PHYS 101, Spring 2009
HW 2 Solutions
Chapter 6
3) Sunspots are darker because they are cooler than the surrounding material, by
up to 1500 K (see page 142). From Chapter 4, cooler material radiates less energy,
and thus the sunspots look darker than the surrounding photosphere. If they
could be seen on their own, they would actually be quite bright.
14) From Section 6.3.2, the material ejected in flares moves at speeds of 500 – 1000
km/s. The distance of the Earth from the Sun (Table 6.1 or Appendix 6) is 1.5x108
km. The time taken equals the distance divided by the velocity (yellow box
before problem). So the time taken will range from (1.5x108 km)/(1000 km/s) =
1.5x105 seconds, to (1.5x108 km)/(500 km/s) = 3x105 seconds. Converting to a
more useful unit of time (days) gives a range from 1.7 to 3.5 days.
17) If the velocities differ by 4 km/s, one edge must be coming towards us at 2
km/s, while the other is receding at 2 km/s. The circumference of the sun is π
times its diameter, which is 1.39x106 km (Table 6.1 or Appendix 6). So the
circumference of the Sun is (3.14)x(1.39x106) = 4.37x106 km. To move 4.37x106 km
at a speed of 2 km/s takes a time of (4.37x106 km)/(2 km/s) = 2.19x106 seconds,
or 25.4 days. This agrees well with the 25 day period quoted on page 143.
Chapter 7
12) Any transformation from a lighter element to a heavier element will be
fusion; any transformation from a heavier element to a lighter element will be
fission. See Appendix 13 for a list of the elements.
a) Fusion
b) Fusion
c) Fission
d) Fusion
e) Fusion
22) The Sun’s energy comes from its central regions because that is the only
region hot enough for the fusion of hydrogen to helium to occur. From Figure
7.12, all of the Sun’s luminosity is generated within 20% of the center. The
original hydrogen is also partially depleted within 20% of the center. These two
things are correlated because it is the depletion of the original hydrogen (by
fusing it into helium) that is generating the Sun’s luminosity.
28) The mass of the Sun is 1.99x1030 kg (Table 6.1 or Appendix 6), so 1% of this
mass is 1.99x1028 kg. Every second the Sun converts 4x106 tons of matter to energy
(given in problem), this equals 3.64x109 kg (multiplying by the conversion factor
of 909 given in class). So to lose 1% of its mass, it will take the Sun a time equal to
(1.99x1028 kg)/(3.64x109 kg/s) = 5.47x1018 s. Converting this to years gives
1.74x1011 years, or 174 billion years. The estimated age of the Sun so far is
roughly 5 billion years, so the Sun has not been in existence nearly long enough
to lose even 1% of its mass.