Solar Mass

Nobody weighs the Sun directly. What we measure superbly well is GM⊙, the product that actually appears in the orbit equations, known to about ten significant figures from decades of planetary radar and spacecraft tracking. Dividing by the Newtonian constant of gravitation to get a mass in kilograms throws almost all of that precision away, because G is the worst-measured of the fundamental constants at roughly 22 parts per million. The uncertainty quoted here is entirely G's; the Sun's mass is not the vague part.

This is why professional dynamics is done in GM and why the IAU now recommends quoting stellar masses as ratios to a nominal solar mass parameter rather than in kilograms. The Sun is also losing mass — about 4.3 million tonnes a second to radiation, plus the solar wind — but that is only a part in 10¹³ per year, far below the measurement floor.