Hello Justin,

We can tell the mass of the Sun by observing the orbits of the planets around it and using Newton's law of gravitation. Kepler's law states that the period of a planet's orbit is proportional to the distance to the sun to the power (3/2). This means that if you where four times further away from the Sun than the Earth, the planet would take 8 times longer to orbit the Sun (i.e. 8 years). Kepler's law is a proportional relationship that was turned into "real physics" by Isacc Newton who showed that the orbital period and distance relation was related directly to the mass of the Sun (the mass of any of the planets even Jupiter is so much smaller than the Sun that they have little effect on the relationship). Once the precise distance of the Earth form the Sun was determined Newton's Law can use the orbital period to measure the mass of the Sun.

Cheers - David