Finding the Mass of the Sun
Solving for the Mass of the Sun
Because the gravitational attraction of our Sun for the Earth is the centripetal force causing the Earth's circular motion around the Sun, we can use Netwon's law of universal gravitation to find the mass of the Sun without ever actually visiting the Sun. This is the same technique you would use to determine the mass of Cygnus X-1 with a probe. The Earth, orbiting the Sun, plays the same role as the probe sent to orbit Cygnus X-1.
From this, it follows that:
Because 'm' can be eliminated from both sides of the equation, and because 'd', the distance from the Earth to the Sun is also 'r', the orbital radius of Earth around the Sun, the equation can be rearranged to solve for the mass of the Sun:
To actually compute the mass of the Sun, we need to know how far the Earth is from the Sun and how fast it is moving around the Sun.