FINAL  EXAMINATION,  JUNE/JULY  2000

 

PH317

SPACE  PHYSICS  &  ASTROPHYSICS

(ENGINEERING)

 

            TIME: THREE  hours for working

                        TEN  minutes for perusal before examination begins.

 

This examination consists of TWO sections:

Section A consists of 100 questions, each of which has five possible responses.  Only one response is allowed for each question.  If two or more responses seem possible, choose the best or most nearly correct response.  If you cannot answer the question and do not wish to guess,  I will award one-quarter of the question value.  Please indicate this by crossing out the question number.  Note the questions begin with number 51.  Responses 1-50 are unused.  Begin with response 51 on side 2 of the answer sheet.

Section B consists of four questions.  Show all work.

Calculators are permitted.

Some useful formulae for section A, usual notation:

Fundamental constants:

h=6.626196·10-34 J·s

e=1.6021917·10-19 C

me=9.1095580·10-31 kg

c=299792458 m·s-1

k=1.3806220·10-23 J·K-1

mp=1.6726140·10-27 kg

G=6.673·10-11 N·m2·kg-2

NA=6.022094·1026 kmol-1

amu=1.660531·10-27 kg

Astronomical and derived constants:

pc=206265 AU=3.26 lt yr

year@3.1557·107 s

AU=1.496108km

eV=1.6021917·10-19 J

l(1eV)®1239.8 nm

    g=9.7895 ms-2

Msun=1.991030kg

Rsun=6.96105km

Lsun=4·1026 W

MVsun=+4.79

Vsun=-26.78

Assume  AV=3CE

 

PART A

Turn Answer sheet over.     Put name on top.     Begin with 51.

 

51        The spectral class of our sun (Sol) is

            a)  S0 L           b)  K2 Ia          c)  A0 V          d)  F5 V           e)  G2 V

 

52        Near earth circular orbital speed (km/s) is

            a)  0.75,     b)  7500,     c)  0.0075,     d)  75,     e)  7.5 km/s.

 

53        How many magnitudes fainter would the sun appear to an observer located on Eros (Eros is 2.6 AU from the Sun)?

            a)  2.07,           b)  0.06,           c)  2.66,           d)  6.76,           e)  0.83 magnitudes.

 

54        The geocentric parallax (baseline=6378 km) of Eros (arcseconds) at opposition (see problem 53 above) is about [there are 206265" in a radian,  Earth is 1 AU from sun]

            a)  5.48,           b)  3.37,           c)  1.14,           d)  2.71,           e)  8.62.

 

55        The distance, in parsec, to a star with a parallax of 0.002 arcsec is

            a)  143,            b)  200,            c)  750,            d)  500,            e)  50 pc.

 

56        The type C asteroid 107 Camilla has a semimajor axis of 3.49AU and a period (years) of

                        a)  3.5,     b)  6.5,     c)  9.5,     d)  12.5,     e)  15.5 years.

 

57        The space velocity of the sun (km/s) relative to all stars within forty pc is about

            a)  235,            b)  6000,          c)  0.14,           d)  55,              e) 20.

 

58        Mirach shines at magnitude +2.07 and Almach shines at magnitude +2.10 so Almach is fainter than Mirach by a factor of

            a)  2.085,         b)  3,                c)  1.01,           d)  0.03            e)  1.03.

 

59        Mirach shines at magnitude +2.07 and has a parallax of 0.016 arcsec.  The absolute magnitude of Mirach must be about

            a)  -0.9,           b)  +1.8,          c)  -1.8,           d)  +2.1,          e)  +1.6

 

60        The colour of our sun Sol is +0.62 so Sol is brighter in the V band than the B band by a factor of about

            a)  4.17,           b)  1.77,           c)  1.61,           d)  3.14            e)  2.77.

 

61        The colour of Beta Crucis is B-V=-0.23 and is spectral class

            a)  B,               b)  K,               c)  A,               d)  G,               e)  F.

 

62        Deneb has very strong Balmer lines and is rich in lines of ionized metals so is classified

            a)  A,               b)  M,              c)  O,               d)  G,               e)  K

63        10 Lacertae has lines of ionized nitrogen and helium and is spectral class

            a)  A,               b)  M,              c)  O,               d)  G,               e)  K

64        The earth’s orbital speed of 30 km/s results in a maximum spectral shift in the spectrum of a star having d=0° of   Dl/l=

                        a) 3.0·10-4,       b) 1.5·10-9,       c) 1.5·10-1,       d)  1.5·10-4,       e) 3.5·10-4..

 

65        Most nearby stars (<10 pc) appear on the H-R diagram

            a)  along the upper main sequence,      d)  along the subdwarf (sd) sequence,

            b)  on the giant branch,                        e)  uniformly spaced along the main sequence.

            c)  to the right of the "forbidden zone",

 

66        A number of  nearby stars (<10 pc) lie

            a) well above the giant branch,           d) well below the main sequence,

            b) in the instability strip,                     e) along the subdwarf (sd) sequence.

            c) to the left of the instability strip,

 

67        If the nearby stars are a good sample, our sun is

            a) relatively faint,                                d) unique in having a planetary system,

            b) an average star,                               e) relatively old.

            c) relatively massive,

 

68        If you observe the spectrum of an M5 Ib star you can estimate its distance via

            a)  cluster parallax,                             d)  trigonometric parallax,

            b)  dynamic parallax,                          e)  statistical parallax.

            c)  spectroscopic parallax,

 

69        The K line of ionized calcium  lies at 3933.68Å.  If the feature is seen in the spectrum of a star shifted to  3934.07Å,  its radial velocity [km/s] is

            a)  +28,            b)  -30,           c)  +3.8,           d)  -68,           e)  +7 km/s.

 

70        Eclipsing binary stars are particularly useful since they provide stellar

            a) distances,   b) luminosities,   c) parallaxes,   d) rotation rates,   e) radii.

 

Data on five stars:

(Problems 71-78)
 
Star

m

M

A

1.5

5.0

B

8.4

7.7

C

13.9

15.0

D

3.7

3.7

E

16.7

-7.0

Which of the above stars

71        is nearest,

72        is most distant,

73        is 10 pc away,

74        appears brightest,

75        appears faintest,

76        is intrinsically brightest,

77        is intrinsically least luminous,

78        is most like the sun?                                                                                       

 

 

79        The second most common constituent of cosmic rays is

            a)  H I,             b)  H II,           c) deuterium,   d)  tritium,       e) He II

 

80        The tangential velocity [km/s] of a star having proper motion 0.2 arcsec per year (m”=0.2”/yr) and distance 80pc is

            a)  75.8,           b)  142,            c)  7.58,           d)  14.2,           e)  1.42 km/s.

 

81        The tangential velocity [km/s] of a star having proper motion 0.02 arcsec per year (m”=0.02”/yr) and parallax two milliarcsec (p”=0.002”) is about

            a)  5,                b)  50,              c)  500,            d)  5000,          e)  50000 km/s.

 

82        A star has a proper motion of 3 arcsec per year, a parallax of 0.474 arcsec, a tangential velocity of 30 km/s and a radial velocity of 40 km/s.  The space motion [km/s] of the star is

            a)  5,                b)  50,              c)  500,            d)  5000,          e)  50000 km/s.

 

83        The Solar spectrum has many lines of neutral iron and no lines of helium.  Rigel has no neutral iron lines but strong helium lines.  Hence,

            a)  The Sun is a normal star,  Rigel is a supergiant.

            b)  The surface gravity of the Sun is much greater than Rigel’s.

            c)  Rigel has a much higher helium abundance than the Sun.

            d)  Rigel is much hotter than the sun,

            e)  Rigel is a “helium star”.

 

84        The color of a star with B=12.04 and V=10.78 is

            a)  +1.26,         b)  +1.44,        c)  +1.56,         d)  +4.82,        e)  +3.19.

 

85        The spectral class of a star with B=12.04 and V=10.78 is

            a)  G,               b)  B,               c)  A                d)  F,               e)  K.

 

86        The coolest of the following spectral classes is

            a)  G,               b)  B,               c)  A                d)  F,               e)  K.

 

87        The hottest of the following spectral classes is

            a)  G,               b)  B,               c)  A                d)  F,               e)  K.

 

88        The most likely spectral class of a star picked at random in any given volume of space is

            a)  G,               b)  B,               c)  A                d)  F,               e)  K.

89        Our closest neighbour Proxima Centauri is closest to spectral class

            a)  G,               b)  B,               c)  A                d)  F,               e)  K.

90        Tonight at 8PM you can “see” Proxima Centauri (with a telescope)

            a)  rising in the east.                            d)  in the southwest.

            b)  setting in the west.                         e)  well up in the southeast.

            c)  near the meridian.

91        Tonight at 8PM you can see Canopus

            a)  rising in the east.                            d)  in the southwest.

            b)  setting in the west.                         e)  well up in the southeast.

            c)  near the meridian.

 

92        Tonight at 8PM you can see Vega, Altair and Grus

            a)  rising in the east.                            d)  in the southwest.

            b)  setting in the west.                         e)  well up in the southeast.

            c)  near the meridian.

 

 

Binary star class

a

visual

Which of the five classes of binary stars in the table
 
b

spectroscopic

c

spectrum

d

eclipsing

e

dynamical

93        now applies to Sirius,

94        originally applied to Sirius (technically still does),

95        gives stellar radii as well as masses,

96        requires a knowledge of distance (parallax) to give mass,

97        yields mass/sin3i,

98        applies to Algol (b Per),

99        usually has the shortest period,

100      usually has the longest period?

101      requires a knowledge of distance (parallax) to give mass,

==============================================

102      A G0 I star should have an absolute V magnitude of -4.4, a color index B-V=+0.75 and an effective temperature of 4700 K.  If a G0 I star is observed to have B=+24.5 and V=+23.5, the unreddened V magnitude is most likely to be

            a)  +24.5,         b)  +23.5,        c)  +26.5,         d)  +20.5,        e)  +22.7

103      A G0 I star should have an absolute V magnitude of -4.4, a color index B-V=+0.75 and an effective temperature of 4700 K.  If a G0 I star is observed to have B=+26.5 and V=+26.5, the distance [Mpc] is

            a)  0.15,           b)  0.01,           c)  7.50,           d)  3.14,           E)  1.50 Mpc.

104      The release of energy inside the sun is accompanied by

            a)  increase of mass of the sun,

            b)  conversion of H to C with no change of mass of the sun,

            c)  neutrino emission and decrease of mass of the sun,

            d)  decrease of the radius of the sun,

            e)  conversion of H to molecular H2 with decrease of mass of the sun.

105.     Most of the solar neutrinos produced in the sun cannot be detected by Davis's experiment because most of the neutrinos

            a)  exit along the solar rotation axis and so miss the earth,

            b)  are too energetic to be captured,

            c)  have too little energy to be captured,

            d)  are stopped by the kilometre of shielding around the detector,

            e)  are absorbed by the solar envelope.

 

            Which of the following orbital elements,

                        a)  a,     b)  e,     c)  i,     d)  W,      e)  w,

            is, or refers to

106      the vernal equinox,

107      the size of an orbit,

108      the shape of an orbit,

109      an angle in the plane of the bodies orbit,

110      half the distance between the two points of the orbit nearest the foci.

===============================

111      The apparent angular size of the sun is

                        a)  23½°,       b)  23½°,       c)  ½°,       d)  1½°,       e)  6½°.

112      The apparent angular diameter of Venus changes through the year by a factor of

                        a)  22,       b)  16,       c)  6,       d)  3¼,       e)  12.

 

Which of the following gases

                        a)  hydrogen,  b)  helium,  c)  nitrogen,  d)  carbon dioxide,  e)  methane,

113      is most abundant in the atmosphere of Uranus,

114      is most abundant in the atmosphere of Venus,

115      is most abundant in the earth’s atmosphere,

116      is most abundant in the atmosphere of Titan,

117      is most abundant in the “atmospheres” of the Moon and Mercury.

==================================

118      The most widely believed current theory of the formation of the Moon involves

            a)  fission of a larger body,

            b)  capture of a body formed elsewhere in the solar system,

            c)  the impact of a Mars sized body with the Earth,

            d)  capture of a body in retrograde orbit then tidal change of orbit inclination,

            e)  co-formation in the primordial nebula with preformation fractionation.

119      Saturn’s heat source is probably

                        a)  precipitation of helium,                  d)  radioactive decay,

                        b)  freezing of hydrogen,                     e)  gravitational contraction.

                        c)  gravitational collapse,

120      The name of the third Galilean satellite is

                        a)  Amalthea      b) Janus,      c) Callisto,     d) Leda,     e) Ganymede.

121      During most of the time a star is burning hydrogen its position on the H-R diagram is

            a)  a bit above the ZAMS,

            b)  just below and to the right of the ZAMS,

            c)  right on the ZAMS,

            d)  approaching the ZAMS from below the ZAMS,

            e)  approaching the ZAMS from above and to the right of the ZAMS.

122      As a star turns into a red giant the outer layers expand and cool while the core

            a)  contracts and cools,                       d)  expands and cools,

            b)  contracts and heats,                        e)  expands and heats.

            c)  remains relatively inert,

123      W Virginis stars

            a)  convert H to Li via the PPI chain,

            b)  eject mass at a considerable rate,

            c)  are spectroscopic binary stars with small orbital inclination,

            d)  are spectral class M,

            e)  vary in brightness.

124      The triple alpha (3a) process

            a)  is thought to be responsible for the missing neutrinos,

            b)  is similar to the "atomic bomb",

            c)  involves an unstable isotope of Be (beryllium-8),

            d)  unites three He nuclei to form nitrogen,

            e)  is the major source of energy for stars of mass greater than two solar masses.

125      A Strömgren sphere is

            a)  an ionized region emitting strong 21-cm radiation,

            b)  a huge bubble of highly ionized gas outside the plane of the galaxy,

            c)  an H I region,

            d)  an H II region,

            e)  a planetary nebula.

126      A spectrum binary

            a)  gives a lower limit to the combined masses of the system,

            b)  gives an upper limit to the combined masses of the system,

            c)  involves a system with very small separation between stars,

            d)  has both sharp and diffuse spectral lines,

            e)  has an unusual spectrum..

127      The Russell-Vogt theorem states that

            a)  the lifetime of a cluster depends on its size and total mass,

            b)  mass and chemical composition determine the structure of a star,

            c)  half the energy of a star is radiated, half retained,

            d)  stars to the right of the forbidden zone must collapse,

            e)  the luminosity of a star depends on radius (R2) and temperature (T4).

128      Interstellar reddening

            a)  shifts the energy peak of stars and galaxies to the red,

            b)  is due to strong infrared absorption,

            c)  shifts spectral lines to longer wavelengths,

            d)  is "grey", i.e., essentially wavelength dependent,

            e)  is an absorption that is proportional to 1/wavelength to the fourth power.

129      Mira variables

            a)  are eclipsing binary stars,

            b)  are rapid pulsating Cepheid variables,

            c)  are flare stars,

            d)  lie in the instability strip,

            e)  are red-giant long-period variable stars.

130      High velocity stars

            a)  have high velocities about the galactic centre,

            b)  are population II,

            c)  are ejected from star forming regions

            d)  are associated with pulsars,

            d)  are associated with supernovae.

131      The horizontal branch is

            a)  prominent in the HR diagram of a globular cluster,

            b)  often called the "Hertzsprung gap",

            c)  a line in the HR diagram on which all stars must pulsate,

            d)  a star bridge between the Orion and Perseus arms,

            e)  the bar of stars in SB galaxies.

132      The Hayashi line is

            a)  an evolutionary track on the HR diagram of a fully convective star,

            b)  the boundary between convective and radiative zones in a star,

            c)  also known as the ZAMS,

            d)  the ionized helium equivalent of the 21cm "spin flip" line,

            e)  a strong absorption in the interstellar medium thought to be due to graphite.

133      Bok globules are

            a)  reflection nebulae,                         d)  dark nebulae,

            b)  planetary nebulae,                          e)  emission nebulae.

            c)  bright nebulae,

134      The Fraunhofer spectrum is

            a)  the spectrum of an early F star,      d)  the solar spectrum,

            b)  emission spectrum,                        e)  the solar chromosphere.

            c)  the spectrum of the element Fr,

135      Forbidden lines

            a)  are associated with phosphorescence,

            b)  are never observed outside the laboratory,

            c)  are due to electric dipole transitions,

            d)  are seen in neon signs,

            e)  are never seen in emission.

136      Cluster variables

            a)  are found in OB associations and galactic clusters,

            b)  are found in T associations,

            c)  are groups or clusters of variable stars,

            d)  are found in globular clusters,

            e)  have multiple periods that "beat".

137      Circumstellar dust is

            a)  solid grains surrounding a star,

            b)  the column of dust between us and a star,

            c)  a dense region of debris blown off a highly evolved star,

            d)  a blanket around a star blocking all radiation,

            e)  now thought to be large complex organic molecules.

138      Balmer lines are

            a)  absorption lines from the first excited state to the continuum,

            b)  resonance lines in the hydrogen spectrum,

            c)  a series of emission or absorption lines involving the first excited level of H,

            d)  for example the n=3 to n=4,5,6,... transitions in H,

            e)  forbidden lines in the H spectrum.

139      Wolf-Rayet stars

            a)  are cool giant stars that occasionally "soot-over",

            b)  are extreme population II,

            c)  are shell stars, often with a strong N spectrum,

            d)  are stars that have just arrived on the ZAMS,

            e)  cannot exist in regions of dense gas and dust.

140      Oort's constants refer to

            a)  galactic rotation,                            d)  the galactic distance scale,

            b)  interstellar reddening,                    e)  stellar evolutionary models.

            c)  spectral line intensity ratios,

Which of the following variable star classes

                        a)  Mira,

                        b)  Classical Cepheid,

                        c)  Cluster,

                        d)  W Virginis,

                        e)  Algol,

141      is brightest in absolute terms,

142      is the most useful large distance indicator,

143      is the most useful globular cluster distance indicator,

144      is the most useful mass indicator,

145      have periods on order of 0.5-1.0 days?

=====================================

Which of the following spectral classes

a)  A

b)  B

c)  G

d)  K

e)  O

146      will apply to the sun 2,000,000,000 years hence

147      would the sun have been 3,000,000,000 years ago

148      has MB=MV,

=====================================

            Which of the following Martian features

                        a)  Olympus,                d)  Marineris,

                        b)  Arisis,                    e)  Syrtis Major,

                        c)  Chryse

149      is one of the largest shield volcanoes in the solar system,

150      is a large (possibly rift) valley.

Part B

Answer any three of the following four questions.

Question 1.

An electron of momentum p is at a distance r from a stationary proton.  The system has a kinetic energy K= p2 /2me and potential energy U = -ke2 /r.  Its total energy is E = K + U.  If the electron is bound to the proton to form a hydrogen atom, its average position is at the proton but the uncertainty in its position is approximately equal to the radius r of its orbit.  The electron’s average momentum will be zero, but the uncertainty in its momentum will be given by the uncertainty principle.  Treat the atom as a one-dimensional system in the following:

(a)  Estimate the uncertainly in the electron’s momentum in terms of r.                       (6 marks)

(b)  Estimate the electron’s kinetic, potential, and total energies in terms of r            (6 marks)

(c)  The actual value of r is the one that minimizes the total energy, resulting in a stable atom.  Find the value of r and the resulting total energy.  Compare your answer with the predictions of the Bohr theory.                                                                                         (8 marks)

 

Question 2.

A particle is confined between rigid walls separated by a distance L = 0.189 nm.  The particle is in the second excited state (n = 3).  Evaluate the probability to find the particle in an interval of width 1 pm (10-12m) located at:

(a)       x = 0.188 nm;                                                                                      (5 marks)

(b)       x = 0.031 nm;                                                                                      (5 marks)

(c)       x = 0.079 m.                                                                                        (5 marks)

What would be the corresponding results for a classical particle?                 (5 marks)

(Hint: You do not need to perform integration to solve this problem)

 

Question 3.

Consider the normal Zeeman effect applied to the 3d to 2p transition.

(a)             Sketch an energy-level diagram that shows the splitting of the 3d and 2p levels in an external magnetic field.  Indicate all possible transitions from each m1 state of the 3d level to each m1 state of the 2p level.

(b)            Which transitions satisfy the  or 0 selection rule?

(c)             Show that there are only three different transition energies emitted.

 

Question 4.

Calculate the degree of ionization when I = 10V  (somewhere between metals and non-metals) at T=10,000K when the electron density is 1023 m-3 (a situation in a high current arc).  Compare that with the population of excited level in an atom.