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1. (a)
Award[2]for all correct and[1]for two correct. 2
(b)
Award[2]for all correct and[1]for two correct. 2[4]
2. (a)
(i) circle labelled R as shown above; 1
Accept answers that include the star B within the circle.
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(ii) circle labelled W as shown above; 1
(iii) any line (not necessarily straight) going from top left to
bottom right, through or near all or most of stars; 1
(b) star B has lower temperature;
star B has (slightly) larger luminosity / stars have approximately
same luminosity;
surface area calculated fromL = AT4, so star B has larger
surface area/diameter / to give the same/similar luminosity
at lower temperature, star B must have bigger diameter/
surface area; 3
(c) (from HR diagram)LA
= 105L
S;
b =2
4 dL
used;
to give9
35
A
S
S
A
S
A
109.4
104.110
==b
b
L
L
d
d
;
hence dA
= 1.7 108
AU;
= 800 pc 4
Do not award a mark for the conversion from AU to pc.
(d) the parallax angle is too small to be measured accurately / the
distance is greater than the limit for stellar parallax , which is 100 pc; 4Accept any value from 100-800 pc for limit.
Do not accept its too far away.[11]
3. (a) the universe is expanding / many galaxies are moving away from us; 1
(b) the CMBR fills all of space / is uniform / is distributed equally,
consistent with an explosion (at start of universe);the temperature of the radiation (2.7 K) is consistent with cooling
due to expansion/redshift; 2
(c) max
=7
33
100.7
109.2109.2
=
TT
T=4100 K; 2[5]
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4. (a)
5.3
S
K
S
K
=
m
m
L
L
;
mK
=Ss
5.3
1
45.3
1
5.3
S
S
K 9.16]100.2[ mmmL
L==
;
hence mK
17 mS
2
(b) Khad will become a red supergiant/superred/superred giant;
a supernova will take place;
the core/remnant will form a neutron star or black hole; 3[5]
5. (a) (i) recessional speed of a galaxy is directly proportional to
distance from Earth / v = H0dwith symbols defined; 1
(ii) local velocity of Andromeda relative to Earth greater than
(recessional) speed due to expansion of universe / OWTTE; 1
(b) (i) relative speed between two points in universe separated
by distance dis v = T
d
where Tis the age of the universe;
v = Td
=H0dtherefore T= 0
1
H; 2
(ii) T= 1000
1046.926.310
80
1 156
= 4 1017
(s); 1
Do not deduct unit mark if seconds not given, as question asks
for answer in seconds.[5]
6. (a) (i) a collection of stars that form a recognizable group (as
viewed from Earth);
that need not be/are not close to each other/gravitationally bound; 2
(ii) stars that are gravitationally bound/forming an open
arrangement/close to each other (in space); 1
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(b) (i) 5.1 + [0.6] = 5lg
10
d
;
(d=138 pc)
1 pc = 3.1 1016
m;
138 3.1 1016
= 4.3 1018
;
4 1018 m 3
(ii) L =26
2187
108.3
]103.4[4106.1
;
9.8 104L
Sunor8.4 10
4L
Sun(if 4.0 used); 2
(iii) T=
4
2
4Sun
790
1108.9
T
3600 Kor3500 K; 2
(c)
(i) position labelled B within shaded area; 1
Award[1]if label B is missing but point is clear.
(ii) generally the correct shape; (allow broad line) 1
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(d) over time spectral lines regularly split into two lines and then
recombine;
as one star approaches observer the other recedes;
leading to Doppler shifts in opposite directions; 3[15]
7. (a) (i) a collection of stars that form a recognizable group (as
viewed from Earth);
that need not be/are not close to each other/gravitationally bound; 2
(ii) stars that are gravitationally bound/forming an open
arrangement/close to each other (in space); 1
(b) (i) 5.1 + [0.6] = 5lg
10
d
;
(d=138 pc)
1 pc = 3.1 1016
m;
138 3.1 1016
= 4.3 1018
;
4 1018
m 3
(ii) L =26
2187
108.3
]103.4[4106.1
;
9.8 10
4
LSunor8.4 10
4
LSun(if 4.0 used); 2
(iii) T=
4
2
4Sun
790
1108.9
T
3600 Kor3500 K; 2
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(c)
(i) position labelled B within shaded area; 1
Award[1]if label B is missing but point is clear.
(ii) generally the correct shape; (allow broad line) 1
(d) over time spectral lines regularly split into two lines and then
recombine;
as one star approaches observer the other recedes;
leading to Doppler shifts in opposite directions; 3[15]
8. (a) if less than critical density, universe expands without limit;
if equal to critical density universe stops expanding after aninfinite amount of time;
if greater than critical density, universe expands first then contracts; 3
Award[1 max]if terms open, flat and closed are used and not defined.
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(b) there is matter that cannot be detected;
which is likely to consist of dark matter/neutrinos;
or
difficulty of measuring volume accurately;
because of difficulty of measuring distances accurately;
or
matter is not evenly distributed;
so density may vary from place to place; 2[5]
9. (a) (i) sets upper limit on mass of white dwarf; 1
(ii) sets upper limit on mass of neutron star; 1
(b) (if in the supernova phase) the mass blown leaves behind a mass
of 1.4MSun
/ less than the Chandrasekhar limit;
the star will evolve to a white dwarf;
mass greater than about 1.4MSun
, but less than the OV limit, will evolve
(because of the OV limit) into a neutron star; 3[5]
10. (a) red shift used to measure recessional speed of galaxies;
named measurement to yield distance to galaxies (e.g. Cepheid
variable, Supernova);
repeat for many galaxies/clusters of galaxies;
Hubble constant is gradient of speeddistance graph; (any symbols
used must be defined) 3 max
To award[3]reference must be made to galaxies in at least
one of the marking points.
(b) v = 60 6
8
1026.3
100.6
;
= 1.1 104
km s1
; 2[5]
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11. (a) (i)
angular position of star measured;
relative to the background of fixed stars;
in two positions six months apart;
p is 2
1
of the angle of separation/ p indicated on diagram; 4
(ii) d=
== pc3866.2
419.0
11
p2.39 pc;
= 2.3866 3.26 ly = 7.78 ly; 2
(iii) beyond this distance the parallax angle is too small to be
measured (accurately)/ OWTTE; 1
(b) L =4d2b;
ss
ww
s
w
bd
bd
L
L2
2
=;
ds= 1 AU, d
w= 7.78 6.3 10
4= 4.9 10
5AU;
s
w
L
L
= [4.9 105]2
3.7 1015
= 8.9 104
; 4
Allow ECF from (a)(ii).
(c) A =
= 48
23
42800107.5
105.3
T
L
= 1.0 10
17m
2;
r=
=
4
100.1
4
17A
= 8.9 107
m; 2
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(d) temperature too low to be white dwarf;
luminosity too low to be red giant;
radius too small to be a red giant; 2 max
Answer must be consistent with answer in (c) for third marking point.[15]
12. (a) density at which universe will expand forever but rate of expansion
will approach zero / the density at which the universe will begin
to contract after infinite amount of time / the density for which
the curvature of the universe is zero / OWTTE; 1
Reference to flat model without definition does not gain mark.
(b) value of density determines whether or not universe will expand
forever, or at some point, begin to contract;
at density less than critical density, universe will expand forever;
at density greater than critical density, universe will stop expandingand contract; 3
If second and third marks gained, first mark is also gained by implication.
(c) dark matter does not radiate/cannot be directly measured/seen; 1[5]
13. (a) gas cloud collapses under its own gravity;
gravitational potential energy changes to kinetic energy of particles;eventually temperature/pressure at centre is so great that fusion occurs; 3
(b) (initial) mass; 1
(c) (i) carbon / oxygen / neon; 1
(ii) iron; 1[6]
14. (a) c
v
;
=
= 15 skm614751000.3
122
122147v
61500 km s1
;
d=
== Mpc67.819
75
61475
0H
v
820Mpc; 3
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(b) difficulty in determining galactic distances; 1[4]
15. (a) (i) luminosity is a function of surface and temperature (of star);
(same class) same temperature (therefore greater surface area); 2
(ii) LC
=80LS; (accept answer in the range of 60 to 100) 1
(iii)
2
S
C
S
C
=
r
r
L
L
=80;
rC
2= 80r
S
2 r
C= 8.9r
S; 2
(b) (i) 0.6; (accept answer in the range of 0.4 to 0.8) 1
(ii)
=
10log5ofuse
dMm
0.0 0.6 =5log10
d
;
10
d
=100.12
;
d=7.6 pc; 3
(iii) Vega appears dimmer;
hence distance over-estimated; 2
accept:
Vega will look redder (because blue light scatters more in dust);
so Vega looks cooler/lower apparent temperature (thus
wrong position on HR diagram);
(c) the inward gravitational pressure is balanced by the outwardradiative pressure; 1
[12]
16. (a) (Big Bang theory predicts that CMB will) correspond to the black-body
at 3K;
the graph is of a black-body curve;
T=3
3
10
109.2
3 K; 3
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(b) measurement of mass in a given volume is (very) uncertain/difficult;
there exists dark matter that is difficult to observe;
measurement of distances is uncertain/difficult;
matter not uniformly distributed; 2 max[5]
17. (a) stars:3)17(19.4
75
= 3.6 103
(ly3
):
galaxies:36 )100.4(19.4
26
= 9.7 10
20(ly
3); 2
Award[1 max]if the response does not use the volume of the
sphere but uses the cube instead.
(b)19
3
1010
= (3.8 )1016
orstar population density greater than
galaxies population density by an order of magnitude 16; 1[3]
18. (a) (i) luminosity is a function of surface and temperature (of star);
(same class) same temperature (therefore greater surface area); 2
(ii) LC =80LS; (accept answer in the range of 60 to 100) 1
(iii)
2
S
C
S
C
=
r
r
L
L
=80;
rC
2= 80r
S
2 r
C= 8.9r
S; 2
(b) (i) 0.6; (accept answer in the range of 0.4 to 0.8) 1
(ii)
=
10log5ofuse
dMm
0.0 0.6 =5log10
d
;
10
d
=100.12
;
d=7.6 pc; 3
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(iii) Vega appears dimmer;
hence distance over-estimated; 2
accept:
Vega will look redder (because blue light scatters more in dust);
so Vega looks cooler/lower apparent temperature (thus
wrong position on HR diagram);
[11]
19. (a) (Big Bang theory predicts that CMB will) correspond to the black-body
at 3K;
the graph is of a black-body curve;
T=3
3
10
109.2
3 K; 3
(b) measurement of mass in a given volume is (very) uncertain/difficult;
there exists dark matter that is difficult to observe;
measurement of distances is uncertain/difficult;
matter not uniformly distributed; 2 max
(c) in the early universe the (average) kinetic energy was very high
breaking apart any nuclei/atoms/too high for atoms to form / as
universe expands it cools down allowing nuclei in atoms to form; 1[6]
20. (a) (using massluminosity relation for main sequence)5.3
1
25
1
=
L
= 7.8 104
8 104:
therefore, star obeys mass-luminosity relation and therefore
main sequence; 2
or
8 104
= 25n;
log[8.4 104] =n log25
n =3.5
therefore star obeys mass-luminosity relation and therefore
main sequence;
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(b) MS supergiant;
supernova explosion leaving behind core;
core becomes black hole or neutron star depending on
Oppenheimer-Volkoff limit / black hole because the
Oppenheimer-Volkoff limit is exceeded / neutron
star because below the Oppenheimer-Volkoff limit; 3
[5]
21. (a) v =
c = 8.396
04.5
3 108;
v =3.81 106
m s1
/ 1.27 102
c; 2
(b) (i) Cepheids / Supernovae; 1
(ii) recognition of age = inverse of slope;
=16
24
sm109.15
m100.6
(= 3.8 1017
s) 1017
s 2[5]
22. (a) constellation:
a collection/group of stars that form a recognizable pattern (as
viewed from Earth) / a group/pattern of stars not close
together (in space);
stellar cluster:
a group of stars (including gas and dust) held together by gravity/
forming a globular/open arrangement / a group of stars close to
each other (in space); 2
(b) (i) the apparent magnitude of PA
is (much) smaller than that of PB;
in the apparent magnitude scale the smaller the magnitude
the brighter the star; 2
Accept argument in terms of PB
being fainter than PA
.
or
apparent brightness of PA
is greater than PB;
apparent brightness is intensity at surface of Earth;
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(ii) the absolute magnitude of PA
is smaller than that of PB;
the absolute magnitude is the apparent magnitude at a
distance of 10 pc (from Earth);
so at the same distances from Earth PA
is much brighter
than PB
so must be more luminous; 3
Accept argument in terms of PB being fainter than PA.
or
absolute magnitude of PA
is less than absolute magnitude of PB;
absolute magnitude is a measure of luminosity;
lower values of absolute magnitude refer to brighter/more
luminous star;
or
Accept answer based on answer to (c).
distances are the same from (c);
sinceL = 4d2
b PA is brighter than PB;
(c) m Mfor PA
= 2.28 and m Mfor PB
= 2.30;
since m M= 5lg10
d
then dfor each is very nearly same; 2
Accept answer based on calculation of individual ds (~3.5 pc).
(d) same distance from Earth and in the same region of space; 1
(e) recognize that the ratio of the luminosities is the same as the ratio
of apparent brightness;
=
=
12
8
B
A
1046.1
1006.2
L
L
1.41 104; 2
(f)
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(i) PA
10 000 K at 10; (labelled A) 1
(ii) PB
10 000 K at 103
; (labelled B) 1
(g) white dwarf; 1Allow ECF from diagram.
[15]
23. (a) space and time originated from a single point in a large explosion /
an expanding universe that originated from a single point / OWTTE; 1
(b) (i) temperature of the universe immediately after the Big Bang
was very high;as it expanded it cooled down;
the wavelength of the CMB corresponds to a temperature
consistent with this cooling down / OWTTE;
red shift is due to expansion of universe; 3 max
(ii) indicates that the universe is expanding; 1[5]
24. (a) constellation:a collection/group of stars that form a recognizable pattern (as viewed
from Earth) / a group/pattern of stars not close together (in space);
stellar cluster:
a group of stars (including gas and dust) held together by gravity/
forming a globular/open arrangement / a group of stars close to
each other (in space); 2
(b) (i) the apparent magnitude of PA
is (much) smaller than that of PB;
in the apparent magnitude scale the smaller the magnitude the
brighter the star; 2Accept argument in terms of P
Bbeing fainter than P
A.
or
apparent brightness of PA
is greater than PB;
apparent brightness is intensity at surface of Earth;
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(ii) the absolute magnitude of PA
is smaller than that of PB;
the absolute magnitude is the apparent magnitude at a
distance of 10 pc (from Earth);
so at the same distances from Earth PA
is much brighter
than PB
so must be more luminous; 3
Accept argument in terms of PB being fainter than PA.
or
absolute magnitude of PA
is less than absolute magnitude of PB;
absolute magnitude is a measure of luminosity;
lower values of absolute magnitude refer to brighter/more
luminous star;
or
Accept answer based on answer to (c).
distances are the same from (c);
sinceL =4d2
b PA is brighter than PB;
(c) m Mfor PA
= 2.28 and m Mfor PB
= 2.30;
since m M= 5lg10
d
then dfor each is very nearly same; 2
Accept answer based on calculation of individual ds (~3.5 pc).
(d) same distance from Earth and in the same region of space; 1
(e) recognize that the ratio of the luminosities is the same as the ratio
of apparent brightness;
=
=
12
8
B
A
1046.1
1006.2
L
L
1.41 104; 2
(f)
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(i) PA
10 000 K at 10; (labelled A) 1
(ii) PB
10 000 K at 103
; (labelled B) 1
(g) white dwarf; 1Allow ECF from diagram.
(h) to the red giant region (approximately either side ofL = 102
and T= 2500 K);
(judge by eye)
to the white dwarf region (approximately either side ofL =102
and T= 10 000 K);
(judge by eye) 2
(i)
5.3
R
11
150
=
M
or150 =MR
3.5;
evidence of algebraic manipulation e.g. MR=
5.3
1
]150[ ;
=4.2MS
To award[2]there must be evidence of algebraic manipulation shown.
(j) (i) neutron star; 1
(ii) (because of) neutron degeneracy pressure / Pauli exclusionprinciple excludes further collapse; 2
[21]
25. (a) space and time originated from a single point in a large explosion /
an expanding universe that originated from a single point / OWTTE; 1
(b) (i) temperature of the universe immediately after the Big Bang
was very high;as it expanded it cooled down;
the wavelength of the CMB corresponds to a temperature
consistent with this cooling down / OWTTE;
red shift is due to expansion of universe; 3 max
(ii) indicates that the universe is expanding; 1
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(c) the amount of red-shift enables the recession speed of a galaxy to be
determined;
Hubbles law states that the recession speed is proportional to
its distance from Earth/v =H0dwith terms defined;
if the constant of proportionality/H0is known then dcan be determined; 3
(d) it is difficult to determine an accurate value of the Hubble
constant / difficult to measure the red-shift / Hubble constant
had different values in the past; 1[9]
26. (a) apparent magnitude is a measure of how bright a star appears from Earth;
absolute magnitude is a measure of how bright a star would appear from a
distance of 10 pc; 2
(b) (i) Achernar; 1
(ii) stars differ by M= 16;
for M= 1 we have a ratio of luminosities by a factor of5 100 2.51
or2.5;
so
165
E
A)100(=
L
L
2.5 106or2.3 10
6; 3
Award[2 max]for use of apparent magnitude difference and
an answer for the ratio of 6.3 105.
(iii) d=
51010
Mm
;
10 5
5.3
10 ;
50 pc 2
(c) A
M
L
L
=1;
1 =42
A
42M
)5(4
4
TR
TR
;
A
M
R
R
= 25; 3
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(d) it has to be hot star/a B star;
with low luminosity/high absolute magnitude;
hence EG129; 3[14]
27. (a) T=3
3
1007.1
109.2
;
T= 2.7K; 2
Accept wavelengths in the range 1.05 to 1.10 for a temperature
range 2.64 to 2.76 K.
Award[0]for bald answer.
(b) according to the Big Bang model the temperature of the universe
(and the radiation it contained) in the distant past was very high;
the temperature falls as the universe expands and so does thetemperature of the radiation in the universe; 2
(c) (Hubbles law shows that) the universe is expanding;
therefore in the distant past the universe must have been a very
small/hot/dense point-like object;
or
Doppler shift of spectral lines;
indicates galaxies moving away so in the past they were close to each other; 2[6]
28. (a) the largest mass a neutron star can have (2-3 solar masses) / core
mass which if exceeded leads to a black hole; 1
(b) (i) the star will evolve to become a red super giant;
nuclear reactions involving elements heavier than hydrogen
take place / nuclear reactions produce heavier elements up to iron;
will then explode in a supernova;
the final mass of the core/remnant of the star will be less thanthe Oppenheimer-Volkoff limit/less than a few solar masses/less
than 3 solar masses; 2 max
To award[2]the last marking point is essential.
(ii) neutron (degeneracy) pressure; 1
(c) (i) l= kM2.5
;
so
=
5.2
5.2
sun
Eta
sun
EtaC
M
M
l
l
= (1002.5) = 105; 2
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(ii) Eta Carinae is producing energy disproportionately more
(relative to the available mass) and hence will spend less
time (105
less) on the main sequence / OWTTE; 1
Award[0]for bald answer.[7]
29. (a) distant galaxies move away from Earth;
with a speed proportional to their distance (from Earth); 2
(b) because the motion of nearby galaxies is much more affected by
their mutual gravitational interactions rather than the expansion
of the universe; 1[3]
30. (a) the sign of the output voltage is the same as that of the input voltage; 1
(b) (i) G =
=+
10
901
10; 1
(ii) Vout
(=GVin
=10 2.0) = 20 mV 1
(c) op-amp has a high input resistance and so takes little current;
(open loop) gain is very large so potential difference between
non-inv input and inv input is (effectively) zero;
i.e. Vout
= Vin
;
So G = 1 3
(d) (i) 3.0V; 1
(ii) the resistance between A and B is smaller than 2 M / the
voltmeter draws current; 1
(iii) the voltmeter reads the output voltage of the amplifier and
the input voltage is the potential difference to be measured;
the two are equal since the gain is 1; 2[10]
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31. (a) red supergiant:[3 max]
appears red in colour;
(has a very) large luminosity;
(relatively) low (surface) temperature;
(very) large mass;
(very) large surface area;
constellation:[1 max]a group of stars that form a recognizable pattern (as viewed
from Earth) / OWTTE; 4 max
(b) (i) apparent magnitude is a measure of how bright a star
appears from Earth/observer;
absolute magnitude is the apparent magnitude of a star at
a distance of 10 pc from Earth / how bright a star would
appear if it were at a distance of 10 pc from Earth; 2
(ii) 5lg
10
d
= (1.1 + 5.3 =) 6.4;
d=190 pc;
=11
15
105.1
1046.926.3190
(= 3.9 107
AU) 3
(iii) stellar/spectroscopic parallax; 1
(c) (i) the power per square meter received at the surface of
Earth/observer; 1
(ii) use of L =4bd2;
Sun2
Sun
Antares2
Antares
Sun
Antares
db
db
L
L=
LAntares
(LSun
)=4.3 1011
3.92
1014
;
(= 6.5 104) 3
[14]
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32. (a) red supergiant:[3 max]
appears red in colour;
(has a very) large luminosity;
(relatively) low (surface) temperature;
(very) large mass;
(very) large surface area;
constellation:[1 max]a group of stars that form a recognizable pattern (as viewed
from Earth) / OWTTE; 4 max
(b) (i) apparent magnitude is a measure of how bright a star
appears from Earth/observer;
absolute magnitude is the apparent magnitude of a star at
a distance of 10 pc from Earth / how bright a star would
appear if it were at a distance of 10 pc from Earth; 2
(ii) 5lg
10
d
= (1.1 + 5.3 =) 6.4;
d=190 pc;
=11
15
105.1
1046.926.3190
(= 3.9 107
AU) 3
(iii) stellar/spectroscopic parallax; 1
(c) (i) the power per square meter received at the surface of
Earth/observer; 1
(ii) use of L =4bd2;
Sun2
Sun
Antares2
Antares
Sun
Antares
db
db
L
L=
LAntares
(LSun
)=4.3 1011
3.92
1014
;
(= 6.5 104) 3
(d) (lower limit) lg[6.5 104] =4 lg M; (M= 16)
(upper limit) lg[6.5 104] =3 lg M; (M=40) 2
(e) the mass limit for a star to become a white dwarf =1.4MS;
in its evolution Alnitak will become a supernova;
(even in this phase) its initial mass is so large that it could not
blow away/lose enough mass to reach 1.4MS
/ to become a
white dwarf / OWTTE; 3
(f) neutron star / black hole; 1
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[20]
33. (a) Newtons model states that the universe is infinite (static) and
uniform; this means that stars are uniformly spaced;
and that if it is infinite there must be a star at every point inspace / a star along every line of sight;
since there are regions without stars, Newtons model must
be inadequate; 3 max
(b) both space and time originated with the Big Bang;
the universe is expanding (and not infinite);
due to the expansion, light from the Big Bang is red-shifted
to the microwave region so regions between stars will not
appear bright;
light from very distant stars will not have reached us yet;
the universe has not existed for all time; 3 max[6]
34. (a) very difficult to measure dprecisely / experimental uncertainties in v
d
;
when the recession speed is large / when the galaxies are at great distances; 2
(b) useH0=60 km s
1Mpc
1;
use T= 0
1
Hto give T=5 10
17s ; (ECF if incorrect value of H
0is chosen) 2
[4]
35. (a) (i) gives the relative (visual) brightness of stars as seen from Earth;
e.g. a magnitude 1 star is 100 times brighter than a magnitude 6 star; 2
To award[2]the idea of a relative scale must be clear.
(ii) the apparent magnitude a star would have if it were 10 pc from Earth; 1
(b) (i) 510log
Mmd =
;
=1.03;
d=10 101.03
;
=108 pc 3
Accept answer based on substitution for d= 108.
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(ii) L =4d2b;
Sun
2
Sun
B
2
B
Sun
B
bd
bd
L
L=
;
LB
= [108 2.05]2
1010
7.00 1012
LSun
;
=3.43 103
LSun 3Accept answer based on substitution L
B=3.43 L
Sun.
(c) in the region [30 50, 2.5 5.0]; 1
(d)
Cepheid as shown; 1Judge by eye for reasonable range of magnitude and temperature.
(e) the outer layers undergo a periodic expansion and contraction/
periodic fluctuations in temperature; 1
(f) period/frequency with which luminosity varies;
apparent brightness / apparent magnitude; 2[14]
36. (a) Newtons model assumed a uniform infinite (and static) universe;
therefore number of stars in shell is proportional toR2;
intensity of radiation/light from shell reaching Earth is proportional to2
1
R ;
since according to Newtons model such shells stretch to infinity /
the sky can never be dark/will always be light / OWTTE; 4
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(b) the universe is expanding;
the universe has a beginning;
the stars (and galaxies) are not uniformly distributed; 2 max[6]
37. (a) (i) gives the relative (visual) brightness of stars as seen from Earth;
e.g. a magnitude 1 star is 100 times brighter than a magnitude 6 star; 2
To award[2]the idea of a relative scale must be clear.
(ii) the apparent magnitude a star would have if it were 10 pc from Earth; 1
(b) (i) 510log
Mmd =
;
=1.03;d=10 10
1.03;
=108 pc 3
Accept answer based on substitution for d= 108.
(ii) L =4d2b;
Sun
2
Sun
B
2
B
Sun
B
bd
bd
L
L=
;
LB
= [108 2.05]2
1010
7.00 1012
LSun
;
=3.43 103LSun
3
Accept answer based on substitution LB
=3.43 LSun
.
(c) 3.4 103
=
5.3
Sun
B
M
M
;
MB
=5.3
1
3 ]104.3[ M
Sum; (allow other evidence of algebraic manipulation)
MB
10MSun
2
(d) Sun: white dwarf;
Becrux: neutron star black hole; 2
(e) (i) in the region [30 50, 2.5 5.0]; 1
(ii) line from B to region 5 2, 5 10:
Do not penalize for any line after read giant position.
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(f)
Cepheid as shown; 1
Judge by eye for reasonable range of magnitude and temperature.
(g) the outer layers undergo a periodic expansion and contraction/
periodic fluctuations in temperature; 1
(h) period/frequency with which luminosity varies;
apparent brightness / apparent magnitude; 2[19]
38. (a) Newtons model assumed a uniform infinite (and static) universe;
therefore number of stars in shell is proportional toR2;
intensity of radiation/light from shell reaching Earth is proportional to2
1
R ;
since according to Newtons model such shells stretch to infinity /
the sky can never be dark/will always be light / OWTTE; 4
(b) (i) the early universe/the universe immediately after the Big
Bang was very hot/at very high temperature;
radiation in the universe corresponded to the very high temperature;
as the universe expanded it cooled down and the
wavelength of the radiation increased / OWTTE; 3
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(ii) v =
c
;
= 0.083c or2.5 107
m s1
;
d= 0H
v
;
=340 Mpc; 4[11]
39. (a) constellation: pattern of stars;
Candidates must indicate that stars are not close together.
stellar cluster: group of stars bound by gravitation / in same region of space; 2
(b);
0077.01=d
= 130 pc 1
(c) no atmospheric turbulence / irregular refraction; 1
(d) (i) red / red-orange; (not orange)
blue / blue-white / white; 2
(ii) Betelgeuse looks brighter; 1
(iii) L = 4bd2;
Rearrangement of formula on data sheet required.
d= 4.0 1018 m;
L = 4 2.0 107 (4.0 1018)2;
L = 4.0 1031W; 4
(iv) L = 4 bd2
luminosity of Rigel is about half that of Betelgeuse; (or ECF from (iii))
brightness of Rigel is about 0.1 times that of Betelgeuse;
ss)d brightneinosity anabout lumstatements
on fromt conclusiconsisten(must be adistant;moreisRigelso
3
Do not allow mark for fallacious or no argument.
Award[1 max]for a mere statement that luminosity and brightness
are less so Rigel is more distant.[14]
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40. (a) universe is infinite; 1
(b) number of stars in shell increases asR2;
intensity decreases as
;12
R
brightness of shell is constant;
adding all shells to infinity;
sky would be as bright as Sun / uniformly bright; 5
Award[2 max]for argument based on any line of sight lands on a star.[6]
41. (a) low mass stars will finish burning helium (into carbon and oxygen);
and collapse to a white dwarf; 2
(b) high mass stars will finish burning (silicon) to iron;
and collapse into a neutron star / black hole; 2[4]
42. (a) wavelengths are shifted;
universe is expanding / galaxies receding / Doppler Shift; 2
(b) statement of Hubbles law (egv =Hd) with symbols explained;
v obtained from spectral lines / Doppler Shift; 2
(c) the expansion of the universe is very small on local scales;
it would be impossible to distinguish between random velocities and expansion; 2[6]