 Now, given the mass of a star, we know how long it will burn the core hydrogen it started with. For the Sun, that's around 10 billion years. But how long the fuel will last from now depends on how long ago it started fusing. Let's take a look at one way we know how far long a star is. In a star cluster, like M67, for example, if we can find a star that is just starting to show the symptoms of having run out of its core hydrogen, we'll know from its mass just how old it is. That will then be the age of all 1100 plus stars in the cluster, because they all formed at the same time. We need to understand what observable effects we can use when a star's fuel runs out. One is, because core temperatures are not high enough to fuse helium, once the hydrogen is used up, fusion in the core ceases. Without fusion, there is no nuclear energy source to supply heat to the central region of the star. The long period of hydrostatic equilibrium ends. Gravity again takes over, and the core begins to contract. As the star's core shrinks, the energy of the inward-falling material is converted to heat. The heat flows outward to cooler regions. The added heat raises the temperature of the layer of hydrogen just outside the core. Once this shell becomes hot enough, hydrogen fusion begins there. The helium core continues to contract, producing more heat all around it. This leads to more fusion in additional shells of fresh hydrogen outside the core. The additional fusion produces still more energy, which also flows out into the upper layers of the star. The first observable result is an increase in the star's luminosity. With all the new energy pouring outward, the outer layers of the star begin to expand. The star eventually grows and grows until it reaches enormous proportions. The expansion of a star's outer layers causes the temperature at the surface to cool. Here we have the second major observable result. The star's surface temperature decreases. The star becomes simultaneously more luminous and cooler. On the HR diagram we see that the star leaves the main sequence and moves upward because it's brighter, and to the right because it's cooler. Detecting this is then a matter of finding stars in a cluster leaving the main sequence. Here's a map of M67 stars to the HR diagram. You can see where the stars are currently moving off the main line. This is called the turnoff point. There are no longer any stars in the cluster higher on the main line. The turnoff point gives us the luminosity of the stars moving off the main sequence. The mass-luminosity relationship gives us the mass, and with the mass we can calculate the age. For M67 we find that it's around 4 billion years old. We then know the age of all the stars in the cluster. But this does not work for field stars like our sun. Research into rotation rates in sunspots as age predictors called gyrochronology is ongoing. But at this time we have no way to figure out the age of field stars by examination. If we're going to figure out the age of the sun, we'll have to examine the material it formed around the sun. The comets, asteroids, moons, planets, and especially the Earth.