
Solving for the Mass of the Sun
Credit: NASA
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 X1 with a probe. The Earth,
orbiting the Sun, plays the same role as the probe sent to orbit Cygnus
X1.
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.

 The value for G, the universal
constant of gravitation, is 6.67 x 10^{11} N m^{2}
kg^{ 2} (where N is Newtons).
 The distance separating the Earth and the Sun (the orbital radius of
the Earth around the Sun), r, is 1.5 x 10^{8} km.
 The Earth's velocity around the Sun is just the total distance
travelled divided by the time required for the Earth to make one complete
orbit around the Sun, T:

You need to be sure your distance measurement is in meters and your time
measurement is in seconds in order for the units to cancel correctly.
