Hi Julia,

Since we can't measure the core temperature directly we need to calculate it from other things we know. We can figure out how much mass there is in the Sun (from the orbits of the planets). We can also figure out how much volume the Sun has (by geometry and measuring the diameter of the Sun). We know that because of gravity a certain mass should contract to be a certain size. This size for the Sun's mass is smaller than the Sun really is. The difference in size is due to energy pushing the Sun's gas particles apart and making it bigger. Then we relate that amount of energy to a gas temperature.

Best,

Christina