The Sun is a Main Sequence star and therefore derives its energy from the fusion of Hydrogen nuclei into Helium. This process, known as the p-p cycle, starts with four Hydrogen nuclei and produces one Helium nucleus, and energetic positrons, neutrinos, and gamma rays.

Four Hydrogen nuclei have a combined mass of
M_{4H}=6.693X10^{-27} kg,
and one Helium nucleus has a mass of
M_{He}=6.645X10^{-27} kg.
The difference in the initial and final total mass in each fusion process,
M = M_{4H} - M_{He} = 0.048X10^{-27}
kg, is converted into energy (and the Sun "loses" this mass). This is the
famous , where *m* in this
case is the difference in the masses M and *c* is the speed of light.
The amount of energy released every time
this takes place is Mc^{2}=4.3X10^{-12} Joules.

**Star bright: Powering the Sun**

The Sun's total luminosity, 4X10^{26} Watts (or Joules/second)^{1}, is ultimately derived from the energy released by many fusion
reactions each second.

**1.** How many fusion reactions per second are required to sustain the Sun's luminosity of 4X10^{26} Watts?

Your answer should be roughly
100,000,000,000,000,000,000,000,000,000,000,000,000 (10^{38})!!

**2.** The Sun is losing mass each time a fusion reaction occurs.
What is the rate at which the Sun's mass is decreasing
(in kilograms per second)?

Your answer should be about
several billion (10^{9}) kg / s. Since
one ton is 10^{3} kg, express this in millions (10^{6}) of tons per
second. If one car weighs about 2 tons, how many millions of cars per second is this?

**3.** How many years does it take for the Sun to lose the equivalent
of the Earth's mass, M =6X10^{24} kg? Express this number in
years (there are approximately 3X10^{7} seconds in a year).

**That's a mighty long time: Lifetime of the Sun**

**1.** Here are pretty good assumptions about the Sun:

- The Sun was initially composed only of pure Hydrogen;
- The Sun's luminosity does not change over time;
- The Sun will use about 10% of its initial mass in fusion reactions
^{2}; - . The Sun's total mass is approximately 2X10
^{30}kg, which hasn't changed much since the Sun formed.

**2.** We can't directly measure the age of the Sun. However, the oldest rocks
found on the surfaces of the Earth and
the Moon are about 4.5X10^{9} years old. What does this tell us about
the current age of the Sun? How much longer will the Sun remain on the Main Sequence?

**3.** Look at Table 1. The Sun is a G2 star. You might expect that stars
more massive than the Sun will live
longer than the Sun because the massive stars have more fuel available to
burn: for example, a 15 M_{} star should last 15 times longer
than the Sun, or 150X10^{9} years. But according to this table
a 15 M_{} star lasts a mere 11X10^{6} years. Why?

**4.** The age of the Universe is believed to be close to 14X10^{9} years. Which classes of stars have never left the Main Sequence? Explain.

Wed Feb 20 14:20:07 PST 2002