Download +(J - cloudfront.net

k_c_y
Name:.
Astrophysics
1.
Period:
Date:.
_
Worksheet 2
This question is about Cepheid variables.
The variation with time t, of the apparent brightness b, of a Cepheid variable is shown below.
n-
,-.
:!
i
l.2
•
.:
i
.
1.1
.'
,
.
-
!
!
..
'
-
,
-
i-·
,
l.0
•
0.9
--- ..
-,
..
0.8
, ...
;......
o
,
3
2
,.
!
4
7
6
5
8
9
10
Time/ days
Two points in the cycle of the star have been marked A and B.
(a)
(i)
Assuming that the surface temperature of the star stays constant, deduce whether the star
has a larger radius after two days or after six days.
t.t8.~ 2
qc~.!?kr e.
.~
t.?. 2...dey....." ..L±
~.D ..S;.±®.:t...." ..~.~.(\.
(ii)
.....
~
..H:~~
..c;:,&.-.. ')
.."I
.....t..
.r.Q:.d:\\t.s......~~~.t
0.
.rd~.t~l.sk.~b':!.p.
..J?;~~
~
5' reo-- ~
....:'I.±s:
b
f"\d
'r
Ql
pg!.'.~~.J5'.~(.~~
-th. e- L
~.e.~~$..IJ.t:.~:~
....~ ..~ ...
..Q~J. ,.~~t, :±b.~ d.';:s.Th.0.Lt ~
(i)
~.p . s
Explain the importance of Cepheid variables for estimating distances to galaxies.
~~e.rs.b~0.
(b)
L)
K. l~ ..,..lw:.~~ ,.., :1b~ h..&.c.d
dcr_ ,
1h~
o..~d §.Y.:.~.Y..x..y
o.,~s.~.c')
..
~..1;:.?h.g.!·J
or-d
.
The maximum luminosity of this Cepheid variable is 7.2 x 1029 W. Use data from
the graph to determine the distance of the Cepheid variable.
1...-q
LM;X"~
1b
.
Mo-}c-
{,'Z
x 1.6
·t
7_. .•'2.S.' x
l.0
W
-to
L
10
;w4~J<i
cJ"J,-i~ .....
.•....
-' ..
....
.... "'2'
[:2. ~lO
••..vv
2.
This question is about stellar magnitude and brightness.
(a)
State what is meant by apparent magnitude .
f
...h~.~....
ht.:;..,.h± ...0::0. ..... r.l).kj ..e~
(b)
Define absolute magnitude .
...h~w k..r.-~:.q~:t
....J.:.
(c)
.....qrr.(.~td.
.....r.?\...~~r..;' h.
~Q..~..Il,.
0.~.....9.k)es:+ w.o.Y..\.J.....o.f'f.e:c&. ....C± o: d~s1--1)1' a
f~ ~!.:±b. ~~
.:. ±h.~ Q.r-f ..•...M(t~ e d -:\0 p("
Explain why a star with an apparent magnitude of6 radiates approximately 2.5 times more light
power than a star with an apparent magnitude of7 .
M.:D )"
..k.y
M..:?..\
~.b.~.o..)e.~.\.! ~Q.~n.~.+..~.~ 9;f
~.~.S:.~
...S:o. .."'i
JQo. j.!.(~Y?f ~ ..f~.~r.~..:h---o"
J.s
b.t..,..':t.~t..~~~
..~
...e·1·~.Q··\.····::±:O····.··z.··~.5.··\····XL~
....
\.,..~.~.~:0..~~·.!.hf·
...I>. ·..·\>-·{\o.··~·~·S:t.J.~.0.-.9.
..L..:::b
.,-.._
(d)
'
__
.-.
....••••. '__
"'I""'--~_'
__
•.•• ~
.••..•. J
"""r'
- __
-
.~._._.~,...._
~
;;= (,
.l I-S
.
b.r.\ i"'1- t\..O s.;
•...•
The star Capella has an apparent magnitude of+0.05 and its distance from Earth is 14 pc. Estimate
its absolute magnitude.. ..
J...= l"'-t· ~'c,
G:
f/\. C"
cLOc.;
JV\ .. :=;
- 0 .,
0"
I
..
L~d..p ;;
C/
\
)(
~
C""\
;;.
t.I\
c:
:::.
L,S'
X.
tc}5
(\.~lo ')
-
/l~jQ.S;,")
o.~3
~-X
0.0-:; -
D:7'3
-
-
-
2
O.Co~
~
3.
This question is about stars.
Betelgeuse and Rigel are two super giants in the constellation of Orion.
(a)
Distinguish between a constellation and a stellar cluster.
Constellation:
·Fer:·D....
r£:.....1S±QQ:
,
r.\O.:\;; .... ~g..c;..C~~0.r..~.!7
...
:h~~.+b~ ~:. 9.!':.'*~.::.t..~:t.J:~.r.;-.~.~J{
\o":>>JrJ
..~.\':?~~....
Stellar cluster:
..s.~o..l.\~ ....5-Q.'>.;.t.p. ~
..~ ..~
(b)
of
: !;l.~
~~fL ....(.~~~.::
..~.9.~.\l"
$.:p.0(~
~o.""~
k7 ·~·D:A'-'·--+7
{k.9.y..~
The star Betelgeuse has a parallax of 0.0077 arc second. Deduce that its distance from Earth is
approximately 130 pc.
\
"-(l
(c)
State why the Hipparcos satellite which orbits Earth is able to measure stellar parallaxes for stars
at considerably greater distances than 130 pc.
..~Q
(d)
!?:j.~.?.~~~~:l ..~
:..~:£:.:~.~±~:.~
L.. ..~.~.~
..~:.:-.~~±.~.'?"
The table below gives some information about the types and magnitudes of Betelgeuse and Rigel.
Star
Type
Apparent
magnitude
Betelgeuse
M
-0.04
Rigel
B
0.12
Color
Apparent
brightness
2.0x 10-7 Wm-2
R~C\
G\v.e. ' w\";
+e
3.4 x 10-8 W m-2
(i)
Complete the above table for the colors of the stars.
(ii)
State why Betelgeuse has a lower apparent magnitude than Rigel.
(iii)
Given that the distance of Betelgeuse from Earth is 130 pc, calculate the luminosity of
Betelgeuse.
.
IS
,,'"
;oJ. ~
nO
f'-'J ~{;
I
I
Uy
r-
L = Lh",d 2b
:::;
L{\I
'" G·,
(iv)
q.~'" '" (0
ty
(1-
"2.
Q
7<
'>c'o'\[N
ff
1S
--
/V\
\O\~
\9.~.~~ k.f.'~.,.bt<U-
1""')"(
z .»
")C\;"")
W ~'1.
1
The luminosity of Rigel is 2.3 x 1031 W. Without any further calculation, explain whether
Rigel is closer or further than Betelgeuse from Earth.
L
.,
e~
~e~t
<
\-:;
~
2 t;~
L
.:..f
R, 5~ I , yte+-
bcf
4.
This question is about the star Antares.
The following are some data concerning the star Antares. The parallax angle is measured from an ideal
position where no atmospheric turbulence affects measurements.
(a)
Spectral class
M
Parallax angle
5.0 x 10-3 arcsecond
Apparent brightness
1.6 x 10-8 Wm-2
Wavelength of the maximum
intensity of light emitted Amax
935 nm
State the color of Antares.
.(.~ ~ t;?~ ~.p..)
.....
~.~~
(b)
,
.
I
Deduce that the distance of Antares from Earth is 6.2 x 1018 m.
~~0~ ?~O pc."
....
J..:.E..~:~~~
..~.>:...~. :~$..~.y. ..~..~.\J~.~ _o~ ..
,- ,.-.,,,
~J.
.- .. ~.
···~~~···f·~··········0/2~
..·~···'···'·~·~···~i~
..;;·;'~·i·t;·~············I···~··~······
..···,~
-···t··~;::4 ~
y
..··- ·---..j.
(c)
.
L".
"'.
K
I\J
.
Calculate
(i)
the luminosity of Antares;
.
-L- -::;4Tf'd '?:-h-- ---------------
.........................................................................................................................
'-f'T'j-
!\-~ -;_.
((p. Z lI< (0iB ~)
Co
'2..L
)C'
l 0 - 'S
w""" - "t.
:::::::~::~:_:~-:;~L7:~:~::.;:::;:;:5~::::~:·r~~~~::~-:::::::::::-:::::~:::::.::::::::::::::::
(ior·
- ..,
:;;::t~~<"::~;;n::::S.:.;:~,,~~~:~~:~m~
~ kJ
lOQ
'0'
•• ';".~.-; .-.:.
'"0••
=-;.-.~•••
.................... ..
,'
(d)
,
~;'l; • .-. _, ,0';
,
:";.~".;
O. ,-. ;:•••
;; ••••
; ••••
o •••••
~ ., •••••
; •••
,.
_
, ••••••••••••••••••••••••••••••••••••••••
.
The radius RoftheSun is 7.0 x 108 m.Use your answers in (c) to deduce that the radius of
Antares is about 500 R.
...."-'
----
..-L
.........
: -tt'!qirR."\T~
\.
J
~
~ ~~tr~ S "I .
...................................................................
5
5.
This question is about stellar observations.
(a)
spectrum and temperature of a certain star are used to determine its luminosity to be approximately
5.0 x 1031 W. The '!Pparent brightness of the star is 1.4 x 10-9 W m-2. These data can be used to
detennine the distance ofihe'staifromEarth~------""----..-.--..---- - - ..(i)
State the name of this technique used to determine distances to stars .
f_o.-..c.~.ll.a.x
.....5.f..g..~±..c:?.'F...~.~~~.Q
(ii)
Calculate the distance of the star from Earth in parsec.
b::.
~1ld-
'2.
J :: j~l\b
J:;;
;7
$:.>3 >c
to l~
•
fV\.
h
t ~1
q.4(o
(b)
>ct
\0 -s
I'"
~
\ pc...
'3~~{p
.
SLy '"
I
Distances to some .starscan be measured by using fe method of stellar parallax.
(i)' -- Outline this iiielli6d~' . ~..
Dee;..,
.
I
=.
MeO-Sv.te:
. O'-t"'CJV;.I~f-'·-rci$-Y+·-;~.""·of'
\Po. c\< 5 e-o
""..J
of
f; J,p
I
"'f>
~o-,
I
(ii)
.
..-
-,
s+cw-s
0+
& ~ d \ ~+(J('\
c.e,
fl~
-
-
...
-'.
,-'
·<;-+o..r.5
I'
~cu-o\ \vlC
0')0'/"1$'1-
~', K f"\.O,,;-l..
Cc;..r-c
'" +erva
se0
-
-3
Modern techniques enable stellar parallax angles as small as 5.0 x 10 arc-second to be
measured. Calculate the maximum distance that can be measured using the method of
stellar parallax.
-I
S-.O Xlo-')
o r c ~ec
6
Is _
6.
This question is about stellar magnitudes
(a)
and stellar distances.
Star A has an apparent magnitude of 5.0 and is 100 pc from Earth. The luminosity of star A is 4.0
times the luminosity of star B. The apparent brightness
star A is 100 times greater than the
apparenf15i'ig1'itness ofsfar B.
of
OA ~
S.O
W\ p. :
lOo
fC
Deduce that
(i)
-
cJ p.:'-
LA
::::
b8
L~ •. 4 LI3
J, A
J e,' L,6
La
~~)C~)
&g
z:
(ii)
lop,. ;- lOO
star B is 500 pc from Earth;
j
(\oc»
(~)
the absolute magnitude .ofstar AisO.
(l~O Pc.) '2.
QOr01.-::: ct~:>o\~~
c>-p ~(},r
«U"'
t
l()O
'"'
'tOu
\0 ("l':l\n+~~.s>
ci.s-
b 1'~-5
""+
L !P')
n~
~'rL
"M<:A5 l"\ ~
-+ V cl.r0
\5
-
-+u..,
I'- es.s
'~I!"\es
d~f\~~;(""\
--t-'h~1\
<j~-kr
cJ~solv{~
)
O~
6
P~ o-r-er- --t
(\I\.
~
S ('I \
+
\A-~
<;;;
M - M-5
b'; Or-
7
7.
This question is about magnitude and apparent brightness.
(a)
The table gives information on the peak absolute magnitude and the peak apparent brightness of
two Cepheid stars.
--<.- _. ~......,.
-. .- --.. ~- ._(peJk) absolute
(peak) apparent
star
.-
-
magnitude
brightness
Delta Cephei
-3.47
9.;.OxlO-lOWm-2
Zera Geminorum
-4.13
7.2xlO-lOWm-2
State and explain whether Delta Cephei or Zeta Geminorum
(i)
DC
appears brighter from Earth.
...~~
(ii)
b.~.s. g..~.~t.~ o.p~~
is closer to Earth.
Y:::>
C
-,:>
~ e C q u.s e,
is \0 ;., ~ ",.kr-
c lo:>e..r"
~
k.r..t;j~T..M.~J
e co \.\.~~
e "reu-,
.__±b5!~1;~~!:!.::..~~~:::.0
.._~,:~~oJ.\&C.....o..~~..: ~.0d
_.~.t...·.:~J.~
\:~
':,;:~.~:~
..e.f!£>. b··~~:s:·b1.~
.; :.:
(b)
(1vM
~,....Os:~~~
.
The luminosity' of a Cepheid star is variable. Outline the reason for this variation .
..±kt. ....$.~.r..:fQ.~.~:
...C£...+b.i ...$l:~.f:
..~ ...\~ ~.~Y.-.\.i.~t~.~~
/
..':J~±h:~.~
..\9.:.r:-:~~...:Q:N!.:..s..~.f!JJ.~
..t~
?.~!
..~~
~~~~
..
The graph shows.the. variation. with period of the peak luminosity of Cepheid stars.
10000
e$ W!
s « rfo. cz,
Vo..("'-\
1===t=t=t=rnm==4=+ttm:t1
/
J
/
/
.I
V
Lurii"inosity--··
1000
t==t=~J~:::t:t:ttt==t=:t=t=t:t:t:ffi
,
·v· .
,J
100
10
Period/days"
_.
-_/'"--~--
__.._ 1_'
---.:---
-- ._._-----,-
._.'
.. -.- ..'-".-'-
_
---------.-----
8
,_
•
,~,
I·
The luminosity is given in terms of the solar luminosity of3.9xl026W.
(c)
(i)
Outline how data fromThe graph may be used to determine the distance of a galaxy from
Earth.
..
- -.
.1..~1.~~s.Q
~ "'<~~£~L~'~'~':'.i:=~~i},.S,,~~~.\.~~
....
~~~...!~~\~OcS
~
2., ...'!.~.~
....
~r.9..PS
...~
"3 , ..~ ..~.~~~.~
p..sv- ~oc9
.....
~k:~.;0 ..~ ..J.~~.~.r.:
..t?.~.~"~'I
~.Y:.~.:.>.~!.~.~~
q:.~.g:r.:~~
\.\._ t;;~.~
..c~.!.g.:~
-I~
d.iS.+.Q.C.c.~
~.
.6..:7:
:f\b.fV:...
,.. L41Td'L
(ii)
The peak apparent brightness of Zeta Geminorum is 7.2x lO-1 °Wm -2 and the period of
variation ofluminosity is approximately lO days.
Use data from the graph on previous page to deduce that the distance to Zeta Gerninorum
from Earth is about 1.1x 1019 m.
..
,
8.
This question is about determining the surface area of the star Wolf-359.
(a)
Distinguishbetween apparent brightness and apparentmagnitude,
'.'
c ..
o;,;;,,-C'~-\:;'
"" •.•.• 11\1\"'l."
J'!)"'''~''''''''''''''''''''f'.~.l~M.,
Apparent brightness: ..\oW ..~
,&('feo-r>
+0
~e
?.:...~.;'~~.~
'- .•....~~.~
.
....
\: ..~~...0..~.~
..~..~
~~:.~.~.~~
~.Q.~
)....
~
CA S+O\r'
.
±.~~~\~s.~~.?.~~.y.
~ .. ~.f.~.l.j:-.C.~.~
,
..............................................................
(c)
to..";-", "-
f'!"
ey~ ~~ v<\e~cJ
Outline how the surface temperature Of a star is determined.'-
lr ~.~~~~.~
""
ek~ ...+~.~±...~.~ ~.~.~b~.w.
..\ar,-c,'-'1-
Apparent magnitude: .A:...~.~..
(b)
~""rt\
'>I.a ~...
.
~..~:.~ ....
~5y.: ...\S 1/v\0-.,c',
~.~.~.~.~.~.~±~
±.~.~:P..~P\+
v~
::
~.o.:xc:................
L·'1.O
.
KlO
..,....
N\ \IN'.
-~
.
The following data are available for the star Wolf-359 and the Sun.
Apparent brightness ofWolf-359
=
1.97xlO-12Wm-2
. __. Distancer-o.LW.Qlf-359t):omE;jrtn_~_~=A.93"'1(}5Al!-_--.~
3
Surface temperature ofW~lf-359
= 4.00xl0 K
-Surface te~~e~~t;t~;f
S~
- - c· - -c-,_ .. ,
=
.
---3 ----'
6.00x 10K
.,.9 Qy ::;-2 A
'flu
--
9
..
/" ,..,
r..
.
\_.~.
(i). -- .suggest ~bichIl1ethod is used to measure its distance from Earth.
..d.~
.~
. :tQ..0.s.-.~ ~\.'i Je..~.? ±b~o.
....p(j.c.O'U.O"I!'"
----------(ii)
L~D
_ke.-
_.\O.O_~u
.sO
~.$..~J._.__
------------------
~
\ \ ar-
_.._ .
---------------
explain whether its apparent magnitude is greater or less than the apparent magnitude of
the Sun.
...w.9.tf...j.~ .. k:t..h.~g.YY..g.y.. ....QcQ 9.-± ....\9.~ry- ~f
...~.9. ~..t. W\\.~ k.'? n~.~.~ ~.~.f. b~;.1b± .
....;:\ ~ ..Q.~.f. o..P.f.~±
........... 00!!.:C
(iii)
t:X~
.!:J.~
.
J.s ~.~.~~.
SU.0.~
~o,-...
.
deduce that its luminosity is 1.35x l023W. -
L
-:
=
[L
(d)
.•..
Determine the surface area ofWolf-359.
~ ...-"
L
-
A: -
0-14
"2.-3
\.s5
....,
»c
vo
0'~1
XlO-"~1(4
---.~'"'
,."'- ,--
.-- ~r-,-'-
Q.-3o Xl-a
-,-
.,
("".
lS""
W
')6 em.2j<I
W\""2.-
-10