Astro answers

7/27/2019 Astro answers

1/28

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.

IB Questionbank Physics 1


2/28

(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]



3/28

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



4/28

(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



5/28

(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



6/28

(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.



7/28

(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]



8/28

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



9/28

(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



10/28

(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



11/28

(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



12/28

(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;



13/28

(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;



14/28

(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)



15/28

(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;



16/28

(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)



17/28

(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



18/28

(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



19/28

(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



20/28

(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]



21/28

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]



22/28

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



23/28

[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.



24/28

(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



25/28

(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.



26/28

(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



27/28

(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]



28/28

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]

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