momentum as a vector, force as rate of change of
and             momentum, conservation of momentum
departures      (b) momentum, graphs showing force versus time for
collisions etc.
(c) p = mv, F = Δ(mv)/ Δ t

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Lesson   Content                                                              Activities                     Homework

    Know the meaning of the term momentum, and how to
calculate it using p = mv.
 Know that momentum is conserved in collisions,
disintegrations, explosions etc.
 Investigate        experimentally     the     principle  of
conservation of momentum.
 Use the principle of conservation of momentum to do
calculations on collisions, disintegrations, explosions
etc.
Lesson 9-10: Introduce momentum as the “quantity of motion”          Activity 120E “Low friction    Worksheet “Momentum problems”
possessed by a body. Introduce the momentum equation p =             collisions and explosions”     on colliding basketballs.
mv. The following experiments are drawn directly from the            (use video camera?)            Qs 140W “Change in momentum
GCSE separate sciences physics “Forces and Motion”                   Activity 160S “Modelling       as a vector”
module. You should demonstrate all of the experiments                collisions”                    Qs 160S “Collisions of spheres”
qualitatively, and do or analyse a selection of them using the       Worksheet       “Momentum      Qs 170C “Collision with spaceship
video camera. Activity 160S should also be used to simulate          problems”    on    colliding   Earth”
collisions, if desired for homework.                                 basketballs
Use the air track and vehicles to demonstrate the following
collisions, if possible recording each collision using the digital
camera: (1) elastic collision (equal masses); (2) elastic
collision (light + heavy); (3) coalescence (equal masses); (4)
coalescence (light + heavy); (5) disintegration (light + heavy
and/or light + light). Data can be displayed and analysed on
the iMac. Alternatively, you could show the relevant clips from
the Multimedia Motion CD. Some of the collisions could be
pre-recorded if necessary, and you could get different groups
to analyse different collisions, pooling results later.
Get students to analyse the data from some of the
experiments to elucidate/confirm the principle of conservation
of momentum, noting that momentum has direction as well as
magnitude. Where possible, follow up the analysis of each
collision with a numerical question (see question sets right)
based on the type of collision considered, and try to relate
each collision to a “real world” situation, for example the recoil
of a gun when fired. Discuss briefly Galilean invariance as

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Lesson   Content                                                              Activities                    Homework
applied to collisions (BOOK p48).

    Know that the change in momentum of one body in a
collision is equal and opposite to that of the other
body.
 Know the meaning of the term impulse (= change in
momentum = force x time).
 Explain, in terms of FΔt = change in momentum, how
and why the contact time is maximized in ball/racquet
sports.
 Explain, in terms of FΔt = change in momentum, how
and why the impact force is minimized in vehicle
collisions.
 Calculate the change in momentum from a force
versus time graph.
 Sketch how the force versus time graph changes
when, say, the impact time is increased.
Lesson 11: Analyse data from one of the collisions (the              Activity 180S   “Crunch   –   Qs 150S “Impulse and momentum
disintegration is possibly the most instructive) to illustrate the   gently!”                      in collisions”
principle that the change in momentum is the same for each                                         Qs 160S “Collisions of spheres”
body. Use this result to discuss the simple rule that m 1Δv1 =
m2Δv2, illustrating qualitatively with the examples on p50.
Introduce the term impulse, defining it simply as the change in
momentum as discussed above. Show how F = ma gives rise
to FΔt = change in momentum, and discuss the usefulness of
this equation in sport, where maximizing the force and/or
change for the ball/puck. Show how the change in momentum
can be computed from a force versus time graph, as the area
under the graph.
Discuss situations where we desire to minimize the force by
increasing the time over which it acts, such as parachutists
landing, crumple zones on cars. Stress that the area under the
force-time graph will be the same, as the momentum change
is the same, but the force is reduced if the contact time is
increased: show this graphically. Activity 180S explores this

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Lesson        Content                                                              Activities                 Homework
further in detail.
 Explain the operation of a rocket in terms of action-
reaction (Newton 3).
 Apply the relationship F = change in momentum/time
to calculate the thrust of a rocket.
 Apply the relationship F = change in momentum/time,
and the principle of conservation of momentum to
determine the motion of a rocket-powered vehicle
(moving either horizontally or vertically).
Lesson 12: Blow up a balloon and let it fly across the class,        Activity 170D “Testing a   Qs 180S “Jets and rockets”
getting students to brainstorm how it works in terms of              rocket engine”             Qs 190C “Getting a satellite up to
conservation of momentum. Recapping the analysis of the              Launch model rocket        speed”
disintegration on the air track (or discussion of cannon                                        BOOK Qs p54
recoiling on firing cannon ball) may be helpful. Discuss the
action-reaction pair of forces involved: balloon exerts force on
gas, and gas exerts force on balloon. You could also
demonstrate a rocket kit outside on the playing field, possibly
with video recording of the take-off against a scale, so that the
initial acceleration can be determined.
Go through the analysis of momentum conservation for a
rocket ejecting hot gases (see BOOK p53), although note that
this analysis only applies for horizontal motion. Go through a
calculation to determine the initial acceleration of a rocket
launched vertically, possibly using data from the rocket. Note
that the kit rocket motors are classified according to total
impulse (= thrust x burn time).
4.4 Mapping   (a) work done, changes of GPE and KE, gravitational field and
gravity       potential of a point mass, motion in a uniform gravitational field
(b) KE and GPE, gravitational field, gravitational potential,
graphs showing variation of gravitational potential with
distance, gravitational potential as the area under the field
versus distance graph, graphs showing force as the tangent to
a graph of GPE versus distance, equipotential surfaces
(c) GPE change = mgh, work done = FΔs, GPE = -GMm/r,
Vgrav = Egrav/m = -GM/r

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Lesson   Content                                                               Activities                     Homework
 Recall and use the equation ΔGPE = mgΔh for objects
moving in uniform gravitational fields.
 Know that gravitational potential is defined as GPE
per unit mass.
 Sketch field lines and corresponding equipotential
lines for a uniform gravitational field.
 Determine gravitational field strength in a uniform field
from a plot of potential versus displacement (slope of
graph).
 Determine force from a plot of GPE versus
displacement (slope of graph)
 Determine gravitational potential difference from a plot
of field strength versus displacement (area under
graph).
Lesson 13: To begin with, we consider only uniform fields: in         Activity 210D “Gravitational   Qs 200W “Pole vaulting”
later lessons the treatment is extended to radial fields. While       slides” (analyse data from)    Qs 210S “Gravitational potential
doing this lesson, you can stress that the treatment applies for                                     energy and gravitational potential”
situations close to the Earth’s surface where the gravitational
field strength does not change significantly with height.
Recap GCSE/AS work on the equation ΔGPE = mgΔh (weight
x height = gravitational force x vertical distance). Define
gravitational potential as GPE per unit mass, and discuss the
field and corresponding potential energy pictures as per
BOOK p56. Discuss the graphical relationship between field
and potential (field strength = -potential gradient), and similarly
potential difference = area under field versus displacement
graph. These relationships are best understood if specific
numerical examples are considered (see Qs 210S). At this
stage it is acceptable to set the potential at the Earth’s surface
-1
to be 0 J kg . If time permits, you could analyse data collected
in Activity 210D, or set this for homework.
 Analyse spacecraft data to show that gravitational
potential varies with 1/r.
 Use the equation Vgrav = -GM/r to calculate potentials

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Lesson   Content                                                             Activities                     Homework
 Appreciate that a 1/r potential is consistent with an
inverse square gravitational field.
 Determine gravitational field strength in a uniform field
from a plot of potential versus displacement (slope of
tangent).
 Determine force from a plot of GPE versus
displacement (slope of tangent)
 Determine gravitational potential difference from a plot
of field strength versus displacement (area under
graph).
 Compute energy changes for a body moving in a
radial gravitational field, using Vgrav = -GM/r and the
fact that KE + GPE = a constant.
 Sketch and interpret graphs for the combined potential
of a two-body system such as Earth-Moon.
Lesson 14-15: Generalise the relationships field strength = -       Activity 240S Analysing data   Qs 220D “Gravitational PD, field
potential gradient and potential difference = area under field-     from the Apollo 11 mission     strength and potential”
displacement graph to radial fields (p57). Introduce the            to the Moon”
problem of calculating energy changes etc. in a radial field,
one that is not uniform. Explore the variation in gravitational
potential and field using Activity 240S, which uses Apollo 11
data. Alternatively and more succinctly, show (BOOK p57)
2
how the relationship Vgrav = C – ½ v arises, and then get
students to verify that the Apollo 11 data on p58 gives a 1/r
variation of potential with distance. To further illustrate how a
1/r potential gives rise to an inverse square field, go through
the treatment at the top of p58. Although this will only appeal
to the most mathematically inclined, you should at least go
through it to show how the equation Vgrav = -GM/r is consistent
2
with g = GM/r .
Discuss, in at least qualitative terms, the energy changes
experienced by Apollo 11 returning to Earth, in terms of falling
down a potential well whose slope gives the field strength and
hence the acceleration. (A large filter funnel with a marble, or
better still a rubber sheet helps to illustrate this point.) You
should also consider what a graph of the combined Earth plus

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Lesson   Content                                                            Activities                       Homework
Moon potential would look like (see p59).
Activity 230S can be used to further explore the field-potential
relationship.

 Use modelling software to trace equipotentials in a
radial field, probe variation in gravitational potential
from motion data, explore the link between field
Lesson 16: Software activities 250S, 260S and 280S.                Activity 250S “Variations in
field and potential”
Activity   260S      “Probing
gravitational potential”
Activity 280S “Relating field
and potential”

   Know that, with no forces other than gravity acting, the
total mechanical energy for a body in a gravitational
field equals its KE plus its GPE.
 Explain correctly the term escape velocity.
 Calculate the escape velocity for a planet given its
 Calculate the speed of arrival of a meteorite at the
Earth, from a knowledge of its initial speed, distance
from Earth, and the mass and radius of the Earth.
 Explain the slingshot effect for speeding up
spacecraft.
Lesson 17: Discuss how to calculate the escape velocity from       Activity     230S   “Inferring   Qs 250S “Summary questions for
the Earth from a consideration of the (constant) total             fields”                          Chapter 11”
mechanical energy (TME = GPE + KE). Note that a spacecraft                                          BOOK Qs p60
could “escape” at any speed, but the “escape velocity”
corresponds to the speed that needs to be reached if the craft
is going to coast to infinity, slowing to a halt as it does so.
Consider also the situation where meteorites etc. arrive at the
Earth: equivalent to the escape situation run in reverse. You
can extend this treatment to situations where the initial speed

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Lesson   Content                                                           Activities                  Homework
and distance of the meteorite from the Earth are known, not
just assuming it starts from infinity with zero speed. Activity
230S can also be used to show the changes in GPE and KE,
the total energy remaining constant.
Discuss the slingshot technique for speeding up spacecraft
 Understand the interplay of KE, GPE and other factors
in determining how best to launch a satellite into a
particular orbit.
Lesson 18: Optional, do if time permits. Students do Activity     Activity 290S “Setting up   Qs 230D “Changing orbits”
290S on putting satellites in orbit, and Qs 230D.                 energetic orbits”           Qs 240D Why is a black hole
Qs 230D “Changing orbits”   black?”
Rosetta mission”
Huygens mission to Saturn”
Do test on Chapter 11                                                                         BOOK Qs p62

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